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Effect of integrating children’s literature and SQRQCQ problem solving learning on elementary school student’s mathematical reading comprehension skillTita Mulyati, Wahyudin, Tatang Herman & Tatang Mulyana
pp. 217232  Article Number: iejme.2017.008
Abstract The aim of this research was to examine the effect of learning application of SQRQCQ problem solving with children’s literature toward the reading comprehension skills of elementary school students. This research involved 105 fifth grade students in three intact classes in Bandung. The quasiexperimental research with control class without pretest was done, but previously prior math knowledge test was conducted to find out the equality of each class ability and grouping them into high, medium, and low. The research data was obtained from test on the prior knowledge in math and written posttest based on two mathematical texts, and each text contain four questions. Data were analyzed using oneway ANOVA and twoway ANOVA. The results from the research show that 1) the learning of SQRQCQ problem solving with children’s literature leads to higher effect on the achievement of mathematical reading comprehension skill if compared to both student groups getting other learning, 2) students with high prior math knowledge has higher mathematical reading comprehension skill if compared to two other level of prior knowledge, and 3) there is no interaction effects between the learning done and prior knowledge on the mathematical reading comprehension skill. The research recommended that SQRQCQ problem solving learning with children’s literature can be used on mathematics learning in elementary school in order to supporting mathematical reading comprehension skill. Keywords: mathematical reading comprehension, SQRQCQ problem solving learning, children’s literature References Abidin, Y., Mulyati, T., dan Yunansah, H. (2015). Pembelajaran literasi dalam konteks pendidikan multiliterasi, integratif, dan berdiferensiasi. Bandung: Rizqi Press. Badan Standardisasi Nasional Pendidikan (BSNP) (2006). Pedoman penyusunan kurikulum tingkat satuan pendidikan. Jakarta: Depdiknas. Bakeman, R. (2005). Recommended efect size statistics for repeated measures designs. Behaviour Research Methods, 37 (3), 379384. Barone, D. M. (2011). Children's literature in the classroom: Engaging lifelong readers. New York, NY: Guilford Press. Basol, B., Ozel, S., dan Ozel, Z.E.Y. (2011). “The relationship between reading comprehension competence and word problem comprehension among thirdgrade students”. Journal of European Education, Volume 1 Issue 1 2011. Campbell, L. dan Campbell, B. (2009). Mindful learning: 101 proven strategies for student and teacher success. CA: Corwin Press. Covey. S.R. (2008). Seven Habits Of Highly Effective People. Ringkasan Padat diolah oleh Sumargi Raharjo. Cetak pdf oleh MGI /PersonalEnhanced Public Project. Funke, J. (2013). “Human problem solving in 2012”. Journal of Problem Solving, Volume 6, Issue 1, pages 219. Hite, S. (2009). Improving problem solving by improving reading skills. Tesis pada Universitas NebraskaLincoln. Imam, O.A., AbasMastura, M, Jamil, H. (2013). “Correlation between reading comprehension skills and students’ performance in mathematics”. International Journal of Evaluation and Research in Education (IJERE) Vol.2, No.1, March 2013, pp. 1~8 ISSN: 22528822. Ismaimuza, D. (2011). “Kemampuan berpikir kritis matematis ditinjau dari pengetahuan awal siswa”. Jurnal Pendidikan Matematika, Volume 2 Nomor 1, Januari 2011. Kenney, J.M. (2005). Literacy strategies for improving mathematics instruction. USA: ASCD. Lally, P., van Jaarsveld, C.H.M., Potts, H.W.W., dan Wardle, J. (2010). “How are habits formed: Modelling habit formation in the real world”. European Journal of Social Psychology,vol. 40, issue 6, pages 998–1009. Lester, J.H. dan Head, M.H. (1999). Literacy and learning: reading in the content areas. Louisiana: Louisiana Public Broadcasting. Lie, A. (2002). Cooperative learning: Mempraktikkan cooperative learning di ruangruang kelas. Jakarta: PT Grasindo. Morocco, C.C., Aguilar, C.M., dan Bershad, C.J. (2008). Supported literacy for adolescents: Transforming teaching and content learning for the twentyﬁrst century. CA: JosseyBass. Murray, J. (2013). “The Factors that Influence Mathematics Achievement at the Berbice Campus”. International Journal of Business and Social Science, Vol. 4 No. 10 [Special Issue –August 2013]. Orhun, N. (2003). Effects of Some Properties 5. Grade Students on the Performance of Mathematical Problem Solving. The Mathematics Education into the 21st Century Project Proceedings of the international Conference The Decidable and the Undecidable in Mathematics Education Brno, Czech Republic, September 2003. Ozsoy, G., Kuruyer, H.G., dan Cakiroglu, A. (2015). “Evaluation of student’s mathematical problem solving skills ini relation to their reading level”. International Electronic Journal of Elementary Education, 8(1), 113132. Pearce, D.L., Bruun, F., Skinner, K., dan LopezMohler, C. (2013). “What teachers say about student difficulties solving mathematical word problems in grades 25”. International Electronic Journal of Mathematics Education, Vol.8, No.1. Phonapichat, P., Wongwanich, S., dan Sujiva, S. (2014). “An analysis of elementary school students’ difficulties in mathematical problem solving”. ProcediaSocial and Behavioral Sciences, 116(2014), 31693174. Raduan, I.H. (2010). “Error analysis and the corresponding cognitive activities committed by year five primary students in solving mathematical word problems”. Procedia Social and Behavioral Sciences 2 (2010) 3836–3838. Roschelle, J. (1995). Learning in Interactive Environments: Prior Knowledge and New Experience. (Online). Tersedia: http://www.exploratorium.edu/ifiarchive/resources/museumeducation/ priorknowledge.html. (10 Juli 2016). Rose, K. (2011). The effect of SQRQCQ on fourth graders’ math word problem performance. Tesis pada Bowling Green State University. Sawyer, W.E. (2012). Growing up with literature. Edisi keenam. USA: Wadsworth. Simanjuntak, L., dkk. (1992). Metode mengajar matematika I. Jakarta: Rineka Cipta. Tankersley, K. (2005). Literacy strategies for grades 412: Reinforcing the threads of reading. USA: ASCD. TeacherVision (tt). Mindful Learning: 101 Proven Strategies for Student and Teacher Success. (Online). Tersedia: https://www.teachervision.com. (17 Juli 2016) Torner, Schoenfeld, & Reiss (2007). “Problem solving in the mathematics classroom: the German perspective”. ZDM Mathematics Education, (2007) 39:431–441. DOI 10.1007/s1185800700405. VileniusTuohimma, P.M., Aunola, K., dan Nurmi, J. (2008). “The association between mathematical word problems and reading comprehension”. Educational Psychology, Vol. 28, No. 4, July 2008, 409–426. Wahyudin (2008). Pembelajaran dan modelmodel pembelajaran. Jakarta: CV. IPA Abong. Wood, W. dan Neal, D.T. (2007). “A new look at habits and the habitgoal interface”. Psychological Review, vol. 114, no. 4, 843– 863. 
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2 
Development Comic Based Problem Solving in GeometryPardimin & Sri Adi Widodo
pp. 233241  Article Number: iejme.2017.009
Abstract Learning devices are tools or equipment to carry out the process that will enable educators and learners perform the learning activities. Learning media is one of the learning tools that support the success of the learning process. This article discusses the development of instructional media for students of classes VII comics on rectangular material. This comic instructional media 4D method that is designed to define, design, development, and dissemination. In the first phase done to establish and define the terms of development, the second phase of the comic instructional media designed to obtain a prototype or product design and development phase is done with the media to determine the feasibility prototype, and prototype revision in order to obtain a hypothetical media. The results of the assessment sheet obtained that the feasibility media validator obtained an average score of 3.93 with very good. The process of developing a comic on the subject of geometry only through 3 phases: define, by analyzing the curriculum, and to formulate basic competencies and indicators of achievement of learning outcomes, the design phase is done by creating a comic prototypebased troubleshooting with a black and white design, develop. Keywords: Problem Solving; Comic; Geometry References Jurnal Edukasi @Elektro, 5(1), 11 – 18. Bulut, M., Akçakın, H.U., Kaya, G & Akçakın, V. (2016). The Effects of GeoGebra On Third Grade Primary Students’ Academic Achievement in Fractions. International Electronic Journal of Mathematics Education (IEJME), 11(2), 347 – 355. Effendi, L.A. (2012). Pembelajaran Matematika Dengan Metode Penemuan Terbimbing Untuk Meningkatkan Kemampuan Representasi Dan Pemecahan Masalah Matematis Siswa SMP. Jurnal Penelitian Pendidikan, 13(2), 1 – 10. Ismail, A.K., Sugiman & Hendikawati, P. (2013). Efektivitas Model Pembelajaran Teams Group Tournament Dengan Menggunakan Media “3 in 1” Dalam Pembelajaran Matematika. Unnes Journal of Mathematics Education, 2(2), 25 – 32. Maula, N., Rohmad & Soedjoko, E. (2013). Keefektifan Pembelajaran Model TAPPS Berbantuan Worksheet Terhadap Kemampuan Memecahkan Masalah Materi Lingkaran. Unnes Journal of Mathematics Education (UJME), 2(1), 19 – 27. Nugroho, A.A. (2011). Pengembangan Perangkat Pembelajaran Matematika Berbasis SMART Dengan Strategi TAI Pada Materi segitiga Kelas VII. Jurnal Aksioma, 2(2). Pardimin & Widodo, S.A. (2016). Increasing Skills of Student in Junior High School to Problem Solving in Geometry with Guided. Journal of Education and Learning, 10(4), 390395. Permendikbud No. 65 Tahun 2013 tentang Standar Proses Pendidikan Dasar dan Menengah Prasetyo, Z. K, et al. (2011). Pengembangan Perangkat Pembelajaran Sains Terpadu Untuk Meningkatkan Kognitif, Keterampilan Proses, Kreativitas serta Menerapkan Konsep Ilmiah Peserta Didik SMP. Postgraduate program UNY. Sholihah, W., Susanto, & Sugiarti, T. (2014). Pengembangan Bahan Ajar (Buku Siswa) Matematika Untuk Siswa Tunarungu Berdasarkan Standar Isi Dan Karakteristik Siswa Tunarungu Pada Sub Pokok Bahasan Menentukan Hubungan Dua Garis, Besar Sudut, Dan Jenis Sudut Kelas Vii Smplb/B Taman Pendidikan Dan Asuhan (TPA) Jember Tahun Ajaran 2012/2013. Jurnal Pancaran, 4(1), 219 – 228. Sugiyono. (2009). Metode Penelitian Pendidikan: Pendakatan Kualitatif, Kuantitatif, dan R&D. Bandung: Alfabeta. Sukmadinata, N. S. (2005). Metode Penelitian Pendidikan. Jakarta: PPS UI dan Remaja Rosdakarya. Supriyono, Setiawan, T. B., & Trapsilasiwi, D. (2014). Pengembangan Perangkat Pembelajaran Matematika Model Student Facilitator And Explaining Setting Contextual Teaching And Learning (CTL) Pada Sub Pokok Bahasan Prisma dan Limas Kelas VIII Semester Genap. Jurnal Pancaran, 3(2), 5362. Thiangarajan S., Semmel D., & Semmel M. I. (1974). Instructional Development For Training Teachers Of Exceptional Children: A Sourcebook. Minneapolis: Central for Innovation on Teaching the Handicapped. Wahyudi, B.S., Hariyadi, S., & Hariani, A.S,. (2014). Pengembangan Bahan Ajar Berbasis Model Problem Based Learning Pada Pokok Bahasan Pencemaran Lingkungan Untuk Meningkatkan Hasil Belajar Siswa Kelas X SMA Negeri Grujugan Bondowoso. Jurnal Pancaran, 3(3), 83 – 92. Wibowo, E.J. (2013). Media Pembelajaran Interaktif Matematika Untuk Siswa Sekolah Dasar Kelas IV. Seruni: Seminar Riset Unggulan Nasional Informatika dan Komputer. 75 – 78. Widodo, S. A. (2010). Permasalahan Pengajaran Matematika Di Sekolah Menengah Ditinjau Dari Teori Perkembangan. Majalah Ilmiah Wacana Akademika, 3(8). Widodo, S. A. (2017). Development of Teaching Materials Algebraic Equation To Improve Problem Solving. Infinity, 6 (1), 6170 Widodo, S.A & Sujadi, A.A. (2015). Analisis Kesalahan Mahasiswa Dalam Memecahkan Masalah Trigonometri. Jurnal Sosiohumaniora, 1(1), 51 – 63. Widodo, S.A. (2012). Proses Berpikir Mahasiswa Dalam Menyelesaikan Masalah Matematika Berdasarkan Tipe Kepribadian Idealist. Laporan Penelitian. Yogyakarta: UST Widodo, S.A. (2013). Analisis Kesalahan Dalam Pemecahan Masalah Divergensi Tipe Membuktikan Pada Mahasiswa Matematika. Jurnal Pendidikan Dan Pengajaran, 46(2), 106 – 113. Widodo, S.A. (2014). Kesalahan dalam Pemecahan Masalah Divergensi pada Mahasiswa Matematika. Jurnal Admathedu, 4(1). Widodo, S.A. (2015). Keefektivan Team Accelerated Instruction Terhadap Kemampuan Pemecahan Masalah dan Prestasi Belajar Matematika Siswa Kelas VIII. Jurnal Kreano: Jurnal Matematika Kreatif Dan Inovatif, 6(2), 127 – 134. Yuniati, N., Bambang E.P, Gesang K.N. (2011). Pembuatan Media Pembelajaran Interaktif Ilmu Pengetahuan Alam Pada Sekolah Dasar Negeri Kroyo 1 Sragen. Journal Speed: Sentra Penelitian Engineering dan Edukasi, 3(4), 2529. Yusnita, E. 2011. Pembelajaran Kontekstual berlatar pondok pesantren pada materi garis dan sudut di kelas VII MTS. Prosiding Seminar Nasional Matematika Dan Pendidikan Matematika UNY. PM 11 – PM 18. 
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3 
Factors Affecting the Development of Mathematical Knowledge for Teaching and Mathematical Beliefs of Prospective Primary TeachersIfada Novikasari
pp. 243264  Article Number: iejme.2017.010
Abstract This study aimed to obtain a description of the factors that influenced the knowledge development of teaching mathematics and mathematical beliefs owned by the students of prospective primary school teacher. The subjects of this study were 69 students of prospective primary school teacher in the second year that joined with the course of mathematics learning. The method used was quantitative descriptive method in which data collection techniques used tests, questionnaires and interviews. The results showed that the students of prospective primary school teacher had several factors that affected the test results of the mathematical knowledge for teaching and mathematical beliefs they had. The type of the highest mathematical beliefs, i.e. constructivist, began to emerge in two prospective primary school teachers who had the test results of the knowledge of teaching mathematics in the high category, with an educational background of vocational school and high school in social studies field. Keywords: factors, mathematical knowledge for teaching, mathematical beliefs, prospective primary teachers References Ambrose, R. (2004). Initiating Change in Prospective Primary School Teachers’ Orientations to Mathematics Teaching by Building on Beliefs. Journal of Mathematics Teacher Education, 7, pp.91–119. Arikunto, S. (2005). DasarDasarEvaluasiPendidikan. Jakarta: Bumi Aksara. Ball, D. (1990). The Mathematical Understandings that Prospective Teachers bring to Teacher Education. Primary School Journal, 90, pp. 449466. Ball, D. (2000). Bridging Practices: Intertwining Content and Pedagogy in Teaching and Learning to Teach. Journal of Teacher Education, 51 (3), pp. 241247. Ball, D., & Bass, H. (2009). With an Eye on the Mathematics Horizon: Knowing Mathematics for Teaching to Learners’ Mathematics Futures. Paper is Based on a Keynote Address at The 43rdJahrestagung für Didaktik der Mathematik Held in Oldenburg, Germany, March 1 – 4, 2009. Ball, D., Hill, H. C., & Bass, H. (2005). Knowing Mathematics for Teaching: Who Knows Mathematics Well Enough to Teach Third Grade, and How Can We Decide? Journal of the American Federation of Teachers, pp. 1422. Ball, D., Thames, M., & Phelps, G. (2008). Content Knowledge for Teaching What Makes It Special? Journal of Teacher Education, 59 (5), pp. 389407. Bicer, A., Capraro, M., Capraro, R. (2013) The Effects of Parents’ SES and Education Level on Students’ Mathematics Achievement: Examining the Mediation Effects of Parental Expectations and Parental Communication. The Online Journal of New Horizon in Education, Vol 3, Issue 4. Bornstein, M. H., & Bradley, R., H. (2003). Socioeconomic Status, Parenting, and Child Development. New Jersey: Lawrence Erlbaum Associates, Inc. Brakoniecki, A. (2009). Mathematics Knowledge For Teaching Exhibited By Preservice Teachers Responding To Mathematics And Pedagogical Contexts. Swars, S. L., Stinson, D. W., & LemonsSmith, S. (Eds.). Proceedings of the 31st annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Atlanta, GA: Georgia State University. Cheang W. K., Yeo K. J., Chan C. , LimTeo S. K., Chua K. G., & Ng L. E. (2007). Development of Mathematics Pedagogical Content Knowledge in Student Teachers. The Mathematics Educator, 10 (2), pp. 2754. Choo, T.L., & DarlingHammond, L. (2011). Creating Effective Teachers and Leaders in Singapore In Linda DarlingHammond and Robert Rothman, eds., Teacher and Leader Effectiveness in HighPerforming Education Systems. Washington, DC: Alliance for Excellent Education and Stanford, CA: Stanford Center for Opportunity Policy in Education Corcoran, T. (1995). Helping Teachers Teach Well: Transforming Professional Development. CPRE Policy Briefs. RB16 June 1995. Demir, I., Kilic, S., & Unal, H. (2010). Effects of Students’ and Schools’ Characteristics on Mathematics Achievement: Findings from PISA 2006, Procedia social and Behavioral Science, 2, pp. 30993103. Ernest. (1989). Impact of Beliefs on the Teaching of Mathematics’, in P. Ernest, Ed. Mathematics Teaching: The State of the Art, London: Falmer Press, pp. 249254. Eynde, P., Corte, E., & Verschaffel, L. (2002). Framing Students' MathematicsRelated Beliefs.Leder, G., Pehkonen, E., Törner, G. (Eds.), Beliefs: A Hidden Variable in Mathematics Education?(pp.1337). Dordrecht, The Netherlands: Kluwer Academic Publishers. GoldrickRab, S., Harris, D., &Trostel, P. (2009). Why Financial Aid Matters (or Does Not) for College Success: Toward a New Interdisciplinary Perspective. In Higher Education: Handbook of Theory and Research, Smart, J. (Editor), Springer, Volume 24. Guo, G., & Harris, K. M. (2000) The Mechanism Mediating the Effects of Poverty on Children’s Intellectual Development, Demography, 37, pp. 431447. Hill, H.C,, Ball, D.L., & Schilling, S.G. (2008). Unpacking Pedagogical Content Knowledge: Conceptualizing and Measuring Teachers’ TopicSpecific Knowledge of Students. Journal for Research in Mathematics Education, 39 (4), pp. 372400. Leder, G., Pehkonen, E., & Törner, G. (2002). Beliefs: A Hidden Variable in Mathematics Education? Dordrecht, The Netherlands: Kluwer Academic Publishers. Luft, J., & Roehirg, G. (2007). Capturing Science Teachers’ Epistemological Beliefss: The Development of the Teacher Beliefs Interview. Electronic Journal of Science Education, 11 (2), pp. 3863. Ma, L. (1999). Knowing and teaching Primary mathematics: Teachers' understanding of fundamental mathematics in China and the United States. Mahwah, N.J: Lawrence Erlbaum Associates. McLeod, D. (1992). Research on Affect in Mathematics Education: a Reconceptualization. In D. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning. New York: MacMillan Publishing Company. McLeod, D., B., & McLeod, S., H. (2002). Synthesis  Beliefs and Mathematics Education: Implications for Learning, Teaching, and Research. In Leder, G., Pehkonen, E., Törner, G. Beliefss: A Hidden Variable in Mathematics Education? Kluwer Academic Publishers. Mosvold, R., &Fauskanger, J. (2013).Teachers’ Beliefs about Mathematical Knowledge for Teaching Definitions. International Electronic Journal of Mathematics Education, 8 (2), pp. 4361. Mushtaq, I., Khan, S.N. (2012). Factors Affecting Students’ Academic Performance.Global Journal of Management and Business Research, 12 (9), pp. 1722. Noble, J., Roberts, L., & Sawyer, L. (2006). Student Achievement, Behavior, Perceptions, and other Factors Affecting ACT Scores. ACT Research Report Series 2006  1. http://www.act.org/research/researchers/reports/pdf/ ACT_RR20061.pdf (20 Juni 2015). Northcote, M. (2009). Educational Beliefs of Higher Education Teachers and Students: Implications for Teacher Education. Australian Journal of Teacher Education, 34 (3), pp. 6981. Novikasari, I. (2013). Analisis Kompetensi Matematika Kelas IV di dalam Kurikulum 2013. MakalahDiseminarkan di P4TK Yogyakarta, November 2013. Okioga, C., K. (2013). The Impact of Students’ Socioeconomic Background on Academic Performance in Universities, a Case of Students in Kisii University College.American International Journal of Social Science, Vol.2 (2), pp. 3846. Petrou, M., &Goulding, M. 2011. Conceptualizing Teachers’ Mathematical Knowledge in Teaching. In Rowland, T & Ruthven, K (Ed.), Mathematical Knowledge in Teaching. www.springer.com (15 November 2014). Philipp, R. A. (2007). Mathematics teachers’ beliefs and affect. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 257315). United States: Information Age Publishing. Powell, A. ,& Hanna, E. (2006). Understanding Teachers’ Mathematics Knowledge for Teaching: A Theoretical and Methodological Approach. Proceedings 30th Conference of the International Group for the Psychology of Mathematics Education, 4, pp. 369376. Raymond, A. (1997). Inconsistency between a beginning Primary teacher’s mathematics beliefs and practice.Journal for Research in Mathematics Education, 28(5), 555576 Schmidt, W., & Kennedy, M. (1990). Teachers' and Teacher Candidates' Beliefs About Subject Matter and about Teaching Responsibilities. Michigan: The National Center for Research on Teacher Education. Schoenfeld, A. H., & Kilpatrick, J. (2008). Toward a Theory of Proficiency in Teaching Mathematics. In D. Tirosh& T. Wood (Eds.), The international handbook of mathematics teacher education: Tools and processes in mathematics teacher education. Rotterdam: Sense Publishers. Shalberg, Pasi. (2011). Developing Effective Teachers and School Leaders: The Case of Finland In Linda DarlingHammond and Robert Rothman, eds., Teacher and Leader Effectiveness in HighPerforming Education Systems. Washington, DC: Alliance for Excellent Education and Stanford, CA: Stanford Center for Opportunity Policy in Education Somayajulu, R. B. (2012). Building PreService Teacher’s Mathematical Knowledge for Teaching of High School Geometry. Dissertation: The Ohio State University. Starkey, P., & Klein, A. (2000). Fostering Parental for Children’s Mathematical Development. Early Education & Development, 11 (5), pp. 659680 Sudjana.(2005). Penilaian Hasil Proses BelajarMengajar.Bandung: Rosdakarya. Tatto, M. T., Schwille, J., Senk, S., Ingvarson, L., Peck, R., & Rowley, G. (2008). Teacher Education and Development Study in Mathematics (TEDSM): Policy, practice, and readiness to teach primary and secondary mathematics. Conceptual framework. East Lansing, MI: Teacher Education and Development International Study Center, College of Education, Michigan State University. Topkaya, E.Z., Uztosun, M., S. (2012). Choosing Teaching as a Career: Motivations of Preservice English Teachers in Turkey. Journal of Language Teaching and Research, 3 (1), pp. 126134. Törner, G., & Pehkonen, E. (1999). Teachers‘ Beliefs on Mathematics Teaching– comparing different selfestimation methods a case study. http://www.uniduisburg.de/FB11/PROJECTS/MAVI.html (20February 2014). Wayt, l. (2012). The Impact of Students’ Academic and Social Relationships on College Student Persistence. Thesis: University of Nebraska. Welder, R., &Simonsen, L. (2011). Primary teachers’ mathematics knowledge for teaching prerequisite algebra concepts.IUMPST: The Journal. Vol 1, January, 2011. Zerpa, C., Kajander, A., Van Barneveld, C. (2009). Factors That Impact Preservice Teachers’ Growth In Conceptual Mathematical Knowledge During A Mathematics Methods Course. International Electronic Journal of Mathematics Education, Vol.4, No.2, pp. 5776. 
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4 
A Five Circles Model for Designing Mathematics Teacher Education Programs and Framing Common Standards for EducatorsYenealem Ayalew
pp. 265280  Article Number: iejme.2017.011
Abstract Mathematics teacher education is a complex, interdisciplinary enterprise requiring knowledge of teaching and learning as well as knowledge of mathematics. The Education and Training policy of Ethiopia reminds Teacher training institutions to gear their programmes towards the appropriate educational level for which they train teachers. Candidates of an inservice mathematics teacher training program have double identities: school teacher and university student. Yet, there is no vivid standard for Mathematics Teacher Educators in the country. Three basic questions were raised and answered by this study. What are the possible sources of stakeholders’ roles in training mathematics teachers? What would be the roles of mathematics teacher educators? What minimum competencies are expected of mathematics educators? A qualitative content analysis research approach was followed. By analyzing data collected from 25 inservice teachers, consulting official documents and reviewing related literatures, I have developed a framework of standards that illustrates an Educator’s roles, competencies and challenges as composite functions of practicing teachers’ experience and students’ expectation. This work will have impact on the theory of preparing Mathematics Teacher Educators and brings a new model of developing a Mathematics teacher education program. Keywords: Mathematics, Teacher Educator, standards References Barter, M., Buchele, U., ReuterHerzer, M. & Selka, R. (1989). Creative Tasks for Independence and Motivation, Berlin: Bundesinstitut. Brodie, K. (2010). Teaching Mathematical Reasoning in Secondary School Classrooms. New York: Springer. Brown, T. & McNamara, O. (2005). New Teacher Identity and Regulative Government: The Discursive Formation of Primary Mathematics Teacher Education. New York: Springer. Carnoy, M. et al (2009). Do Countries Paying Teachers Higher Relative Salaries Have Higher Student Mathematics Achievement? Amsterdam: International Association for the Evaluation of Educational Achievement (IEA). Cowan, P. (2006). Teaching Mathematics: A Handbook for Primary and Secondary School Teachers. London: Routledge. Dalelo, A., T/Mariam, A., & Kassaye, M.. (2008). The Structure and Content of Secondary School Teacher Education programs: International and National Experiences, Journal of Education for Development, Vol. II, No. II, Addis Ababa. Foote, M. [Ed.] (2010). Mathematics Teaching and learning in K12: Equity and Professional Development. New York: Palgrave Macmillan. Gates, P. [Ed.] (2001). Issues in Mathematics Teaching. London: RoutledgeFalmer. Glenda, A. & Margaret, W. (2009). Effective Pedagogy in Mathematics. Brussels: International Academy of Education. Jaworski, B. et al [Eds.] (1999). Mathematics Teacher Education: Critical International Perspectives. London: Falmer Press. Kassa, K. & Amdemeskel, Y. (2013). Practices and Challenges of PostGraduate Diploma in Teaching Programme: The Case of Haramaya University, Ethopia. ereflection journal, Vol. II (IV), P.254274. Kessel , C. [Ed.]. (2009). Teaching Teachers Mathematics: Research, Idea, Projects and Evaluation. Berkeley: Mathematical Science Research Institute. Leikin, R. & Zazkis, K. [Eds.] (2010). Learning through Teaching Mathematics, Mathematics Teacher Education 5. New York: Springer. Leu, E. & Ginsburg, M. (2011). First Principles: Designing Effective Education Program for InService Teacher Professional Development. Educational Quality Improvement Program 1 (EQUIP1). Retrieved from www.equip123.net MoE (2007). Ethiopian Teachers’ Development Program Blue Print. Addis Ababa: Educational Materials Production and Distribution Enterprise. MoE (2012). Professional Standard for Ethiopian School Teachers. Retrieved from www.edu.gov.et NCTM (2000). Principles and Standards for School Mathematics. Retrieved from www.nctm.org Roesken, B. (2011). Hidden Dimensions in the Professional Development of Mathematics Teachers: InService Educator for and With Teachers. Rotterdam: Sense Publishers. Semela, T. (2014) Teacher Preparation in Ethiopia: a Critical Analysis of Reforms, Cambridge Journal of Education, 44:1, 113145. Simon, M. (2008). The Challenge of Mathematics Teacher Education in the Area of mathematics Education Reform. In B. Jaworski & T. Wood (Eds.), The Mathematics Teacher Educator as a Developing professional, 1729. Sullivan, P. (2011). Teaching Mathematics: Using ResearchInformed Strategies. Camberwell: ACER Press. Zaslavsky, O & Sullivan, P. [Eds.] (2011). Constructing Knowledge for Teaching Secondary Mathematics: Tasks to Enhance Prospective and Practicing Teacher Learning. New York: Springer. Zaslavsky, O. (2008). Meeting the Challenges of Mathematics Teacher Education through Design and Use of Tasks that Facilitate Teacher Learning. In B. Jaworski and T. Wood (eds.), the Mathematics Teacher Educator as a Developing Professional, 93–114. Rotterdam: Sense Publishers. 
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5 
Science and Engineering Students’ Difficulties With Fractions At EntryLevel To UniversityJohanna Coetzee & Kuttickattu J. Mammen
pp. 281310  Article Number: iejme.2017.012
Abstract This study was carried out at a South African university. The aim of the study was to test entrylevel students’ fractions skills in order to facilitate teaching at appropriate levels. The sample consisted of 94 firstyear entry level students (54 mainstream and 40 extended stream) who were enrolled for national diplomas in science and engineering, out of a population of 120 students. The instrument had 20 items, including three multiple choice questions (MCQs). The data were analyzed using Microsoft Excel 2013. The main finding was that entrylevel students enrolled for engineering and science diplomas performed poorly in a test of numeracy skills. The average score (47.8%) was regarded as a cause for concern, especially considering that the test was pitched at Grade 8 level. The study also found that students struggled to apply proportional reasoning when dealing with word problems. Mathematics teachers and lecturers need to be aware of students’ difficulties and ought to attempt to assist them to overcome such challenges. It is hoped that this paper will be useful to mathematics curriculum implementers at school level, subject advisors at the district level, preservice teacher educators at Teachers’ colleges and universities, and university lecturers teaching mathematics at first year level. Keywords: mathematics education; numeracy; fractions; ratios; proportions References {C}Akyuz, G. (2015). Determining the Numeracy and Algebra Errors of Students in a Twoyear Vocational School. Community Collge Journal of Research and Practice, 39(3), 252264. Bailey, D.H, Zhou. X., Zhang, Y., Cui, J., Fuchs, L.S., Jordan, N. C., Gersten, R. & Siegler, R. S. (2015). Development of fraction concepts and procedures in U.S and Chinese children. J Exp Child Psychol, 129, 6883. Ball, D.L. (1990). The mathematical understandings that prospective teachers bring to teacher education. 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Retrieved 24 March 2016 from http://www.jet.org.za/publications/initialteachereducationresearchproject/copy_of_bowiereportonmathscoursesofferedat5casestudyinstitutions18feb.pdf. Bowie, L. & Frith, V. (2006). Concerns about the South African Mathematical Literacy curriculum arising from experience of material development. Pythagoras, 64, 2936. Brousseau, G., Brousseau, N. & Warfield, V. (2004). Rationals and decimals as required in the school curriculum. Part 1: Rationals as measurements. Journal of Mathematical Behavior, 23, 120. Cai, J. (1995). A Cognitive Analysis of U. S. and Chinese Students' Mathematical Performance on Tasks Involving Computation, Simple Problem Solving, and Complex Problem Solving (Vol. monograph series 7). Reston, VA: National Council of Teachers of Mathematics. Campbell, A. (2009). Remediation of Firstyear mathematics students algebra difficulties. (MSc), University of KwaZuluNatal, KwaZuluNatal, South Africa. Retrieved 30 April 2014 from http://researchspace.ukzn.ac.za/xmlui/bitstream/handle/10413/761/Campbell_A_2009.pdf?sequence=1 Case, J. (2006). Issues facing engineering education in South Africa. Paper presented at the Engineering Education for Sustainable Development: Proceedings of the 3rd African Regional Conference, 2627 September 2006, University of Pretoria, Pretoria, South Africa, 2627 September 2006. Cetin, H & Ertekin, E. (2011). The relationship between eighth grade primary school students' proportional reasoning skills and success in solving equations. International Journal of Instruction, 4(1), 4762. Clarke, D. (2006). Fractions as division: The forgotten notion. Australian Primary Mathematics Classroom, 11(3), 410. Coetzee, J. & Mammen, K. J. (2016). Challenges Faced by Entrylevel University Students in Word Problems Involving Fractions Terminology. International Journal of Education Sciences (IJES)., 15(3), 461473. DoBE, (2011a). National Curriculum Statement (NCS): Curriculum and Assessment Policy Statement (CAPS) Further Education and Training Phase MATHEMATICS GR 79. Pretoria: Department of Basic Education. Retrieved 30 April 2014 from http://www.education.gov.za. DoBE, (2011b). National Curriculum Statement (NCS): Curriculum and Assessment Policy Statement (CAPS) Further Education and Training Phase MATHEMATICS Grades 1012. Pretoria, South Africa: Department of Basic Education. Retrieved 30 April 2014 from http://www.education.gov.za. DoBE, (2011c). National Curriculum Statement (NCS): Curriculum and Assessment Policy Statement (CAPS) Intermediate Phase MATHEMATICS GR 46. Pretoria: Department of Basic Education. Retrieved 30 April 2014 from http://www.education.gov.za. DoBE, (2012). National Senior Certificate 2012: National diagnostic report on learners’ performance. Pretoria, South Africa: Department of Basic Education. Retrieved 15 October 2015 from http://www.education.gov.za. Dorko, A & Speer, N. (2014). Calculus Students' Understanding of Units. Paper presented at the 17th Annual Conference on Research in Undergraduate Mathematics Education, February 26  March 2, 2014, Denver, Colorado. Duffin, J. (2003). Numeracy in Higher Education. In J. K. Peter Kahn (Ed.), Effective Learning and Teaching in Mathematics and Its Applications: Routledge, London. Fonseca, K & Petersen, N. (2015). Online supplementary mathematics tuition in a firstyear childhood teacher education programme. South African Journal of Childhood Education, 5(3), 9 pages. Gabaldon, T.A. (2015). Strength in Numbers: Teaching Numeracy in the Context of Business Associations. St. Louis University Law Journal, 59, 701709. Graffeo, M., Polonio, L. & Bonini, N. (2015). Individual differences in competent consumer choice: the role of cognitive reflection and numeracy skills. Frontiers in Psychology, 6. Gravetter, F.J. & Wallnau, L.B. (2009). Statistics for the Behavioral Sciences (8th ed.). Belmont, CA: Wadsworth. Houston, J., Tenza, S.P., Hough, S., Singh, R. & Booyse, C. (2015). The rationale for teaching Quantitative Literacy in 21st century South Africa: A case for the renaming of Mathematical Literacy. The Independent Journal of Teaching and Learning, 10. Retrieved 6 April 2016 from http://hdl.handle.net/11622/53 Johnson, A.W. & Johnson, R. (2002). Cooperative Learning Methods: A metaanalysis. Journal of Research in Education, 12(1), 514. Jukes, L & Gilchrist, M. (2006). Concerns about numeracy skills of nursing students. Education in Practice, 6(4), 192198. Kremmer, M., Brimble, M., Freudenberg, B. & Cameron, C. (2010). Numeracy of First Year Commerce Students: Preliminary Analysis of an Intervention. The International Journal of Learning, 17(1), 113. Lamon, S.L. (2001). Presenting and Representing: From Fractions to Rational Numbers. In A. Cuoco & F. Curcio (Eds.), The Roles Of Representations in School Mathematics2001 Yearbook (pp. 146165). Reston: NCTM. Lesh, R., Post, T. & Behr, M. (1988). Proportional Reasoning. In J. Hiebert & M. Behr (Eds.), Number Concepts and Operations in the Middle Grades (pp. 93118). Reston, VA: Lawrence Erlbaum & National Council of Teachers of Mathematics. Lin, C.Y., Becker, J., Byun, MR., Yang, D.C. & Huang, T.W. (2013). Preservice Teachers’ Conceptual and Procedural Knowledge of Fraction Operations: A Comparative Study of the United States and Taiwan. School Science and Mathematics, 113(1), 4151. Livy, S. & Herbert, S. (2013). SecondYear PreService Teachers’ Responses to Proportional Reasoning Test Items. Australian Journal of Teacher Education, 38(11), 1732. Long, C., Dunne, T. & De Kock, H. (2014). Mathematics, curriculum and assessment: The role of taxonomies in the quest for coherence. Pythagoras 35, 35(2), 14. LortieForgues, H., Tian, J. & Siegler, R.S. (2015). Why Is Learning Fraction and Decimal Arithmetic So Difficult. Developmental Review, 38, 201221. Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers' knowledge of fundamental mathematics in China and the United States. Mahwah, NJ: Erlbaum. Naureen, D. & Vicki, N.T. (2012). The role of numeracy skills in graduate employability. Education and Training, 54(5), 419434. NMAP, (2008). Foundations for Success: The final report of the National Mathematics Advisory Panel. Washington, DC: National Mathematics Advisory Panel. Retrieved 27 February 2016 from http://www2.ed.gov/about/bdscomm/list/mathpanel/report/finalreport.pdf. OECD, (2013). OECD Skills Outlook 2013: First Results from the Survey of Adult Skills. Paris: OECD Publishing. Retrieved 4 April 2016 from www.oecd.org/skills/. Pienaar, E. (2014). Learning About And Understanding Fractions And Their Role In The High School Curriculum. (Master of Education), University of Stellenbosch, Stellenbosch. Retrieved 15 October 2015 from https://www.google.co.za/#q=Learning+About+And+Understanding+Fractions+And+Their+Role+In+The+High+School+Curriculum Pinker, S. (1998). How the mind works. London: Penguin Books Reyna, V.F., Nelson, W.L., Han, P.K. & Dieckmann, N.F. (2009). How Numeracy Influences Risk Comprehension and Medical Decision Making. Psychological bulletin, 135(6), 943973. RiveraBatiz, F.L. (1992). Quantitative Literacy and the Likelihood of Employment among Young Adults in the United States. The Journal of Human Resources, 27(2), 313328. Rizvi, N.F. & Lawson, M.J. (2007). Prospective teachers’ knowledge: Concept of division International Education Journal, 8(2), 377392. Roohr, K.C., Graf, E.A. & Liu, O.L. (2014). Assessing Quantitative Literacy in Higher Education: An Overview of Existing Research and Assessments With Recommendations for NextGeneration Assessment. ETS Research Report Series, 2014(2), 126. Schneider, M. & Siegler, R.S. (2010). Representations of the magnitudes of fractions. Journal of Experimental Psychology: Human Perception and Performance, 36(5), 12271238. Schollar, E. (2008). Towards Evidencebased Educational Development in South Africa: Eric Schollar and Associates c.c. Retrieved 21 March 2016 from https://www.ru.ac.za/media/rhodesuniversity/content/sanc/documents/Schollar%20%202008%20%20Final%20Report%20Short%20Version%20The%20Primary%20Mathematics%20Research%20Project%2020042007%20%20Towards%20eveidencebased%20educational%20de.pdf. Siegler, R.S., Duncan, G.J ., DavisKean, P.E., Duckworth, K., Claessens, A., Engel, M., Susperreguy, M.I. & Chen, M. (2012a). Early Predictors of High School Mathematics Achievement. Psychological Science, 23(7), 691697. Siegler, R.S., Fazio, L.K., Bailey, D.H. & Zhou, X. (2012b). Fractions: the new frontier for theories of numerical development. Trends in Cognitive Sciences, 17(1), 1319. Siegler, R.S. & LortieForgues H. (2015). Conceptual Knowledge of Fraction Arithmetic. Journal of Educational Psychology, 107(3), 909918. Siegler, R.S. & Thompson, CA. (2014). Numerical landmarks are usefulexcept when they're not. J Exp Child Psychol, 120, 3958. Siegler, R.S., Thompson, C.A. & Schneider, M. (2011). An integrated theory of whole number and fractions development. Cognitive Psychology, 62(2011), 273296. Spaull, N. & Kotze, J. (2015). Starting behind and staying behind in South Africa: The case of insurmountable learning deficits in mathematics. International Journal of Educational Development, 41, 1324. Sun, L.G. & Wang, L. (2005). Mathematics: Spring, Fifth grade. Nanjing, Jiangsu Province: Phoenix Education. Titus, J. (1995). The concept of fractional number among deaf and hard of hearing students. American Annals of the Deaf, 140(3), 255263. Torbeyns, J., Schneider, M., Xin, Z, & Siegler, R.S. (2014). Bridging the Gap: Fraction understanding is central to mathematics achievement in students from three different continents. Learning and Instruction, 19. 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Kindergartners’ Use of Symbols in the Semiotic Representation of 3Dimensional ChangesAinhoa Berciano, Clara JiménezGestal & María Salgado
pp. 311331  Article Number: iejme.2017.013
Abstract Orientation skill’s development is one of the topics studied in Mathematics Education because of its difficulty. In this article, we are concerned about the orientation skill of fiveyearold children. For this end, we show a case study and a preliminary quantitative study of the symbolization used by children to depict graphically 3dimensional changes in a plane. For this purpose, we have designed an activity based on Realistic Mathematics Education, where the children should find a treasure at the Childhood Education School and represent the itinerary between the classroom and the treasure in a map. We have also measured their spatial abilities through a specific test. The results show that, in one way or another, all the children understand the notion of 3dimensionality and the changes in verticality, which they depict with specific symbols on the corresponding map. In any event, the semiotic representation depends on the orientation skill of the children. Thus, the types of symbols use vary with their orientation skills. Keywords: Childhood Education, map, orientation, Realistic Mathematics Education, semiotic representation, symbolization References Alsina, A. (2012). Hacia un enfoque globalizado de la educación matemática en las primeras edades [Towards a holistic approach to mathematics education at the early ages]. Números, 80, 724. Carruthers, E. & Worthington, M. (2005). Making sense of mathematical graphics: the development of understanding abstract symbolism. European Early Childhood Education Research Journal, 13(1), 5779. Clements, D. H. (1998). Geometric and spatial thinking in young children. Retrieved from ERIC database (ED436232). Clements, D. H. (1999). Geometric and spatial thinking in young children. In J. V. Copley (Ed.), Mathematics in the early years (6679). Reston, VA: National Council of Teachers of Mathematics. Clements, D. H. & Sarama, J. (2009). Learning and Teaching Early Math. The learning trajectories approach. NY, New York: Routledge. De la Cruz, M. V. (1988). Pruebas de Diagnóstico preescolar. Madrid: TEA Ediciones. DeLoache, J. S. (1991). Symbolic functioning in very young children: understanding of picture and models. Child Development, 62(4), 736752. Elia, I., Gagatsis, A. & Demetriou, A. (2007). The effects of different modes of representation on the solution of onestep additive problems. Learning and Instruction, 17, 658672. Elia, I., Gagatsis, A., Michael, P., Georgiu, A. & Van den HeuvelPanhuizen, M. (2011). Kindergartners’ use of gestures in the generation and communication of spatial thinking. In M. Pytlak, T. Rowland, & E. Swoboda (Eds.), Proceedings of the Seventh Congress of the European Society for Research in Mathematics Education (18421851). Rzeszów, Poland: University od Rzeszów. Fernández Blanco, Mª. T. (2011). Una aproximación ontosemiótica a la Visualización y el Razonamiento Espacial [An ontosemiotic approach to visualization and spatial reasoning] (Doctoral dissertation). Retrieved from TESEO (947559). Freudenthal, H. (1973). Mathematics as an Educational Task. Dordrecht, The Netherlands: Reidel Publishing Company. Hershkowitz, R., Parzysz, B. & Van Dormolen, J. (1996). Space and shape. In A. J. Bishop (Ed.), International handbook of mathematics education 1 (161204). Dordrecht, The Netherlands: Kluwer. Kotsopoulos, D., Cordy, M. & Langemeyer, M. (2015). Children’s understanding of largescale mapping tasks: an analysis of talk, drawings, and gesture. ZDM Mathematics Education, 47, 451463. Landau, B., Gleitman, H., & Spelke, E. (1981). Spatial knowledge and geometric representation in a child blind from birth. Science, 213, 12751277, Ministerio de Educación y Ciencia. (2008). ORDEN ECI/3960/2007, Currículo español de Educación Infantil [Spanish Early Childhood Education Curriculum]. Retrieved from https://www.boe.es/boe/dias/2008/01/05/pdfs/A0101601036.pdf National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author. Organisation for Economic Cooperation and Development. (2011). Pisa in Focus 2011/1. Retrieved from http://www.oecd.org/pisa/pisaproducts/pisainfocus/PiF1_esp_revised.pdf Resnick, I., Verdine, B. N., Golinkoff, R. & HirschPasek, K. (2016). Geometric toys in the attic? A corpus analysis of early exposure to geometric shapes. Early Childhood Research Quarterly 36, 358365. Sarama, J. & Clements, D. H. (2009). Early Childhood Mathematics Education Research. Learning Trajectories for Young Children. New York, NY: Routledge. Van den HeuvelPanhuizen, M. (2000). Mathematics education in the Netherlands: A guided tour. Utrecht, The Netherlands: Utrecht University. Yuzawa, M., Bart, W. M., Yuzawa, M., & Junko, I. (2005). Young children’s knowledge and strategies for comparing sizes. Early Childhood Research Quarterly 20, 239253. 
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7 
PME Learning Model : The Conceptual Theoretical Study Of Metacognition Learning In Mathematics Problem Solving Based On ConstructivismIhdi Amin & Scolastika Mariani
pp. 333352  Article Number: iejme.2017.014
Abstract Learning mathematics until today still left a lot of records that had to be improved, including passive learning, low ability of learners in problemsolving activities, the rarity of authentic assessment, emphasizing only on cognition, and others. This was a study of the literatures concerning the teaching of metacognition in mathematical problem solving. The PME learning model was a modified theory of DarlingHammond (2003), which was a theoreticalconceptual product that offered the strategies to improve the ability of metacognition in problem solving. This metacognition strategies implemented through metacognitive activities, ie : planning, monitoring, and evaluating (PME). On PME learning model: (1) the activity planning, monitoring, evaluating explicitly raised in the core activities of learning and mathematical problemsolving activities; (2) the learning process recommended using social constructivist teaching in small groups; (3) placing the role and duties of teachers as counselors, classroom manager, motivator, facilitator, and evaluator; (4) The support system for the effectiveness of PME learning model were: Lesson Plan (LP) and Worksheet for students (WS); and (5) the direct effect was expected increasing of the metacognition ability, and the nurturant effect was expected to increase in problem solving performance. Keywords: Metacognition strategies, constructivist teaching, mathematical problem solving References Ali, R.,Hukamdad, Akhter, A., & Khan, A. (2010). Effect of Using Problem Solving Method in Teaching Mathematics on the Achievement of Mathematics Students.Asian Sosial Science, 6(2), 67 – 72, Pakistan. Arifin. 2010. Konsep Perencanaan, Pendekatan Dan Model Perencanaan Pendidikan. uploaded on July 15, 2016. https://drarifin.wordpress.com/2010/07/15/konsepperencanaanpendekatandanmodelperencanaanpendidikan/ Aurah, Catherine M. ; Setlhomo KoloiKeaikitse, Calvin Isaacs, Holmes Finch. (2011). The Role Of Metacognition In Everyday Problem Solving Among Primary Students In Kenya.Problems of education in the 21st century. Volume 30, 2011 Baki, A., (1997). Educating Mathematics Teachers. Medical Journal of Islamic Academy of Sciences, 10(3): 93102. Carlson, M.P. and Bloom, I. (2005). The Cyclic Nature of Problem Solving: An Emergent Multidimensional ProblemSolving (MPS) Framework. Journal: Educational Studies in Mathematics, 58(1), 45 – 75. Tersedia: http://www.jstor.org /stable/25047137. Carr, M., Alexander, J., & FoldesBennet, T. (1994).Metacognition and Mathematics Strategy Use.Applied Cognitive Psychology, 8, 583595. Cobb, P., Jaworski, B., & Presmeg, N. (1996). Emergent and Sosiocultural Views of Mathematical Activity.Theory of Mathematical Learning, Lawrance Erlbaum Associates, pp. 3 – 19. DarlingHammond, L. et al, (2003).The Learning Classroom: Theory into Practice. Stanford University: Annenberg/CPB. Available :https://www.learner.org/ courses/learning classroom/support/09_metacog.pdf. Downing K.J. (2009).SelfEfficacy And Metacognitive Development. The International Journal Of Learning. Volume 16, Number 4. Tersedia: http://Www.LearningJournal.Com, ISSN 14479494. Duncan, G., & Met, M. (2010).STARTALK: From paper to practice. College Park,MD: National Foreign Language Center at the University of Maryland.Available at www.startalk.umd.edu/lesson_planning. Feist, Jess & Feist, Gregory J. (2013).Teori Kepribadian (Theory of Personality, 7thed). Jakarta: Salemba Humanika. Gartmann, S. and Freiberg, M. (1993). Metacognition and Mathematical Problem Solving : Helping Students to Ask The Right Questions. Journal: The Mathematics Educator, 6(1), 9 – 13. Ghasempour, Z., Bakar, M.D., & Jahanshahloo.G.R. (2013).Innovation in Teaching and Learning through Problem PosingTasks and Metacognitive Strategies.International Journal of Pedagogical Innovations, 1(1), 53 – 62. Handoko, TH. (1984). Manajemen. Yogyakarta : BPFE Havenga, Marietjie ; Betty Breed; Elsa Mentz, Desmond Govender; Irene Govender; Frank Dignum, Virginia Dignum. (2013). Metacognitive and ProblemSolving Skills to Promote SelfDirected Learning in Computer Programming :Teachers’ Experiences SAeDUC JOURNAL Volume 10, Number 2 October 2013 Herbst, P.G. (2006). Teaching Geometry With Problems: Negotiating Instructional Situation and Mathematical Tasks. Journal for Research in Mathematics Education, 37(4), 313 – 347. Hoe, L.N., Shook Cheong, A.C., Lee Peng Yee, L.P. (2001). The Role of Metacognition in the Learning of Mathematics among LowAchieving Students.Teaching and Learning Journal, 22(2), 18 – 30. Hudojo, H. (1988). 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Mathematics Education In Singapore  An Insider’s Perspective. IndoMSJME, 5(1), 116 Kramarski B., Mevarech, Z.R., and Arami, A. (2002).The Effects of Metacognitive Instruction on Solving Mathematical Authentic Tasks.Educational Studies in Mathematics, 49, 225–250. Ku, Kelly Y. L. & Ho, Irene T. (2010).Metacognitive strategies that enhance critical thinking.Journal: Metacognition Learning, 5, 251–267. Kuhn, D. & Dean Jr, D. (2004). Metacognition: A Bridge Between Cognitive Psychology and Educational Practice. Theory into Practice, 43(4), 268 – 273. Lee,Ngan Hoe ; Agnes Shook Cheong Chang ; Lee Peng Yee. (2001). The role of metacognition in The learning of mathematics among lowachieving students. Teaching and Learning, 22(2), 1830. Lester Jr, F.K. (2013).Thoughts about Research on Mathematical Problem Solving Instruction. Jorunal: The Mathematics Enthusiast (TME), 10(1) & 2, 245 – 278. Maccini, P., & Gagnon, J.C., (2002). Perceptions And Application Of NCTM Standarts By Special And General Education Teachers. Exceptional Children, 68, 325344. Muijs &Reynolds . (2008). Effective Teaching. Yogyakarya: Rosdakarya Okoza, J. & Aluede, O. (2013).Understanding metacognitive awareness among teachers in the school system: issues and benefits. Inkanyiso, Journal Humanistic & Sosial Science, 5(1). Patrick, Thompson , W. (2013). Constructivism in Mathematics Education. In Lerman, S. (Ed.) Encyclopedia of Mathematics Education : Springer Reference (www.springerreference.com). SpringerVerlag Berlin Heidelberg. DOI: 10.1007/SpringerReference_313210 20130510 00:00:07 UTC Rusman. (2013). Modelmodel Pembelajaran: MengembangkanProfesionalisme Guru (Cetakan ke6). Jakarta: PT. RajaGrafindoPersada. Sahin, SM ; Fatma Kendir. (2013). The Effect of Using Metacognitive Strategies for solving Geometry Problems on Students’ Achievement and Attitude. 2013. Educational Research and Reviews, 8(19), 17771792. 10 October 2013. 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8 
Using Courseware Instruction to Improve Junior High School Students’ Spatial Visualization SkillsSamuel Adaboh, Robert Akpalu, Isaac OwusuDarko & Samuel Stevens Boateng
pp. 353365  Article Number: iejme.2017.015
Abstract This study basically focused on the use of instruction to assist Junior High School (JHS 1) students at Dodowa Presbyterian Basic School (Ghana), to achieve high spatial visualization skills which will eventually translate into their mathematics achievement. The test instrument used for the data collection was an adapted form of the Middle Grades Mathematics Project (MGMP) spatial visualization test which comprised of 40 items with an internal consistency reliability of 0.81. The simple random sampling technique was used to assign 50 students to control and experimental groups. Pretestposttest control group design was employed for the study. A pairedsample ttest and split plot ANOVA were used to analyze the data. The results showed that even though there was some improvement in spatial visualization skills across board (both control and experimental groups), there was a statistically significant improvement in spatial visualization skills among the experimental group. The study also indicated that there were no gender differences in spatial visualization skills both at the pretest and posttest levels. Keywords: spatial visualization skills, spatial ability, guided discovery teaching method, pretest and posttest References Bansilal, S., James, A., & Naidoo, M (2010), Whose voice matters? Learners. South African Journal of education, (30), 153165. Battista, M. T. (1990). Spatial visualization and gender differences in high school geometry. Journal for Research in Mathematics Education, 21, 47–60. Battista, M. T., Clements, D. H., Sarama, J., & Swaminathan, S. (1997). Development of students' spatial thinking in a unit on geometric motions and area. University of Chicago Press. Battista, M. T., & Clements, D. H. (1998). Students’ spatial structuring of 2D arrays of squares. JRME Online, 29(5), 503532. Battista, M.T. & Wheatley, G. H. (1989). Spatial visualization, formal reasoning, and geometricsolving strategies of preservice elementary teachers. Focus on Learning Problems in Mathematics 11(4):1730. BenChaim, D., Lappan, G., & Houang, R.T. (1988). The effects of instruction on spatial visualisation skills of middle school boys and girls. American Educational Research Journal, 25 (1), 5171. Bruner, J. (1966). Toward a theory of instruction. Cambridge, MA: Harvard University Press. Carter, C. S., LaRussa, M. A., & Bodner, G. M. (1987). A study of two measures of spatial ability as predictors of success in different levels of general chemistry. Journal of Research in Science Teaching, 24, 645657. Clements, M. A. (1983). The question of how spatial ability is defined, and its relevance to Mathematics Education. Zentralblatt fur Didaktik der Mathematik, 15, 820. Education Strategic Plan (ESP) 20032015, Volume I. Retrieved on 25/7/2016 from http://planipolis.iiep.unesco.org/upload/Ghana/Ghana%20Education%20Strategic%20Plan.pdf Fennema, J. & Sherman, J. (1977). Sexrelated differences in mathematics achievement, spatial visualization and affective factors. American Educational Research Journal, Vol.14: 5171, Halpern, D. F. (1986) Sex Differences in Cognitive Abilities. Hillsdale, N. J. Lawrence Erlbaum Association. McGee, M. G. (1979). Human spatial abilities: Psychometric studies and environmental, genetic, hormonal, and neurological influences. Psychological Bulletin, 86(5), 889918. Mereku, D.K., (2004). Mathematics curriculum implementation in Ghana 2nd ed. Accra: Danjoe Production. Mix, K. S., & Cheng, Y.L. (2012). The relation between space and math: Developmental and educational implications. In J. B. Benson (Ed.), Advances in child development and behaviour (Vol. 42, pp. 197–243). San Diego, CA: Academic Press. Ministry of Education (2002) Meeting the Challenges of Education in the twenty first century: Report of the president’s committee on review of education reforms in Ghana. Accra, Ghana. National Council of Teachers of Mathematics (NCTM) (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: NCTM Oke, M.G. & Bello M. A. (2014). An appraisal of candidates’ achievement in the West African Senior School Certificate Examination (WASSCE) among WAEC member countries. Sherrod, S. E., Dwyer, J. & Narayan, R. (2009). Developing science and mathematics integrated activities for middle school students. International Journal of Mathematical Education in Science and Technology. Volume 40(2), 247257. Sorby, S. A. (2007). Developing 3D spatial skills for engineering students. Australasian Journal of Engineering Education, 13(1), 1–11. Tartre, L. (1990). Spatial orientation skill and mathematical problem solving. Journal for Research in Mathematics Education, 21 (3), 216229. USA. Yue, J. (2002). Do basic mathematical skills improve spatial visualization abilities? Proceedings of the 2002 American Society for Engineering Education Annual Conference & Exposition, Session 3286. 
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Process of Mathematical Representation Translation from Verbal into GraphicDwi Rahmawati, Purwantoa, Subanji, Erry Hidayanto, Rahmad Bustanul Anwar
pp. 367381  Article Number: iejme.2017.016
Abstract The ability to do translation from one form of representation to another representation form is a fundamental ability to build a conceptual and mathematical thinking. Related to the important of translation process, this study aimed to investigate the process of mathematical representation translation from verbal to graph. This research was a qualitative research. Pengambilan data dilakukan dengan lembar tugas dan wawancara setelah subjek menyelesaikan tugas yang diberikan.Collecting data was done through the assignment sheet and interviews after the subjects completed the task given. Hasil penelitian menunjukkan bahwa mahasiswa mampu melakukan proses translasi dari representasi verbal ke grafik dengan baik pada tiap tahapan translasi.The result showed that the students were able to do the process of translation from verbal representation to graph well at every stage of the translation. The translation process was done in four stages: unpacking the source, preliminary coordination, constructing the targets, and determining equivalence. The translation process of verbal to graph representations required more than one translation process.Proses translasi dilakukan melalui empat tahap yaitu unpacking the source, preliminary coordination, constructing the target, dan determining equivalence . This process through the intermediary of some other representations like symbolic, schematic, equations, numerical. In general, students do the same activity except at preliminary coordination activity. Dalam aktivitas preliminary coordination , dapat dilakukan dengan dua cara yaitu mahasiswa menentukan rumus hubungan antara jarak dan waktu dari kejadian yang diberikan, dan dengan menghubungkan antara jarak kedua mobil dan bertambahnya waktuPreliminary coordination activity can be done in two ways, namely students determined the formula of the relationship between distance and time, and by connecting the distance between the two cars and the increasing time. Semakin bertambah waktu semakin berkurang jarak kedua mobil.The more the time increased, the distance the two cars decreased. Keywords: translation process; verbal representation, grahical representation References Bal, A. P. (2015). Skills Of Using And Transform Multiple Representations Of The Prospective Teachers. Journal of Mathematical Behavior, 197(Hal.), 582588. Bosse, M. J., Gyamfi, K. A& Chandler, K. (2011). Translation among Mathematical Representation: Teacher Belief and Practices. (Online), (http://www.cimt.org.uk/journal/bosse4.pdf) Bosse, M. J., Gyamfi, K. A& Chandler, K. (2012). Lost in Translation: Examining Translation Errors Assosiated with Mathematical Representation. School science and Mathematics, 112(3),159170 Bosse, M. J., Gyamfi, K. A& Chandler, K. (2014). Students Differented Translation Processes, (Online),(http://www.cimt.plymouth.ac.uk/journal/bosse5.pdf). Bruner, J. (1966). Towards a theory of instruction. Cambridge, MA: Harvard University Press. Cai, J., & Lester, F. K. 2005. Solution representations and pedagogical representations in Chinese and U. S. classrooms. Journal of Mathematical Behavior, 24, 221237. Celik, D.& Arslan, A. S. (2012). The Analysis of Teacher Candidats Translating skill in Multiple Representations, (Online), (http://ilkogretimonline.org.tr/vol11say1/v11s1m18.pdf ). Creswell, J.W. (2012). Educational Research. Pearson. Duval, R. 2006. The cognitive analysis of problems of comprehension in the learning of mathematics. Mediterranean Journal for Research in Mathematics Education, 1(2), 116. Gagatsis, A. & Elia, I. (2004). The Effects of Different Modes of Representation on Mathematical Problem Solving. Proceedings of The 28th Conference of The International Group for The PMA, 2, 447454. Gagatsis, A., & Shiakalli, M. (2004). Ability to translate from one representation of the concept of function to another and mathematical problem solving. Educational Psychology, 24(5), 645657. Goldin, G. A. (2002). Representational systems, learning, and problem solving in mathematics. Journal of Mathematical Behavior, 17(2), 137165. İpek, A. S., & Okumuş, S. (2012). İlköğretim matematik öğretmen adaylarının matematiksel problem çözmede kullandıkları temsiller. Gaziantep Üniversitesi Sosyal Bilimler Dergis, 11(3), 681 700. Janvier, C. (1987). Translation Processes in Mathematics Education. Dalam Janvier(Ed). Problems of Representation in the Teaching and Learning of Mathematics, 2732, Hillsdale, NJ: Lawrence Erlbaum Associates. Lesh, R., Post, T., & Behr, M. (1987). Representations and translations among representations in mathematics learning and problem solving. New Jersey: Lawrence Erlbaum Associates. McCoy,L.P., et. Al. (1996). Using Multiple Representation to Communicate: an Algebra Challenge. Reston. VA: NCTM National Council of Teachers of Mathematics. (2000). Principles and Standards for School Mathematics. Reston, VA: NCTM. National Council of Teachers of Mathematics. 2000. Principles and Standards for School Mathematics. Reston, VA: NCTM. Pape, S.J.& Tchoshanov, M.A. (2001). The Role of Representation(s) in Developing Mathematical Understanding. Theory into Practice, 40(2), 118125. Tripathi, P. N. (2008). Developing mathematical understanding through multiple representations. Mathematics Teaching in Middle School, 13(89), 438445. Villegas, J. L., Castro, E., & Gutierrez, J. (2009). Representation in problem solving: A case study with optimization problems. Electronic Journal Of Research In Educational Psychology, 7(1), 279308. Yerushalmy, M. (1997). Designing Representations: Reasoning about Functions of Two Variables. Journal for Research in Mathematics Education, 27 (4), 4314. 
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Investigating FifthGrade Students’ Construction of Mathematical Knowledge through Classroom DiscussionRini Setianingsih, Cholis Sa’dijah, Abdur Rahman As’ari, Makbul Muksar
pp. 383396  Article Number: iejme.2017.017
Abstract This study is descriptivequalitative in nature, aims to examine, (1) How do the students construct the mathematical knowledge (i.e. statistics for elementary school) through classroom discussion?, (2) What role are the students and the teacher playing in the discussion?, (3) What impact do their contributions have in the construction of new mathematical knowledge? As subjects of this study are 21 fifthgrade students of SD Labschool Unesa. Data were collected by using observation sheets, and by videotaping the class lessons with three cameras. The results suggest that both the teacher and the students participated actively in small group discussion, and played the majority of roles offered in an effective discussion. At the end of the lesson, there was a whole class discussion that functioned as meaning negotiation – to facilitate the students to share solutions and strategies with the whole class, and promote student reflection on the different strategies. This suggests that even ‘difficult materials’ can be successfully constructed by fifthgrade students using classroom discussion. Therefore, it is suggested that classroom discussion can be chosen as one of learning methods in a mathematics classroom in which the teacher provides appropriate mathematics contents and uses productive strategies to facilitate the learning processes. Keywords: Classroom discussion, Mathematical knowledge, Statistics, Elementary school References As’ari, A.R. (2016). Menjawab Tantangan Pengembangan 4C’s Melalui Pengembangan Kurikulum dan Pembelajaran Matematika. Makalah Utama. Prosiding Seminar Nasional Pendidikan Matematika,17. ISBN: 9786021150191. Malang: Pascasarjana Universitas Negeri Malang. Association Center for Best Practices, Council of Chief State School Officers, (2010). Retrieved from www.corestandards.org/assets/ccssiintroduction.pdf. Bauersfeld, H. (Eds.). (1991). The Emergence of Mathematical Meaning: Interaction in Classroom Cultures. Hillside, NJ: Lawrence Erlbaum Associates. Black, L. (2004). TeacherPupil Talk in Whole Class Discussions and Process of Social Positioning within the Primary School Classroom. Language and Education, 18 (5), 347–360. Boaler, J. (2008) Promoting ‘Relational Equity’and High Mathematics Achievement Through an Innovative Mixed Ability Approach. British Educational Research Journal, 34 (2), 167194. Taylor & Francis. Retrieved from https://dx.doi.org/10.1080/01411920701532145. Boaler, J. (1998). Open and Closed Mathematics: Student Experiences and Understandings. Journal for Research in Mathematics Education, 29(1), 41–62. Bruce, C.D. (2007). Student Interaction in the Math Classroom: Stealing Ideas or Building Understanding. What Works? Research Monograph # 1 Research into Practice. Ontario: the Literacy and Numeracy Secretariat and the Ontario Association of Deans of Education. Chapin, S.H., O’Connor, C., and Anderson, N.C. (2003). Classroom Discussions: Using Math Talk in Elementary Classrooms. Math Solutions 11. Retrieved from http://www.mathsolutions.com/ documents/0941355535_L.pdf Clayton, H. (2014). Keys to Productive Discussions in the Math Classroom. Making the Common Core Come Alive! Vol. 3 (4). Retrieved from http:// www.justaskpublications.com. Cohen, E.G. (1994). Designing Groupwork: Strategies for the Heterogeneous Classroom. New York, NY: Teachers College Press. Retrieved from https://book.google.co.id Dekker, R. & ElshoutMohr, M. (2004). Teacher Interventions Aimed at mathematical Level Raising during Collaborative Learning. Educational Studies in Mathematics, Vol. 56 (1), 3965. Retrieved from http://www.jstor.org/stable/4150263. Ding, M., Li, X., Piccolo, D., and Kulm, G. (2007). Teaching Interventions in Cooperative Learning Mathematics Classes. The Journal of Educational Research, Vol. 100, 162175. HufferdAckles, K.., Fuson, K.C., and GamoranSherin, M. (2004).Describing Levels and Components of a Mathtalk Learning Community. Journal of Research in Mathematics Education, 35(2), 81–116. Kaplan, A., Gheen, M., and Midgley, C. (2002). Classroom Goal Structure and Student Disruptive Behaviour. British Journal of Educational Psychology, Vol. 72 (2), 191211. Lantolf, J.P. (2000) Sociocultural Theory and Second Language Learning. Oxford, UK: Oxford University Press. Math Solutions Professional Development. (2011) Sausalito, CA: Math Solutions. Retrieved from www.mathsolutions.com/documents/qanda_usingmathtalk.pdf. Mercer, N. (1995) The Guided Construction of Knowledge: Talk Amongst Teachers and Learners. Church Point, NSW: Footprint Books. Nathan, M.J. & Knuth, E.J. (2003). A study of Whole Classroom MathematicalDiscourseandeacherChange. Cognition and Instruction, 27 (2), 175–207. National Education Association (NEA). (2011). Preparing 21st Century Students for a Global Society: An Educator’s Guide to the “Four Cs”. Washington: National Education. National Council of Teachers of Mathematics. (2000). Principles and Standards for School Mathematics. Reston, VA: National Council of Teachers of Mathematics. Nunan, D. (2010). Second Language Teaching & Learning. Newbury House of Teacher Development. Michigan: Heinle & Heinle. Partnership for 21st Century Skills. (2011). 21st Century Skills Map: Math. Washington: P21.org. Pusat Kurikulum. (2013). Kurikulum 2013. Jakarta: Depdiknas. Sharan, S. & Sharan, Y. (1992). Expanding Cooperative Learning Through Group Investigation. Colchester, VT: Teachers College Press. Slavin, R.E (1980). Cooperative learning. Review of Educational Research. Vol. 50: 315342. Baltimore, MD: Center for Social Organization of Schools, John Hopkins University. Vygotsky, L. (1978). Mind in Society: The Development of Higher Psychological Processes. Cambridge, MA: Harvard University Press. Wagganer, E.L. (2015). Creating Math Talk Communities. Retrieved from http://www.nctm.org/ Publications/TeachingChildrenMathematics/2015/Vol22/Issue4/CreatingMathTalkCommunities/ Well, G. (2002). Learning and Teaching for Understanding: The Key Role of Collaborative Knowledge Building. Social Constructivist Teaching, Vol. 9, 1–41. Elsevier Science Ltd. Webb, N.M. (2009) The Teacher’s Role in Promoting Collaborative Dialogue in the Classroom. British Journal of Educational Psychology, Vol. 79, 1–28. The British Psychological Society. Retrieved from http://www.bpsjournals.co.uk. William, M. and Burden, R. (1997). Psychology for Language Teachers. Cambridge, UK: Cambridge University Press. Yackel, E., Cobb, P., & Wood, T. (1991). SmallGroup Interactions as a Source of Learning Opportunities in SecondGrade Mathematics. Journal for research in Mathematics Education, Vol. 22 (5). Retrieved from http://mathforum.org 
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TeachingLearning Mathematics in a Virtual Environment. Empirical Evidence in Scenarios of Higher EducationLizzeth Aurora NavarroIbarra, Omar Cuevas Salazar, Julia Xochitl Peralta García & Julio César Ansaldo Leyva
pp. 397408  Article Number: iejme.2017.018
Abstract Tomorrow’s citizens must have the basic tools necessary for total development. Among these tools are mathematics and technology. In the present research we propose taking advantage of technology for teachinglearning mathematics. The objective is to determine whether a Virtual Leaning Environment (VLE) for mathematics can diminish the indexes of failing and improve academic performance. The study has a pretestposttest quasiexperimental design with a nonequivalent control group. The participants are engineering students at the Instituto Tecnológico de Sonora (Technological Institute of Sonora), Mexico. 68 students participated in the experimental group and 60 in the control group. The experimental group studied academic subjects using VLE while the control group studied in a classroom with a professor who explained the concepts. The results show significant difference in the index of failing and academic performance. The implementation of VLE for mathematics would be beneficial to the extent that it is designed using pedagogical practices within a context supported by technology. Keywords: Technology, learning environment, Mathematics, first year university student References Bain, A., & Weston, M. (2012). The Learning Edge. What technology can do to educate all children. New York: Teachers College Press. Bravo, M. (2012). Capítulo 10. Enseñanzaaprendizaje de las matemáticas utilizando como apoyo ambientes virtuales de aprendizaje. In Y. Sandoval, A. Arenas, E. López, J. Cabero y J. Aguaded (Coords.), Las tecnologías de la información en contextos educativos: nuevos escenarios de aprendizaje (pp. 177202). Columbia: Universidad Santiago de Cali. Bulman, G., & Fairlie, R. W. (2016). Chapter 5. Technology and Education: Computers, Software, and the Internet. In E. A. Hanushek, S. J. Machin y L. Woessmann (Eds.), Handbook of the Economics of Education. Volume 5 (pp. 239280). Amsterdam: Elsevier. Cabero, J. (2013). El aprendizaje autorregulado como marco teórico para la aplicación educativa de las comunidades virtuales y los entornos personales de aprendizaje. Revista Teoría de la Educación: Educación y Cultura en la Sociedad de la Información, 14(2), 133156. Cabero, J., & Llorente, M. del C. (2006). La rosa de los vientos: Dominios tecnológicos de las TIC’s por los estudiantes. Sevilla, España: Editorial Marquet@. Childress, M. (2016). 29. Utopian Futures for Learning Technologies. In N. Rushby and D. W. Surry (Eds.), The Wiley Handbook of Learning Technology (pp. 557570). Hoboken, New Jersey: John Wiley & Sons, Inc. Clark, R., & Mayer, R. (2016). ELearning and the Science of Instruction: Proven Guidelines for Consumers and Designers of Multimedia Learning. Hoboken, New Jersey: John Wiley & Sons, Inc. European Commission (2016). A New Skills Agenda for Europe. Working together to strengthen human capital, employability and competitiveness. Communication from the commission to the European parliament, the council, the European economic and social committee and the committee of the regions. Recovered from: http://ec.europa.eu/social/main.jsp?catId=1223 Fullan, M., & Langworthy, M. (2013). Towards a New End: New Pedagogies for Deep Learning. Seattle: Collaborative Impact. Hattie, J., & Yates, G. (2013). Visible Learning and the Science of How We Learn. United Kingdom: Routledge. Khan, B. H. (2016). Revolutionizing Modern Education through Meaningful ELearning Implementatiton. Hershey PA, USA: IGI Global. OCDE (2016). Resultados de PISA 2015. Nota país. México. Recovered from: https://www.oecd.org/pisa/PISA2015MexicoESP.pdf OCDE (2017). Acerca de la Organización para la Cooperación y el Desarrollo Económicos (OCDE). Recovered from: http://www.oecd.org/centrodemexico/laocde/ Onrubia, J. (2016). Aprender y enseñar en entornos virtuales: actividad conjunta, ayuda pedagógica y construcción del conocimiento. RED Revista de Educación a Distancia, 50(3), 114. PISA (2017). Programme for International Student Assessment. PISA en español. Recovered from: https://www.oecd.org/pisa/pisaenespaol.htm PLANEA (2016). Publicación de Resultados 2016. Recovered from: http://planea.sep.gob.mx/content/general/docs/2016/DifusionPLANEA_EMS.pdf PLANEA (2017). Plan Nacional para la Evaluación de los Aprendizajes. Recovered from: http://www.planea.sep.gob.mx/ Salinas, P., Alanís, J., Pulido, R., Santos, F., Escobedo, J., & Garza, J. (2012). Cálculo Aplicado. Competencias matemáticas a través de contextos. Tomo I. D.F., México: Cengage Learning Editores. Silva, J. (2011). Diseño y moderación de entornos virtuales de aprendizaje (EVA). Barcelona, España: Editorial UOC. Zakaria, N. A., & Khalid, F. (2016). The Benefits and Constraints of the Use of Information and Communication Technology (ICT) in Teaching Mathematics. Creative Education, 7, 15371544. 
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Investigating the Mediating Role of Learning Strategies (Cognitive and Metacognitive) between Emotional Intelligence and Academic Performance among Students of Smart and Ordinary SchoolIsmail Sadipour, Soghra Ebrahimi Ghavam, Noorali Farrokhi, Hassan Assadzadeh, Nahid Sameti
pp. 409420  Article Number: iejme.2017.019
Abstract Education system is efficient and successful when the academic achievement of students in different periods shows highest and lowest numbers. Smart schools are an environment that has the potential necessary to accomplish this goal. However, academic performance is affected by many variables. The aim of this study was investigating the mediating role of learning strategies (cognitive and metacognitive) between emotional intelligence and academic performance among students of smart and ordinary school. The study in term of method is predictive correlational. The population in this study consisted of all high school students in Tehran using multistage cluster sampling 583 students were selected as sample. The results showed that the direct and indirect effect of emotional intelligence and achievement motivation on students 'academic performance is significant. The direct and indirect effect of emotional intelligence and achievement motivation on students' academic performance in smart schools is significantly higher than its impact on the academic performance of students in ordinary schools. The role of smart schools in important variables such as emotional intelligence, achievement motivation and academic performance makes the role of smart schools brighter and stronger. Using and applying smart and updated technology, on the one hand, improve the teachinglearning in teachers and students, the teachers and students to use the World Wide Web can upgrade their academic level and the development Keywords: smart schools, emotional intelligence, learning strategies, academic performance References Bakhshi Sureshjani, Leila. (2008). Relationship between emotional intelligence and mental health and academic performance of male and female students of Islamic Azad University PA. Journal of Research in Educational SciencesUniversity Curriculum Development Branch (3) 19, 11697 Barker, S. (2002). A prospective longitudinal investigation of social problemsolving appraisal on adjustment to university, stress, health and academic motivation and performance. Personality & Individual Differences, 35, 569, 591. Baron, R. (2000). The emotional quotient inventory (EQI): A measure of emotional intelligence. Toronto. Canada: multihealth system. BarOn, R. (2005). Baron model of emotionalsocial intelligence (ESI). Consortium for Research on Emotional Intelligence in Organizations.Retrieved November 21, 2009,from http://www.eiconsortium.org/pdf/baron_model_of_emotional_social_intellig nce.pdf. BarOn, R. (2006). The BarOn Model of EmotionalSocial Intelligence (ESI). Psicothema, 18, supl., 1325. Cross, D. R., & Paris, S. G. (1988). Developmental and instructional analyses of children's metacognition and reading comprehension. Journal of Educational Psychology, 80(2), 131142. Falavell, John. H (1377). Cognitive development, translation Farhad Maher, Roshd press Fardanesh, Hashem. (2004). Theoretical Foundations of Educational Technology. Tehran: Samt Fartash K. & Davoudi, S.M.M. (2012). Organizational learning: A key to achieve organizational success and to prevent organizational downfall. Spectrum: A journal of multidisciplinary research, volume 1, issue 2, pp. 1940. Glover, J. M., & Bruning, R.H.(1990). Educational psychology: Principles and Application. Boston: Little, Brown. Goleman, D. (2007). Emotional intelligence: Why it can matter more than IQ. New York, NY: Random House. Goleman, Daniel. (2001). Emotional Intelligence. Translation Nasrin Parsa. Tehran, publisher of growth. (Since publication of the original language, 1995) Good, T., & Brophy, J. (1995). Contemporary educational psychology (5th ed). New York: Harper Collins. Hatami, Javad Taghizadeh, J., and Mohebinia, J. (2012). Relationship between emotional intelligence, selfregulated learning and academic selfconcept and academic performance in high school third grade male students in Kashan city. Journal of Educational Studies and School, 2 (12), 3427 http://dl.eram.shirazu.ac.ir/root/Utility/eLearning/shivehnameh_hoshmandsazi900508.pdf Jafari, Mehdi, Ahmad Zadeh, F. (2014). Check the components of emotional intelligence and academic achievement of students. Journal of Kermanshah University of Medical Sciences. 21 (125), 9285 Matemba, C. K., Awinja, J., Otieno, K. O. (2014). Relationship between Problem Solving Approaches and Academic Performance: A Case of Kakamega Municipality, Kenya. International Journal of Human Resource Studies, 4 (4), 1020. Mesrabadi, J. (2001). The effectiveness of learning strategies for highspeed reading, retention and comprehension in different contexts. MA thesis. Allameh Tabatabaei University Ministry of Education. (2011). A smart way to school. Downloaded from the site: Mirzajani, H., & Delaviz Bayekolaei, M. (2013). Emotional Intelligence of Students in Smart School. MiddleEast Journal of Scientific Research 18 (9): 13221329, 2013. ISSN 19909233. Perera, H, N. (2016): The Role of Trait Emotional Intelligence in Academic Performance: Theoretical Overview and Empirical Update. The Journal of Psychology: Interdisciplinary and Applied, 150 (2), 227249. Pressley, M. Brokowshi, j. G. & Schreider, W. (1987). Cognitive Strategies: good strategy users coordinate metacognation and knowledge. Angals of child Development, V4. 89129. Rastgar AA. & Davoudi, S.M.M. (2012). A study of the relationship between employees’ spiritual intelligence and job satisfaction: A survey in Iran’s banking industry. Spectrum: A journal of multidisciplinary research, volume 1, issue 2, pp. 5774. Rastgar AA. & Davoudi, S.M.M. (2012). The link between workplace spirituality, organizational citizenship behavior and job performance in Iran. Arth Prabhand: A journal of economics and management, volume 1, issue 2, pp. 1329. Saif Ali Akbar. (2008). Modern educational psychology. Tehran: Publication time Seifert & Wheeler, P.(1995). Enhancing motivation: a classroom application of selfinstruction strategy training. Research in Education, 51, 110. Shaveran, HR: Salimi, G., Homaee, Reza. (2008). Measure the academic performance of students based on their multiple cultures. Journal of Isfahan University. (1) 9, 160147 
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Developing of Supplementary Books of Mathematics TeachingLearning Process Basedon Coastal Culture for JHS StudentsZaenuri, Hardi Suyitno, Fathur Rokhman & Amin Suyitno
pp. 421430  Article Number: iejme.2017.020
Abstract The coastal area is a residential area of fishermen. In general, kids of fishing families only elementary schools. Therefore, children need to be motivated to be willing to continue their study in junior high school. Thus, needs and should be made a textbook basedon the coastal culture for junior high school (JHS), which was preceded by research activities. The purpose of this study to make the models of supplementary book of mathematics teachinglearning process basedon coastal culture for JHS students. This research activity was a qualitative research. The activities as follows: (1) exploring the coastal culture that can be used as a means to clarify concepts or materials about math, (2) By Focus Group Discussion activity, was prepared a draft of supplementary books of mathematics teachinglearning process based on coastal culture for JHS students. The result is the model of supplementary book of mathematics teachinglearning process basedon coastal culture for JHS students. The conclusion is that mathematics can have benefits in the lives of fishermen, it is expected that the school could become the foundation for improving the pattern of community life of the fishermen environment in the future for their children. Keywords: coastal culture, mathematics, textbook References Bishop, A.J. (1994). Cultural Conflicts in Mathematics Education: Developing a Research Agenda. For the Learning Mathematics. Vol. 14 No. 2. Eraslan, Meric. (2014). The Analysis of the Thinking Styles and Creativity of the Sports Students Studying in the Different Fields of University. Academic Journal: Educational Research and Reviews. Vol. 9 (20). 23 October 2014. Freudenthal. (1991). Revisiting Mathematics Education. China Lectures. Dordrecht Kluwer: Academic Publishers. Gagne, R.M. (1983). Some Issue in Psychology of Mathematics Instruction. Journal for Research in Mathematics Education. 14(1). Gerdes, P. (1988). On Culture, Geometrical Thinking, and Mathematics Education. Educational Studies in Mathematics. Vol. 19: 137162 Gerdes, P. (1996). “On Ethnomathematics and the Transmission of Mathematical Knowledge In and Outside Schools in Africa South of the Sahara.”Les Sciences Hors D'occidentali Me Siecle. (5): 229246. Gomez, Jose G. (2007). What Do We Know About Creativity?. The Journal of Effective Teaching, Vol. 7, No.1, 2007,3134. Güzel, Hatice. (2004). The Relationship Between Students’ Success in Physics Lessons and Their Attitudes Towards Mathematics. Journal of Turkish Science Education. Volume 1, Issue 1, July 2004. Howell, Beth. (2008). Some Student Teachers’ Conceptions of Creativity in Secondary School English. English Language Teaching, Vol. 1 No.2, December 2008. Lipka, J. and Irhke, D. A. (2009). “Ethnomathematics applied to classrooms in Alaska: Math in a Cultural Context.” Nadjafikhah, M, et al. (2012). Mathematical creativity: some definitions and characteristics. ProcediaSocial and Behavioral Sciences: Elsevier. Available online at www.sciencedirect.com. Nutti, Ylva Jannok. (2013). Indigenous teachers’experiences of the implementation of culturebased mathematics activities in Sámi school. Math Ed Res J (2013) 25:57–72. DOI 10.1007/s1339401300676 Schoenfield, AH. (1987). What’s all the fuss about metacognition? In AH Schoenfield (Ed). Cognitive Science and Mathematics Education, Hillslide, NJ: Lawrence Erlbaum Associates. Schoenfield, AH. (1992). Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics, In DA Grows (Ed). Handbook of Research on Mathematics Teaching and Learning. NCTM. New York: Macmilan Publishing Company. Suyitno, Hardi. (2014). Pengenalan Filsafat Matematika. Semarang: Penerbit FMIPA Universitas Negeri Semarang. Uloko, E.S. & Imoko, B. I. (2007). “Effects of ethno mathematics teaching approach and gender on students’ achievement in Locus.” Journal National Association Social Humanity Education. 5 (1): 3136. UNESCO. 1998. Education For the Twentyfirst Century: Issues and Prospect. UNESCO Publishing. Uzoğlu, Mustafa and Büyükkasap, Erdoğan. (2011). The Relationship Between Seventh Grade Students' Intelligence Areas And Their Academic Success In Science And Mathematics. Journal of Turkish Science Education. Volume 8, Issue 3, September 2011. Wang, Amber Yayin. (2011). Context of Creative Thinking: A Comparison on Creative Performance of Student Teachers in Taiwan and The United States. Journal of International and Crosscultural Studies, Volume 2, Issue 1, 2011. 
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14 
Investigating Performance of Plastic Hinge in Steel Frames by Knee BracingBehzad Dezhkam
pp. 431445  Article Number: iejme.2017.021
Abstract Constructing plastic hinges and the way of their distribution and failure mechanism can play an important role on seismic structures design. Mechanism type affect frame sensitivity toward secondary effects, total and local ductility, energy absorption and structure resistance before damage, general instability and destruction. Failure mechanism of moment frames under earthquake effect could be mentioned as three general types (first, second and third). The first type resulted from constructing hinges in beams and columns in the first few story up, the second one resulted from constructing hinges in beams and columns of few upper story and the third type including mechanism of one middle floor. Failure mechanism of general type is a special mode of the second type mechanism in which, plastic hinges locating at the two ends of beams and the first floor columns near the connection to the foundation. Based on researches, this type of mechanism shows the most amount of energy absorption against earth quack. Knee bracing frame is appropriate as an energy dissipation system composed of ductility and lateral stiffness which has good performance against lateral loads specially earthquake. In this paper, forming plastic hinges of components and the base shear of different steel systems and comparing them with knee bracing lateral load system in three, five and seven story frames using regulations of FEMA356 and ATC40. Keywords: Plastic hinge, Steel frames, Knee bracing References Kalkan E. and Kunnath S. K. (2004), "Method of modal combinations for pushover analysis of buildings," in Proc. Of the 13 th World Conference of Earthquake Engineering. Khatib I. F., Mahin S. A., and Pister K. S. (1988), Seismic behavior of concentrically braced steel frames vol. 88: Earthquake Engineering Research Center, University of California. Uriz P. (2008), Toward earthquakeresistant design of concentrically braced steelframe structures: Pacific Earthquake Engineering Research Center. AristizabalOchoa J. D. (1986), "Disposable knee bracing: improvement in seismic design of steel frames," Journal of Structural Engineering, vol. 112, pp. 15441552. Roeder C. W.and Popov E. P. (1978), "Eccentrically braced steel frames for earthquakes," Journal of the Structural Division, vol. 104, pp. 391412. Naeemi M. and Bozorg M. (2009), "Seismic Performance of Knee Braced Frame," Proceedings of World Academy of Science: Engineering & Technology, vol. 50,pp 976980. Kim J.and Seo Y. (2003), "Seismic design of steel structures with bucklingrestrained knee braces," Journal of Constructional Steel Research, vol. 59, pp. 14771497. Balendra T., Sam M. T., and Liaw C. Y. (1990), "Diagonal brace with ductile knee anchor for aseismic steel frame," Earthquake engineering & structural dynamics, vol. 19, pp. 847858. Agency F. E. M. (2000), "Prestandard and Commentary for the Seismic Rehabilitation of Buildings: FEMA356," ed: Federal Emergency Management Agency Washington. Code U. B. (1997), "UBC 97, Code for Seismic Design of Buildings (1997 Edition)," Structural Engineering Design Provisions, vol. 2. Balendra T., Sam M.T., Liaw C.Y., and Lee S.L. (1991), "Preliminary studies into the behaviour of knee braced frames subject to seismic loading," Engineering Structures, vol. 13, pp. 6774. FEMA A. (2005), "440, Improvement of nonlinear static seismic analysis procedures," ed: Federal Emergency Management Agency, Washington DC. Elnashai A. S. (2001), "Advanced inelastic static (pushover) analysis for earthquake applications," Structural engineering and mechanics, vol. 12, pp. 5170. Krawinkler H.and Seneviratna G. (1998), "Pros and cons of a pushover analysis of seismic performance evaluation," Engineering Structures, vol. 20, pp. 452464 Chopra A. K.and Goel R. K. (2002), "A modal pushover analysis procedure for estimating seismic demands for buildings," Earthquake engineering & structural dynamics, vol. 31, pp. 561582. Chopra A. K., Goel R. K., and Chintanapakdee C. (2004), "Evaluation of a modified MPA procedure assuming higher modes as elastic to estimate seismic demands," Earthquake Spectra, vol. 20, pp. 757778. Ghodrati,A and Eghbali,M (2011)"New method of two line pushover for seismic evaluation of steel frames. 5th natinal congress of construction engineering. Mashhad.

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15 
Adoption of Instant Messaging for Mathematics Lessons in Rural SchoolsNkhangweni Lawrence Mashau & Sello Nicolas Mokwena
pp. 447462  Article Number: iejme.2017.022
Abstract The failure rate of mathematics is significantly high in the South African public secondary schools, particularly in rural areas. South Africa has a deficiency of adequately qualified teachers, particularly in mathematics in rural public schools. A lack of interest in a teaching as a career results in fewer young people taking up teaching as a profession, this contributes to shortage of teachers. Instant messaging applications, specifically Mxit provide a platform which learners and teachers can use for learning mathematics. Mxit which is more popular amoung teenagers who use it for communication with their friends and relatives offers mathematics tutoring through Dr Math application hosted by the CSIR Meraka Institute in South Africa. The aim of this study was to establish how pupils and teachers in the rural areas where there is a dire shortage of mathematics teacher can take advantage of Dr Math to improve mathematics knowledge and the matric pass rate. Diffusion of innovation theory was used to determine factors that could promote the adoption of instant messaging for learning mathematics in South African rural public schools. Dr Math has not been well promoted among rural schools and therefore lack of its awareness was found as one of the factors hampering learners to adopt it for learning mathematics in South Africa rural public schools. Keywords: Adoption, Dr Math, Instant Messaging, Learning, Mathematics and Mxit References AlJabri, I.B., & Sohail, M.S. (2012). Mobile Banking Adoption: Application of Diffusion of Innovation theory. Vol 13. No4. Saudi Arabia: College of Industrial Management. Babbie, E. (2007). The practice of social research. (11th edition). Belmont: Wadsworth. Beger, G., & Sinha, A. (2012). South Africa Mobile Generation: Study on South AfricaYoung people on mobiles. New York: Unicef. Bryman, A. (2001). Social Research Methods. New York: Oxford University Press. Butgereit, L. (2009). How Dr Math reaches Pupils with Competitions and Computer Games by using Mxit. Pretoria: ISTAfrica. Butgereit, L. (2011). Seven Characteristics of a Successful Virtual Volunteering Platform. South Africa: ISTAfrica. Butgereit, L.L., & Botha, R.A. (2011). A Lucene stemmer for Mxit lingo. South Africa: Annual Conference on World Wide Web Applications. Butgereit, L., & Botha R.A. (2012). Automated Topic Spotting Provides Added Efficiency in a Chat Based Tutoring Environment. South Africa: ISTAfrica. Casey, M., & Hoehler, J. (2013). Engagement with mobile application. Johannesburg: Deloite & Touche. Cooper, R.C., & Schindler, P.S. (2003). Business Research Methods. New York: McGrawHill. Country report South Africa (2013). General Education System Quality Assessment. South Africa: 9781431518661. Dewitt, D., Siraj, S., & Alias, N. (2014). Collaborative mLearning: A Module for Learning Secondary School Science. Malaysia: International Forum of Educational Technology & Society IFETS). Erasmus, P. (2013). Relationship between emotional intelligence, study orientation in maths and maths achievement of middle adolescent boys and girls. South Africa: North West. Proceedings of the Global Summit on Education (GSE2013). Gerrand, P., & Cunningham, J.B. (2003). The diffusion of Internet banking among Singapore consumers. International Journal of Bank Marketing. Graham, S.E., & Provost, L.E. (2012). Mathematics achievement gaps between suburban learners and their rural and urban peers increase over time. Issue brief NO. 52. Durham: The Carsey Institute at the Scholars' Repository. Graven, M.H. (2013). Poverty, inequality and mathematics performance: the case of South Africa’s postapartheid context. South Africa: Grahamstown. Springer. Haskis, B., & Botha, A. (2013). Identify Tag Word Counterparts for Dr Math. South Africa: AA AI Spring Symposium. Hernandez, J. & Mazzon, J. (2007). Adoption of internet banking: proposition and implementation of an integrated methodology approach. Marketing, 25(2). Hofstee, E. (2011). Constructing a Good Dissertation. Sandton. Interpark Books. Junco, R., & Cotton, S.R. (2010). Perceived academic effects of instant messaging use. USA: Elservier. Kim, H., Lee, M., & Kim, M. (2014). Effects of Mobile Instant Messaging on Collaborative Learning Processes and Outcomes: The Case of South Korea. South Korea: International Forum of Educational Technology & Society (IFETS). Kogg, B. (2002). The role of theory in case study research. PhD course in Research methodology 20021208. Kumar, A., Tewari, A., Shroff, G., Chittamuru, D., Kam, M., & Canny, J. (2010). An Exploratory Study of Unsupervised Mobile Learning in Rural India. USA: HumanComputer Interaction Institute. Kwapisz, J.R., Weiss, G.M., & Moore, S.A. (2010). Activity Recognition using Cell phone Accelerometers. Volume 12. Issue 2. USA: SIGKDD Explorations. Limpopo Basic Education (2014). School performance report Limpopo. Limpopo: Basic Education. Limpopo Department of Education (2014). Strategic Performance Plans. Polokwane: Limpopo Department of Education. Lumandi, M.W. (2014). Reversing the Trend of Dismal Perfomance in Disadvantaged Schools: A Curriculum Evaluation exercise. RomeItaly: MCSER. McDaniel, C., & Gates, R. (2002). Marketing Research. Singapore: SouthWestern. Maphalala, M.C., & Nzama, M.V. (2014). The Proliferation of Cell phones in High Schools: The Implications for the Teaching and Learning Process. RomeItaly: MCSER Publishing. Mokwena, S.N. (2011). Factors influencing the acceptance and use of a school administration and management system in South African high schools. UnpublishedPhD thesis. Pretoria: Tshwane University of technology. Mouton, J. (2001). How to succeed in your Master’s and Doctoral Studies: A South African Guide and Resource Book. (13th edition). Pretoria: Van Schaik. Neuman, W.L. (2007). Basic of Social Research, Qualitative and Quantitative Approaches. (2nd ed). Boston: Person Education, Inc. Ojose, B. (2011). Mathematics Literacy: Are We Able To Put The Mathematics We Learn Into Everyday Use?. Vol. 4 USA: Redlands. OXFORD South Africa Concise Dictionary (2010). South Africa: Megan Hall. QuanHaase, A., & Young, A.L. (2010). Used and Gratification of Social Media: A Comparison of Facebook and Instant Messaging. USA: Bulletin of Science, Technology and Society. Reed, M., Jotischky, N., Newman, M., Mbongue, T., & Escofet, G. (2014). Africa Telecoms Outlook2014, Maximizing digital service opportunities. London: Informa telecoms & media. Robbins, B. (2013). Extending the Dialogue: Interactional and Multimodal Strategies in Synchronous Mobile Mathematics Tutoring on MXit. Cape Town: University of Cape Town. Rogers, E.M. (1995). Diffusion of Innovation, (4th edition). New York: Free Press. Rogers, E.M. (1983). Diffusion of Innovations. New York: Free press. Roux, K., & Dalvit, L. (2014). Mobile Women: Investigating the Digital Gender Divide in Cell phone Use in South Africa Rural Area. South Africa: 401416. Ruan, Q. (2013). Can Instant Messaging Platform QQ Help Solving the Deficiency of EFL Learners' Critical Literacy in China?. China: Atlantis Press. Sekaran, U. (2003). Research Methods for Business: A SkillBuilding Approach, (4th edition). New York: John Wiley & Sons, Inc. Shambare, R., Rugimbana, R., & Sithole, N. (2012). Social networking habits among learners. African Journal of Business Management. Pretoria: Academic Journals, 6(2):578786. Shi, X. (2011). Exploring factors that hinder the adoption of Mobile Services in China A qualitative user analysis with special focus on mobile financial services. University School of economics: Aalto. South Africa mobile report (2014). A Survey of Desktop User’s Attitude and Uses of Mobile Phone. South Africa: iab. Swanepoel, T. (2011). Cybersex and Addiction: A Quantitative Examination of the Use of Mxit Among Adolescents in South Africa. South Africa: UCT Tachie, S.A., & Chireshe, R. (2013). Higher Failure Rate in Mathematics Eximanition in Rural Senior Secondary Schools in Mthatha District, Eastern Cape: Learners’ Attributions. South Africa: KamlaRaj. Tan, M., & Teo, T.S.H. (2000). Factors influencing the adoption of Internet banking. J.Assoc. Info. Syst. 1(5): 2238. Tewari, D.D. (2014). Is Matric Math a Good Predictor of Student’s Perfomance in the First Year of University Degree? A Case Study of Faculty of Management Studies, University of KwazuluNatal, South Africa. South Africa: Kamlaraj. Vosloo, S. (2008). Using Mxit to learn. [Online] Available from: http://www.thoughtleader.co.za/stevevosloo/2008/01/18/usingmxittolearn/. [Accessed 23 April 2015]. Wang, W., Hsieh, J.P., & Song, B. (2010). Understanding User Satisfaction of Instant Messaging Usage: An Empirical Study. China: Natural Science Foundation. Welman, J., & Kruger, S. (2005). Research Methodology. Cape Town: Oxford University Press. Yin, R.K. (2011). Qualitative research from start to finish. New York, NY: The Guilford Press. 
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16 
Vietnamese students’ problemsolving skills in learning about error of measurementsTang Minh Dung & Pham Mong Bao
pp. 463474  Article Number: iejme.2017.023
Abstract Problemsolving is one of the ten core competences that Vietnam’s new comprehensive general education program after 2018 focuses on. Based on the following findings that (a) in the history of mathematics, error and statistics have a closely related relationship with each other but in the current mathematic curriculum, they are taught separately, and (b) in Vietnam, there has not been any research on teaching error of measurements in the current curriculum, this research focuses on assessing Vietnamese students’ problemsolving skills in dealing with errors using statistical tools. The research was conducted following two paralleled approaches: (1) analyzing academic materials according to praxeological organization in relation to components of problemsolving skills so as to clarify the formation and development of problemsolving skills through the education system, (2) building an experiment of processing errors using statistical tools that students have learned in the curriculum and evaluating the degree of problemsolving skills of a sample of 201 students randomly chosen in Ho Chi Minh City. Research results show that although processing errors using statistics has been presented in Mathematics and Physics textbooks, the majority of student failed to propose a solution in the experiment. The research questions the practical teaching of teachers and teacher training in pedagogical universities as well as provides an evaluation of the reality of the current educational system, contributing to the development of mathematics curriculum and textbook composition after 2018. Keywords: Problemsolving skills; error; statistics References Bessot, A., Comiti, C., Le Thi, H. C. & Le Van, T. (2009). Elements fondamentaux de didactique des mathématiques. Ho Chi Minh City: Ho Chi Minh City National University Publisher. Boyé, A. & Comairas, M.C. (2002) Moyenne, mediane, écarttype. Quelques regards sur l’histoire pour éclairer l’enseignement des statistiques. RepèresIREM, 48, 2740. Chevallard, Y. (1999). Analyse des pratiques enseignantes en théorie anthropologique du didactique. Recherche en didactique des mathématiques, 19(2), 221265. Le Thai Bao, T. T. (2012) Approximate number in high school mathematics education. Journal of Science – Special Issue: Education science (Ho Chi Minh City University of Education), 37, 103113. Le Thi, B. H. (2012) Nghiên cứu didactic sự nối khớp giữa máy tính bỏ túi và xấp xỉ thập phân trong phép tính số: Trường hợp giải tam giác (Master’s Thesis). Ho Chi Minh city: Ho Chi Minh City University of Education. Phan, A. T. (2014) Assessment of the problemsolving ability of the students in teaching grade 11 mathematics at middle school (PhD Thesis). Vinh: Vinh University. Polya, G. (1945). How to solve it. Princeton, NJ: Princeton University Press. Schoenfeld, A. H. (1992). Learning to think mathematically: Problemsolving, metacognition, and sense making in mathematics. In D. A. Grouws (Ed.) Handbook of research on mathematics teaching and learning (pp.334370). New York: Macmillan. Toh, T. L., Quek, K. S., Leong, Y. H., DinDyal, J. & Tay, E. G. (2011) Assessing problemsolving in the mathematics curriculum: A new approach. In B. Kaur, & K. Y. Wong (Eds.) Assessment in the mathematics classroom: Association of Mathematics Educators 2011 Yearbook (pp.3366). Singapore: World Scientific. Vu Thi, T. T. (2014) Một nghiên cứu về số gần đúng và sai số trong dạy học toán ở bậc phổ thông (Master’s Thesis). Ho Chi Minh City: Ho Chi Minh City University of Education. 
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17 
Metacognition and Cooperative Learning in the Mathematics ClassroomKhalid S. Alzahrani
pp. 475491  Article Number: iejme.2017.024
Abstract Based on theoretical notions of metacognition in light of the reality of mathematics learning and teaching in Saudi Arabia, this study aimed to explore a teacher’s and students’ perceptions of the nature of the relationship between cooperative learning and an improvement in metacognition. Consequently, a case study design was favoured in order to suit the research agenda and meet its aims. The participants consisted of one case study class from a secondary school in Saudi Arabia. Semistructured interviews and classroom observation were used for data collection. The findings of the data analysis asserts that metacognition can be assisted through the creation of a suitable sociocultural context to encourage the social interaction represented in cooperative learning. This has a role in motivating the establishment of metacognition, as the absence of this social interaction would impede this type of learning. The importance of the student’s role in learning through metacognition was asserted by this study. Keywords: Metacognition, Cooperative Learning and Mathematics Learning References Adey, P., Robertson, A., & Venville, G. (2001). Let's Think! A Programme for Developing Thinking with Five and Six Year Olds.: Slough: NFER Nelson. Artz, A. F., & ArmourThomas, E. (1992). Development of a cognitivemetacognitive framework for protocol analysis of mathematical problem solving in small groups. Cognition and instruction, 9(2), 137175. Artzt, A. F., & Newman, C. M. (1997). How to use cooperative learning in the mathematics class: ERIC. Azevedo, R., & Aleven, V. (2013). Metacognition and learning technologies: an overview of current interdisciplinary research International handbook of metacognition and learning technologies (pp. 116): Springer. Bernard, M., & Bachu, E. (2015). Enhancing the Metacognitive Skill of Novice Programmers Through Collaborative Learning Metacognition: Fundaments, Applications, and Trends (pp. 277298): Springer. Blatchford, P., Kutnick, P., Baines, E., & Galton, M. (2003). Toward a social pedagogy of classroom group work. International Journal of Educational Research, 39(1), 153172. Braun, V., & Clarke, V. (2006). Using thematic analysis in psychology. Qualitative research in psychology, 3(2), 77101. Brown, A. (1987). Metacognition, Executive Control, Self Regulation and Mysterious Mechanisms. In R. K. Franz E. Weinert (Ed.), Metacognition, Motivation and Understanding (3 ed., pp. 65117). The University of Michigan: L. Erlbaum Associates. Buratti, S., & Allwood, C. M. (2015). Regulating Metacognitive Processes—Support for a Metametacognitive Ability Metacognition: Fundaments, Applications, and Trends (pp. 1738): Springer. Chinn, C. (2010). Collaborative and cooperative learning Encyclopedia of crosscultural school psychology (pp. 229232): Springer. Coles, A. (2013). Being alongside: for the teaching and learning of mathematics: Springer Science & Business Media. Desoete, A. (2007). Evaluating and improving the mathematics teachinglearning process through metacognition. Electronic Journal of Research in Educational Psychology, 5(3), 705730. Flavell, J. H. (1979). Metacognition and cognitive monitoring. American Psychologist, 34(10), 906911. Goos, M., & Galbraith, P. (1996). Do it this way! Metacognitive strategies in collaborative mathematical problem solving. Educational studies in mathematics, 30(3), 229260. Hartman, H. (2015). Engaging Adolescent Students’ Metacognition Through WebQuests: A Case Study of Embedded Metacognition Metacognition: Fundaments, Applications, and Trends (pp. 135166): Springer. Hinsz, V. B. (2004). Metacognition and mental models in groups: An illustration with metamemory of group recognition memory. Paper presented at the Annual Society for Experimental Social Psychology Preconference on Small Groups, Fourth, Oct, 1996, Sturbridge Village, MA, US; Portions of this research were presented at the aforementioned conference. Hogan, M. J., Dwyer, C. P., Harney, O. M., Noone, C., & Conway, R. J. (2015). Metacognitive skill development and applied systems science: A framework of metacognitive skills, selfregulatory functions and realworld applications Metacognition: Fundaments, applications, and trends (pp. 75106): Springer. Hurme, T.R., Järvelä, S., Merenluoto, K., & Salonen, P. (2015). What Makes Metacognition as Socially Shared in Mathematical Problem Solving? Metacognition: Fundaments, Applications, and Trends (pp. 259276): Springer. Kluwe, R. H. (1982). Cognitive knowledge and executive control: Metacognition Animal mind—human mind (pp. 201224): Springer. Kramarski, B., & Mevarech, Z. R. (2003). Enhancing mathematical reasoning in the classroom: The effects of cooperative learning and metacognitive training. American Educational Research Journal, 40(1), 281310. Larkin, S. (2006). Collaborative group work and individual development of metacognition in the early years. Research in Science Education, 36(12), 727. Merriam, S. B. (1998). Qualitative Research and Case Study Applications in Education: Revised and Expanded from Case Study Research in Education. San Francisco: Jossey Bass Wiley. Mevarech, Z., & Kramarski, B. (1997). IMPROVE: A multidimensional method for teaching mathematics in heterogeneous classrooms. American Educational Research Journal, 34(2), 365394. Moga, A. (2012). Metacognitive Training Effects on Students Mathematical Performance from Inclusive Classrooms. (PhD), BabeșBolyai University, ClujNapoca. Mokos, E., & Kafoussi, S. (2013). Elementary Student'Spontaneous Metacognitive Functions in Different Types of Mathematical Problems. Journal of Research in Mathematics Education, 2(2), 242267. Panitz, T. (1999). Collaborative versus Cooperative Learning: A Comparison of the Two Concepts Which Will Help Us Understand the Underlying Nature of Interactive Learning. Retrieved from ERIC website: http://eric.ed.gov/?id=ED448443 Pannitz, R. (1996). A definition of collaborative vs. cooperative learning. Cooperative Learning and College Teaching. http://www.londonmet.ac.uk/deliberations/collaborativelearning/panitzpaper.cfm. Rockwood, R. (1995). National Teaching and Learning Forum. Paper presented at the National Teaching and Learning Forum. SandiUrena, S., Cooper, M., & Stevens, R. (2012). Effect of cooperative problembased lab instruction on metacognition and problemsolving skills. Journal of Chemical Education, 89(6), 700706. Stake, R. E. (1995). The art of case study research: Sage Publications. 
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18 
Vocational High School Students’ Perceptions of Success in MathematicsHuseyin Ozdemir & Neslihan OnderOzdemir
pp. 493502  Article Number: iejme.2017.025
Abstract Knowledge of mathematics is significant for each society because mathematics “acts as a ‘gatekeeper’ to social progress” (Gates & VistroYu, 2003, p. 32) and also a gateway for a good profession. The Programme for International Student Assessment (PISA) 2015 was completed by approximately 540,000 15yearold students and published in 2016 PISA report. The 2016 PISA report showed that among 72 countries and economies, Turkey lagged behind most of the countries, i.e., 49th in mathematics, 52nd in science and 50th in reading. Given the state of Turkey, the problems in education should be scrutinised across subjects, including maths. To address this apparent proven problem, we conducted research on vocational high school students (i.e., mostly disadvantaged students). To the best of our knowledge, Turkish students’ perceptions of success in mathematics who are studying in a vocational high school are underresearched. In light of this gap, the present longitudinal study sets out to investigate Turkish Vocational and Technical High School students’ perceptions as learners of mathematics to contribute to the literature (n=165). Openended questions were asked whether students believe that they are successful or unsuccessful and the underlying reasons why. The data were collected through a facetoface structured interview and classroom observation. Among 165 vocational high school students, 61 of them believed that they were successful, 93 believed that they were unsuccessful and 11 students were hesitant. Reasons why students believed they are successful or unsuccessful were collected under five salient themes as follows: (i) reasons arising from students themselves; (ii) reasons arising from students’ perceptions of maths course//their maths abilities, (iii) reasons arising from maths teacher, (iv) reasons arising from students’ educational background, (v) reasons arising from the milieu. Keywords: Success in mathematics, vocational education, vocational students References Aytaş, A., Panal, A., Türker, H. & Oğulcu, F. (2000). Anadolu teknik liselerinde verilen eğitimin etkinliğinin değerlendirilmesi. Ankara: Mesleki ve Teknik Eğitim Araştırma ve Geliştirme Merkezi Başkanlığı. Bandura, A. (1993). Perceived selfefficacy in cognitive development and functioning. Educational Psychologist, 28(2), 117148. Berelson, B. (1952). Content analysis in communication research. Education, 31(4), 454482. Birgin, O., Baloğlu, M., Çatlıoğlu, H. & Gürbüz, R. (2010). An investigation of mathematics anxiety among sixth through eighth grade students in Turkey. Learning and Individual Differences, 20(6), 654658. Borisovaa, O. V., Vasbievaa, D. G., Malykhb, N. I., Vasnevc, S. A. & Vasnevad, N. N. (2017). Trends and Challenges in Development of Continuing Vocational Education and Training in Russia. IEJME, 12(1), 6978. Bulut, M. (2007). Curriculum reform in Turkey: A case of primary school mathematics curriculum. Eurasia Journal of Mathematics, Science & Technology Education, 3(3), 203212. Carlson, M. P. (1999). The mathematical behavior of six successful mathematics graduate students: Influences leading to mathematical success. Educational Studies in Mathematics, 40(3), 237258. Das J. P. & Janzen, C. (2004). Learning Math: Basic concepts, math difficulties and suggestions for intervention. Developmental Disabilities Bulletin, 32(2), 191 205. Garofalo, J. (1989). Beliefs, responses, and mathematics education: Observations from the back of the classroom. School Science and Mathematics, 89(6), 451455. Gates, P. & VistroYu, C. P. (2003). Is mathematics for all? In Second international handbook of mathematics education. Netherlands: Springer. Hannover, B. & Kessels, U. (2004). Selftoprototype matching as a strategy for making academic choices. Why high school students do not like math and science. Learning and Instruction, 14(1), 5167. Hannula, M. S. (2002). Attitude towards mathematics: Emotions, expectations and values. Educational studies in Mathematics, 49(1), 2546. Kaufman, R. A., & English, F. W. (1979). Needs assessment: Concept and application. Educational Technology, 14(2), 164177. Kiryakova, A. V., Tretiakovb, A. N., Kolgac, V. V., Piralovad, O. F. & Dzhamalovae, B. B. (2016). Experimental Study of the Effectiveness of College Students’ Vocational Training in Conditions of Social Partnership. IEJME, 11(3), 457466. Kloosterman, P. & Stage, F. K. (1992). Measuring beliefs about mathematical problem solving. School Science and Mathematics, 92(3), 109115. Kutueva, R. A., Mashkinb, N. A., Yevgrafovac, O. G., Morozovd, A. V., Zakharovae, A. N. & Parkhaevf, V. T. (2017). Practical Recommendations on the Organization of Pedagogical Monitoring in Institutions of Vocational Education. IEJME, 12(1), 313. Leder, G. C., Pehkonen, E. & Törner, G. (2006). Beliefs: A hidden variable in mathematics education? NewYork: Springer Science & Business Media. Longo, G. (1999). Mathematical intelligence, infinity and machines: beyond Godelitis. Journal of Consciousness Studies, 6(12), 191214. Lubienski, S. T. (2000). Problem solving as a means toward mathematics for all: An exploratory look through a class lens. Journal for Research in Mathematics, 15(2), 143155. Mane, F. (1999). Trends in the payoff to academic and occupationspecific skills: the short and medium run returns to academic and vocational high school courses for noncollegebound students. Economics of Education Review, 18(4), 417437. Mohr, C. (2008). Aligning classroom instruction with workplace skills: Equipping CTE students with the math skills necessary for entrylevel carpentry. Techniques: Connecting Education and Careers, 83(8), 34–38. Nicholls, J. G., Cobb, P., Wood, T., Yackel, E. & Patashnick, M. (1990). Assessing students' theories of success in mathematics: Individual and classroom differences. Journal for Research in Mathematics Education, 21(2), 109122. Nogay, S. (2007). Türkiye’de meslek eğitimi sorunu ve çözüm önerisi. Ankara: Meslekî ve Teknik Öğretim Derneği Genel Merkezi. Odell, P. & Schumacher, P. (1998). Attitudes toward mathematics and predictors of college mathematics grades: Gender differences in a 4Year business college. The Journal of Education for Business, 74(1), 3438. OECD. (2004). Learning for tomorrow’s world – first results from PISA 2003. Paris: PISA OECD Publishing OECD. (2016). PISA 2015 Results. Excellence and Equity in Education. Paris: PISA OECD Publishing Ozgen, K., & Bindak, R. (2011). Determination of SelfEfficacy Beliefs of High School Students towards Math Literacy. Educational Sciences: Theory and Practice, 11(2), 10851089. Rudduck, J. & Flutter, J. (2000) Pupil Participation and Pupil Perspective: ‘carving a new order of experience'’. Cambridge Journal of Education, 30(1), 7589. Saunders, J. (2005). Gender and technology in education. A research review. The handbook of gender and education. London: Sage Publications. Schoenfeld, A. H. (1989). Explorations of students' mathematical beliefs and behavior. Journal for Research in Mathematics Education, 3, 338355. Stanic, G. M. & Hart, L. E. (1995). Attitudes, persistence, and mathematics achievement: Qualifying race and sex differences. New directions for equity in mathematics education, 2, 258276. Usul, H., Eroğlu, H. & Akın, O. (2007). Meslek liseleri ve meslek yüksek okullarındaki eğitim süreçleri arasındaki uyum sorununun analizi ve ticaret lisesi örneği. Selçuk Üniversitesi Karaman İktisadi ve İdari Bilimler Fakültesi Dergisi, 12, 235–243. Weber, R. P. (1990). Basic content analysis (No. 49). Sage. Weinstein, G. & Fantini, M. D. (1970). Toward humanistic education: A curriculum of affect. London: Routledge. Williams, P. (2008). Independent review of mathematics teaching in early years settings and primary schools: final report. London: DCSF publications. Wolf, A. (2011). Review of vocational education: The Wolf report. Education, 17(3), 454482. Woods, P. (1990). The Happiest Days? How pupils cope with school. London: Falmer Press. 
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19 
Assessment for Learning in the Calculus Classroom: A Proactive Approach to Engage Students in Active LearningReem Jaafar & Yan Lin
pp. 503520  Article Number: iejme.2017.026
Abstract There is a variety of classroom assessment techniques we can use in the college classroom (Angelo and Cross, 1993). In an effort to diagnose and identify gaps between students’ learning and classroom teaching, we implemented weekly short assessments in a calculus I classroom at an urban community college in the United States. The goals of these assessments were to identify misconceptions, and address them using an appropriate intervention. In this paper, we share these assessments, how they can be used to cement students’ conceptual learning, and how it can help the instructor develop insights into students’ misunderstandings. We also share students’ feedback, challenges and implications for practitioners. Keywords: Assessment, calculus, community college References Angelo, T. A., & Cross, K. P. (1993). Classroom Assessment Techniques: A Handbook for College Teachers.Second Edition (2nd ed.). San Fransisco, CA: JosseyBass. Attorps, I., Björk, K., Radic, M., & Tossavainen, T. (2013). Varied Ways to Teach the Definite Integral Concept. SOURCE International Electronic Journal of Mathematics Education, 8(23), 8199. Bailey, T., Jeong, D. W., & Cho, S. (2010). Referral, enrollment, and completion in developmental education sequences in community colleges. Economics of Education Review, 29(2), 255270. doi:10.1016/j.econedurev.2009.09.002 Bean, J. C. (2011). Engaging ideas: The professor's guide to integrating writing, critical thinking, and active learning in the classroom. San Francisco: JosseyBass. Bonwell, C. C., &Eison, J. A. (1991). Active learning: Creating excitement in the classroom. ASHEEric Higher Education Report No. 1. Washington, DC.: George Washington University. Bolte, L. A. (1999). Using Concept Maps and Interpretive Essays for Assessment in Mathematics. School Science and Mathematics, 99(1), 1930. doi:10.1111/j.19498594.1999.tb17442.x Cross, K. P. (2003). Techniques for Promoting Active Learning. League for Innovation in the Community College Educational Testing Service, AZ: The Cross Papers #7. Cullinane, M. J. (2011). Helping Mathematics Students Survive the PostCalculus Transition. PRIMUS, 21(8), 669684. doi:10.1080/10511971003692830 Dawkins, P. C., & Epperson, J. A. (2014). The development and nature of problemsolving among firstsemester calculus students. International Journal of Mathematical Education in Science and Technology, 45(6), 839862. doi:10.1080/0020739x.2014.884645 Güçler, B. (2013). Examining the discourse on the limit concept in a beginninglevel calculus classroom. Educational Studies in Mathematics (2013), 82, 439–453. Idris, N. 2009. Enhancing Students' Understanding in Calculus Through Writing. International Electronic Journal of Mathematics Education. 4(1): 3655. Iannone, P., & Simpson, A. (2015). Students' preferences in undergraduate mathematics assessment. Studies in Higher Education, 40(6), 10461067. Retrieved from http://dx.doi.org/10.1080/03075079.2013.858683 Jaafar, R. (2016). WritingtoLearn Activities to Provoke Deeper Learning in Calculus. PRIMUS, 26(1), 6782. doi:10.1080/10511970.2015.1053642 Kinley, (2016). Grade Twelve Students Establishing the Relationship Between Differentiation and Integration in Calculus Using graphs. IEJMEMathematics Education, 11(9), 33713385. Maharaj, A., & Wagh, V. (2014). An outline of possible precourse diagnostics for differential calculus. South African Journal of Science, 110(7/8), 17. doi:10.1590/sajs.2014/20130244 Meyers, C., & Jones, T. B. (1993). Promoting active learning: Strategies for the college classroom. San Francisco, CA: JosseyBass. National Research Council, & Bass, H. (1993). Measuring what counts: Conceptual guide for mathematics assessment. Washington, DC: National Academy Press. Porter, M. K., & Masingila, J. O. (2000). Examining the effects of writing on conceptual and procedural knowledge in calculus. Educational Studies in Mathematics, 42(2), 165–177. Pugalee, D. K. (2001). Writing, Mathematics, and Metacognition: Looking for Connections Through Students' Work in Mathematical Problem Solving. School Science and Mathematics, 101(5), 236245. doi:10.1111/j.19498594.2001.tb18026.x Robert, A., & Speer, N. (2001). Research on the teaching and learning of calculus/elementary analysis. In D. Holton (Ed.), The Teaching and Learning of Mathematics at University Level: An ICMI Study (Vol. 7, pp. 283–299). Dordrecht & Boston: Kluwer Academic Publishers. Rybolt, W., & Recck, G. (2012). Conceptual versus Computational Formulae in Calculus and Statistics Courses. The International Journal of Technology, Knowledge, and Society: Annual Review, 8(2), 16. doi:10.18848/18323669/cgp/v08i02/56287. Scheja, M., & Pettersson, K. (2009). Transformation and contextualization: conceptualizing students’ conceptual understandings of threshold concepts in calculus. Higher Education, 59(2), 221241. doi:10.1007/s1073400992447 Thompson, P. W. (1994). Images of rate and operational understanding of the fundamental theorem of calculus. Educational Studies in Mathematics, 26(23), 229274. doi:10.1007/bf01273664 Vincent, B., LaRue, R., Sealey, V., & Engelke, N. (2015). Calculus students' early concept images of tangent lines. International Journal of Mathematical Education in Science and Technology, 46(5), 641657. doi:10.1080/0020739x.2015.1005700. Yoder, J., & Hochevar, C. (2005). Encouraging Active Learning Can Improve Students' Performance on Examinations. Teaching of Psychology, 32(2), 9195. doi:10.1207/s15328023top3202_2 
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Metacognition and Its Role in Mathematics Learning: an Exploration of the Perceptions of a Teacher and Students in a Secondary SchoolKhalid S. Alzahrani
pp. 521537  Article Number: iejme.2017.027
Abstract The study aims to explore teachers’ and students’ perspectives regarding metacognition and its role in mathematics learning. The use of case study was a methodical means to achieve elaborate data and to shed light on issues facing the study. The participants consisted of a case study class from a secondary school in Saudi Arabia. The instruments used for data collection were semistructured interviews and classroom observation. The data produced essential finding based on thematic analysis techniques, regarding study’s aim. Firstly, the traditional method can hinder mathematics teaching and learning through metacognition. Secondly, although metacognitive mathematics instruction should be planned, the strategy that is introduced should be directly targeted at improving the monitoring and regulation of students’ thought when dealing with mathematics problems. Keywords: Metacognition, Mathematics, IMPROVE Programme References Almeqdad, Q. I. (2008). Selfexplanation and explanation in children with learning difficulties. University of Cambridge. Azevedo, R., & Aleven, V. (2013). Metacognition and learning technologies: an overview of current interdisciplinary research International handbook of metacognition and learning technologies (pp. 116): Springer. Bernard, M., & Bachu, E. (2015). Enhancing the Metacognitive Skill of Novice Programmers Through Collaborative Learning Metacognition: Fundaments, Applications, and Trends (pp. 277298): Springer. Braun, V., & Clarke, V. (2006). Using thematic analysis in psychology. Qualitative research in psychology, 3(2), 77101. Brown, A. (1987). Metacognition, Executive Control, Self Regulation and Mysterious Mechanisms. In R. K. Franz E. Weinert (Ed.), Metacognition, Motivation and Understanding (3 ed., pp. 65117). The University of Michigan: L. Erlbaum Associates. Buratti, S., & Allwood, C. M. (2015). Regulating Metacognitive Processes—Support for a Metametacognitive Ability Metacognition: Fundaments, Applications, and Trends (pp. 1738): Springer. CardelleElawar, M. (1992). Effects of teaching metacognitive skills to students with low mathematics ability. Teaching and Teacher Education, 8(2), 109121. Cetin, I., Sendurur, E., & Sendurur, P. (2014). Assessing the Impact of MetaCognitive Training on Students' Understanding of Introductory Programming Concepts. Journal of Educational Computing Research, 50(4), 507524. Coles, A. (2013). Being alongside: for the teaching and learning of mathematics: Springer Science & Business Media. Desoete, A. (2007). Evaluating and improving the mathematics teachinglearning process through metacognition. Electronic Journal of Research in Educational Psychology, 5(3), 705730. Desoete, A. (2009). Metacognitive prediction and evaluation skills and mathematical learning in thirdgrade students. Educational Research and Evaluation, 15(5), 435446. Efklides, A., & Misailidi, P. (2010). Introduction: The present and the future in metacognition Trends and prospects in metacognition research (pp. 118): Springer. Eldar, O., & Miedijensky, S. (2015). Designing a Metacognitive Approach to the Professional Development of Experienced Science Teachers Metacognition: Fundaments, Applications, and Trends (pp. 299319): Springer. Fortunato, I., Hecht, D., Tittle, C., & Alvarez, L. (1991). Metacognition and problem solving. The Arithmetic Teacher, 39(4), 38. Gillies, R. W., & Richard Bailey, M. (1995). The effects of Metacognitive Strategy and Attributional Interventions on the ability of students' to solve mathematical word problems. Paper presented at the AARE Conference, Hobart, Tasmania. Goos, M. (1993). Metacognitive decisions and their influence on problem solving outcomes. Paper presented at the The Sixteenth Annual Conference of the Mathematics Education Research Group of Australasia (MERGA), Brisbane. Grant, G. (2014). A metacognitivebased tutoring program to improve mathematical abilities of rural high school students: An action research study. (Ph.D), Capella University. GrizzleMartin, T. (2014). The Effect of Cognitiveand MetacognitiveBased Instruction on Problem Solving by Elementary Students with Mathematical Learning Difficulties. (Ph.D), Walden University. Hartman, H. J. (2001). Developing students’ metacognitive knowledge and skills Metacognition in learning and instruction (pp. 3368): Springer. Hurme, T.R., Järvelä, S., Merenluoto, K., & Salonen, P. (2015). What Makes Metacognition as Socially Shared in Mathematical Problem Solving? Metacognition: Fundaments, Applications, and Trends (pp. 259276): Springer. Kapa, E. (2001). A metacognitive support during the process of problem solving in a computerized environment. Educational studies in mathematics, 47(3), 317336. Kluwe, R. H. (1982). Cognitive knowledge and executive control: Metacognition Animal mind—human mind (pp. 201224): Springer. Kramarski, B., & Mevarech, Z. R. (2003). Enhancing mathematical reasoning in the classroom: The effects of cooperative learning and metacognitive training. American Educational Research Journal, 40(1), 281310. Kramarski, B., & Michalsky, T. (2013). Student and teacher perspectives on IMPROVE selfregulation prompts in webbased learning International handbook of metacognition and learning technologies (pp. 3551): Springer. Kuhn, D. (2000). Theory of mind, metacognition, and reasoning: A lifespan perspective. In P. R. Mitchell, Kevin John (Ed.), Children's reasoning and the mind (pp. 301326). Hove, England: Psychology Press: Taylor & Francis. la Barra, D., León, M. B., la Barra, D., León, G. E., Urbina, A. M., la Barra, D., & León, B. A. (1998). Towards a global improvement of Engineering Maths Teaching. Paper presented at the Frontiers in Education Conference, 1998. FIE'98. 28th Annual. Larkin, S. (2000). How can we discern metacognition in year one children from interactions between students and teacher. Paper presented at the ESRC Teaching and Learning Research Programme Conference. Larkin, S. (2006). Collaborative group work and individual development of metacognition in the early years. Research in Science Education, 36(12), 727. Larkin, S. (2010). Metacognition in young children: Routledge. Lester, F., Garofalo, J. & Kroll, D.L. . (1989). Bloomington, IN. USA Patent No. Eric Document Reproduction Service No. ED 314 255: M. E. D. Indiana University & Centre. Merriam, S. B. (1998). Qualitative Research and Case Study Applications in Education: Revised and Expanded from Case Study Research in Education. San Francisco: Jossey Bass Wiley. Mevarech, Z., & Fridkin, S. (2006). The effects of IMPROVE on mathematical knowledge, mathematical reasoning and metacognition. Metacognition and Learning, 1(1), 8597. Mevarech, Z., & Kramarski, B. (1997). IMPROVE: A multidimensional method for teaching mathematics in heterogeneous classrooms. American Educational Research Journal, 34(2), 365394. Mevarech, Z. R., & Amrany, C. (2008). Immediate and delayed effects of metacognitive instruction on regulation of cognition and mathematics achievement. Metacognition and Learning, 3(2), 147157. Moga, A. (2012). Metacognitive Training Effects on Students Mathematical Performance from Inclusive Classrooms. (PhD), BabeșBolyai University, ClujNapoca. Mohini, M., & Nai, T. T. (2005). The use of metacognitive process in learning mathematics. Reform, revolution and paradigm shifts in mathematics education, Nov 25th–Dec 1st, 159162. Mutekwe, E. (2014). Unpacking Student Feedback as a Basis for Metacognition and Mediated Learning Experiences: A Sociocultural perspective. Journal of Education and Learning (EduLearn), 8(4), 338348. Naglieri, J. A., & Johnson, D. (2000). Effectiveness of a cognitive strategy intervention in improving arithmetic computation based on the PASS theory. Journal of learning disabilities, 33(6), 591597. Panaoura, A., & Philippou, G. (2005). The measurement of young pupils’ metacognitive ability in mathematics: The case of selfrepresentation and selfevaluation. Paper presented at the Proceedings of CERME. PeñaAyala, A., & Cárdenas, L. (2015). A Conceptual Model of the Metacognitive Activity Metacognition: Fundaments, Applications, and Trends (pp. 3972): Springer. Raoofi, S., Chan, S. H., Mukundan, J., & Rashid, S. M. (2013). Metacognition and Second/Foreign Language Learning. English Language Teaching, 7(1), p36. Robson, C. (2002). Real World Research: A Resource for Social Scientists and PractitionerResearchers (2nd edition ed.): Blackwell: Oxford. Sahin, S. M., & Kendir, F. (2013). The effect of using metacognitive strategies for solving geometry problems on students’ achievement and attitude. Educational Research and Reviews, 8(19), 17771792. Schoenfeld, A. H. (1987). What’s All the Fuss About Metacognitlon. In A. H. Schoenfeld (Ed.), Cognitive science and mathematics education (Vol. 189215). Hillsdale, NJ: Lawrence Erlbaum Associates. Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics. Handbook of research on mathematics teaching and learning, 334370. Schraw, G., & Gutierrez, A. P. (2015). Metacognitive Strategy Instruction that Highlights the Role of Monitoring and Control Processes Metacognition: Fundaments, Applications, and Trends (pp. 316): Springer. Simons, P. R. (1996). Metacognitive strategies: Teaching and assessing. In E. DeCorte, Weinert, F.E. (Ed.), International Encyclopedia of developmental and instructional psychology (pp. 441444). Great Britain: Pergamon. Thomas, G. (2012). Metacognition in science education: Past, present and future considerations. In B. Fraser, Tobin, Kenneth, McRobbie, Campbell J. (Ed.), Second international handbook of science education (pp. 131144): Springer. Tok, Ş. (2013). Effects of the knowwantlearn strategy on students’ mathematics achievement, anxiety and metacognitive skills. Metacognition and Learning, 8(2), 193212. Wolf, S. E., Brush, T., & Saye, J. (2003). Using an information problemsolving model as a metacognitive scaffold for multimediasupported informationbased problems. Journal of Research on Technology in Education, 35(3), 321341. Yimer, A. (2004). Metacognitive and cognitive functioning of college students during mathematical problem solving. (Ph.D), Illinois State University. Yin, R. K. (2014). Case Study Research: Design and Methods: SAGE Publications. Zohar, A., & Barzilai, S. (2013). A review of research on metacognition in science education: current and future directions. Studies in Science Education, 49(2), 121169. 
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Triangular law of students’ Mathematics Interest in Ghana: A Model with motivation and perception as predictorSamuel Asiedu Addo, Charles K. Assuah, Yarhands Dissou Arthur
pp. 539548  Article Number: iejme.2017.028
Abstract The main purpose of this study was to verify by means of structural equation modelling (SEM) how students’ interest in mathematics (SIM) is affected by students’ perception and students’ motivation to learn mathematics. The study further investigated the effect of students’ perception (SP) on students’ motivation (SM) to learn mathematics. The study adopted a simple random sampling technique to administer 150 questionnaires to 10 public Senior High Schools in Ghana. In all, a total number of 1,500 students were given the questionnaire to indicate their responses. However, 1,263 questionnaires were properly administered, representing 84.3% response rate. The constructs reliability for SIM, SP, and SM were 0.71, 0.82, and 0.68 respectively. The further explored how the goodnessoffit influences the measurement model, structural model and the overall model. The findings indicated that when Ghanaian high school students’ have good perception about mathematics and have the motivation to learn mathematics, their interest in mathematics would improve significantly. Keywords: Students’ perception; students’ motivation; students’ interest; Ghana; Mathematics References Arthur, Y., AsieduAddo, S., & Assuah, C. (2017). Students’ Perception and Its Impact on Ghanaian Students’ Interest in Mathematics: Multivariate Statistical Analytical Approach. Asian Research Journal of Mathematics, 4(2), 1–12. http://doi.org/10.9734/ARJOM/2017/33023 Arthur, Y. D., Oduro, F. T., & Boadi, R. K. (2014). Statistical Analysis of Ghanaian Students Attitude and Interest Towards Learning Mathematics . International Journal of Education and Research, 2(6), 661–670. Bong, M. (2004). Academic Motivation in SelfEfficacy, Task Value, Achievement Goal Orientations, and Attributional Beliefs. The Journal of Educational Research, 97(6), 287–298. http://doi.org/10.3200/JOER.97.6.287298 Fornell, C., & Larcker, D. (1981). Evaluating structural equation models with unobservable variables and measurement error. Journal of Marketing Research, 18(3), 39–50. http://doi.org/10.2307/3151312 Githua, B. N., & Mwangi, J. G. (2003). Students ’ mathematics selfconcept and motivation to learn mathematics : relationship and gender differences among Kenya ’ s secondaryschool students in Nairobi and Rift Valley provinces. International Journal of Educational Development 23, 23, 487–499. http://doi.org/10.1016/S07380593(03)000257 Hair, J. F., Black, B., Babin, B., TathamR.L, & R.E, A. (2005). Multivariate Data analysis. Singapore: Peason Education (Pte). Hair, J., Sarstedt, M., & Ringle, C. (2012). An assessment of the use of partial least squares structural equation modeling in marketing research. Journal of the Academy of Marketing Science, 40(3), 414–433. Henseler, J., Ringle, C., & Sinkovics, R. (2009). The use of partial least squares path modeling in international marketing. Advances in International Marketing, 20, 277–319. Ignacio, N., Nieto, L., & Barona, E. (2006). The affective domain in mathematics learning. Retrieved from http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.495.3040 Köǧce, D., Yildiz, C., Aydin, M., & Altindaǧ, R. (2009). Examining elementary school students’ attitudes towards mathematics in terms of some variables. Procedia  Social and Behavioral Sciences, 1(1), 291–295. http://doi.org/10.1016/j.sbspro.2009.01.053 LinnenbrinkGarcia, L., Durik, A. M., Conley, A. M., Barron, K. E., Tauer, J. M., Karabenick, S. A., & Harackiewicz, J. M. (2010). Measuring Situational Interest in Academic Domains. Educational and Psychological Measurement, 70(4), 647–671. http://doi.org/10.1177/0013164409355699 Martin, A. J. (2006). The relationship between teachers’ perceptions of student motivation and engagement and teachers’ enjoyment of and confidence in teaching. AsiaPacific Journal of Teacher Education, 34(1), 73–93. http://doi.org/10.1080/13598660500480100 Matic, L. J. (2014). Mathematical knowledge of nonmathematics students and their beliefs about mathematics. International Electronic Journal of Mathematics Education, 9(1–2), 13–24. Meece, J. L., Wigfield, A., & Eccles, J. S. (1990). Predictors of math anxiety and its influence on young adolescents’ course enrollment intentions and performance in mathematics. Journal of Educational Psychology, 82(1), 60–70. http://doi.org/10.1037/00220663.82.1.60 Mensah, J. K., Okyere, M., & Kuranchie, A. (2013). Student attitude towards Mathematics and performance : Does the teacher attitude matter ? Journal of Education and Practice, 4(3), 132–139. Mutodi, P., & Ngirande, H. (2014a). Exploring Mathematics Anxiety: Mathematics Students’ Experiences. Mediterranean Journal of Social Sciences, 5(1). http://doi.org/10.5901/mjss.2014.v5n1p283 Mutodi, P., & Ngirande, H. (2014b). The Influence of Students ` Perceptions on Mathematics Performance . A Case of a Selected High School in South Africa. Mediterranean Journal of Social Sciences, 5(3), 431–445. http://doi.org/10.5901/mjss.2014.v5n3p431 Pantziara, M., & Philippou, G. (2007). Students ’ motivation and achievement and teachers ’ practices in the classroom, Proceedings of 31th PME Conference 4, 57–64. Singh, K., Granville, M., & Dika, S. (2002a). Mathematics and science achievement: effects of motivation, interest, and academic engagement. The Journal of Educational Research, 95(6), 323–332. http://doi.org/10.1080/00220670209596607 Singh, K., Granville, M., & Dika, S. (2002b). Mathematics and Science Achievement: Effects of Motivation, Interest, and Academic Engagement. The Journal of Educational Research, 95(6), 323–332. http://doi.org/10.1080/00220670209596607 Skaalvik, E. M., & Skaalvik, S. (2008). Selfconcept and selfefficacy in mathematics: Relation with mathematics motivation and achievement. New Developments in the Psychology of Motivation., 105–128. Tooke, D. J., & Lindstrom, L. C. (1998). Effectiveness of mathematics methods course in reducing math anxiety of preserves elementary teacher. School Science & Mathematics, 98(3), 136–139. 
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A Topic Revisited: Students in the Republic of the Maldives Writing Contextual Word ProblemsJason Johnson
pp. 549559  Article Number: iejme.2017.029
Abstract Students dislike for solving word problems is not new for mathematics teachers. Most word problems have no cultural significance or relate to the student. A student dislike for solving word problems could be contributed to the lack of reference to the lived experience of the student (i.e., social class, race, ethnicity, mother language, gender, sexual orientation, and any other demographic characteristics). А study was designed to explore a group of students, on the island of Kuda Hudaa in the Republic of the Maldives, ability to write contextual word problems. Contextual word problems are word problems that relate to a student population in a classroom. The results indicate that all students were able to create contextual word problems for both multiplication and division. Most student written multiplication and division word problems met Marks (1994) three considerations when developing word problems. The intent is to encourage students to write contextual word problems that make learning mathematics more meaningful for students. Keywords: Ethnomathematics, contextual problems, Maldives, word problems, writing References Amit, M. & KlassTsirulnikov, B. (2005). Paving a way to algebraic word problems using a nonalgebra route. Mathematics Teaching in the Middle School, 10, 271 – 276. Basurto, I. (1999). Conditions of reading comprehension which facilitate word problems for second language learners. Reading Improvement, 36(3), 143 – 148. Brown, N. M. (1993). Writing mathematics. Arithmetic Teacher, 41(1), 20 – 21. Burton, M. B. (1991). Grammatical translationinhibitors in two classic word problem sentences. For the Learning of Mathematics, 11(1), 43 – 46. D'Ambrosio, U. (1985). Ethnomathematics and its place in the history and pedagogy of mathematics. For the Learning of Mathematics, 5, 448. D’Ambrosio, U. (2001). What is Ethnomathematics and how can it help children in schools? Teaching Children Mathematics, 7(6), 308310. D’Ambrosio, U. (2009). The program Ethnomathematics: A theoretical basis of the dynamics of intra cultural encounters. Journal of Mathematics and Culture. 1, (1), 1 – 7. Darby, L. (2008). Marking mathematics and science relevant through story. Australian Mathematics Teacher, 64(1), 6 – 11. DiPillo, M. L., Sovich, R., & Moss, B. (1997). Exploring middle graders' mathematical thinking through journals. Mathematics Teaching in the Middle School, 2 (5), 308 – 314. Edie, R. (2009). Making sense of word problems (Master’s Thesis). University of Nebraska – Lincoln. Retrieved from: http://digitalcommons.unl.edu/mathmidactionresearch/42/ Foley, T. E., Parmar, R. S., & Cawley, J. F. (2004). Explanding the agenda in mathematics problem solving for students with mild disabilities: alternative representations. Learning Disabilities, 13(1), 7 – 16. François, K. (2009). The role of Ethnomathematics within mathematics education. Proceedings of the Sixth Congress of the European Society for Research in Mathematics Education (CERME). January 28 – February 1, 2009, Lyon France. Heinze, K. (2005). The language of math. Presentation handouts from TESOL conference. Retrieved from http://www.rtmsd.org/cms/lib/PA01000204/Centricity/Domain/594/Language_of_Math.doc. Hoz, R. & Harel, G. (1990). Higher order knowledge involved in the solution of algebra speed word problems. Journal of Structural Learning, 10(4), 305 – 328. Langeness, J. (2011). Methods to improve student ability in solving math word problems (Master’s Thesis). Hamline University. Retrieved from: http://www.hamline.edu/WorkArea/DownloadAsset.aspx?id=2147514388. LeGere, A. (1991). Collaboration and writing in the mathematics classroom. Mathematics Teacher. 84(3), 166 – 171. Marks, D. (1994). A guide to more sensible word problems. The Mathematics Teacher, 87(8), 610 – 611. Mangan, C. (1989). Choice of operation in multiplication and division word problems: A developmental study. Journal of Structural Learning, 10, 73 – 77. Martinez, J. G. R. (2001). Thinking and writing mathematically: Achilles and the tortoise as an algebraic word problem. Mathematics Teacher, 94(4), 248 – 252. Miller, L. D. (1991). Constructing pedagogical content knowledge from students’ writing in secondary mathematics. Mathematics Education Research Journal, 3(1), 30 – 44. Miller, L. D. (1992). Teacher benefits from using impromptu writing prompts in algebra classes. Journal for Research in Mathematics Education, 23(4), 329 – 340. Patton, M. Q. (2002). Qualitative research and evaluation methods (3rd Ed.). London: Sage Publications. Powell, A.B., & Lopez, J.A. (1989). Writing as a vehicle to learn mathematics: A case study. In P. Connolly & T. Vilardi (Eds.), Writing to learn mathematics and science (pp. 157177). New York: Teachers College Press. Presmeg, N. (1998). Ethnomathematics in teacher education. Journal of Mathematics Teacher Education, 1, 317 – 339. Puchalska, E. & Semadeni, Z. (1987). Children’s reactions to verbal arithmetical problems with missing, surplus or contradictory data. For the Learning of Mathematics, 7(3), 9 – 16. Rubenstein, R. N. & Thoompson, D. R. (2002). Understanding and supporting children’s mathematical vocabulary development. Teaching Children Mathematics, 9(2), 107 – 112. Rudnitsky, A., Etheredge, S., Freeman, S. J. M., and Gilbert, T. G. (1995). Learning to solve addition and subtraction word problems througha structurepluswriting approach. Journal for Research in Mathematics Education, 26(5), 467 – 486. Stix, A. (1994). Picjour math: Pictorial journal writing in mathematics. Arithmetic Teacher, 41(5), 264 – 269. Wedege, T. (2010). Ethnomathematics and mathematical literacy: People knowing mathematics in society. C. Bergsten, E. Jablonka, and T. Wedege (eds). Mathematics and mathematics education: Cultural and social dimensions. 31 – 46. Winograd, K., & Higgins, K. (1994). Reading, writing and talking mathematics: One interdisciplinary possibility. The Reading Teacher, 48, 310 – 319. Xin, Y. P. (2007). Word problem solving tasks in textbooks and their relation to student performance. The Journal of Educational Research, 100(6), 347 – 359. 
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A review of methods for highwayrailway crossings safety management processBehzad Dezhkam ,Seyed Mehrdad Eslami
pp. 561568  Article Number: iejme.2017.030
Abstract This paper reviews the literature concerning the risks associated with Highway Railway Crossings (HRC). The aim of this study is to evaluate and validate previous investigations conducted in the United States and Canada. The main issues addressed in this paper are: a) Identify HRC with potential the average collision frequency or collision severity as black spots, tests that are used to identifying hazardous location and compare the methods, b)Identify the contributing factors to safety problems at an identified HRC location, c)Identification of countermeasures to address the contributing factors. This research has thrown up many questions in need of further investigations on risks associated with HRC to mitigate the accident frequency and injury severity. Keywords: Highwayrailway crossings safety management process References Bahar, G., Masliah, M., Philp, C., Shen, K., Park, P., Bhim, R., 2007. Development of a Traffic Safety Management System: High Proportion Screening Tool: Selection of a High Proportion Testing Tool, State of Utah, US Department of Transportation, Interim Report. Bolduc, D., Bonin, S., 1995. Bayesian analysis of road accidents: accounting for deterministicheterogeneity. In: Proceedings of the Canadian Multidisciplinary Road Safety Conference IX, Montreal, Canada. Brose, C.A., 2001. Geographic Information Systems for Spatial Analysis of Traffic Collision Locations in La Crosse.Saint Mary’s University of Minnesota, Wisconsin.City of Saskatoon, 2009.Traffic Characteristics Report. Cheng, W.,Washington, S., 2005. Experimental evaluation of hotspot identification methods. Accident Analysis and Prevention 37, 870–881. Canadian road/railway grade crossing detailed safety assessment field guide, 2005. Transport Canada. Cheng, W., Washington, S., 2008.New Criteria for Evaluating Methods of Identifying Hot Spots.Transportation Research Record, 2083. TRB, National Research Council, Washington, DC, pp. 76–85. Cognitive Ergonomics Research Laboratory Department of Psychology, University of Calgary, 2002. A human factors analysis of highwayrailway grade crossing accidents in Canada. Transportation Development Centre Transport Canada. Elvik, R., 2007. StateoftheArt Approaches to Road Accident Black Spot Management and Safety Analysis of Road Networks.Report 883. Institute of Transport Economics, Oslo.
Elvik, R., 2008a. Comparative Analysis of Techniques for Identifying Hazardous Road Locations.Transportation Research Record, 2083. TRB, National Research Council, Washington, DC, pp. 72–75. Federal Railroad Administration, 2009. HighwayRail Grade Crossing Guidelines for HighSpeed Passenger Rail.U.S. Department of Transportation. Hauer, E., 2004. Statistical Road Safety Modeling.Transportation Research Record, 1897. TRB, National Research Council, Washington, DC, pp. 81–87. Hauer, E., Allery, B.K., Kononov, J., Griffith, M.S., 2002. Screening the road Network for Sites with Promise.Transportation Research Record, 1784. TRB, National Research Council, Washington, DC, pp. 2732. Hauer, E., Allery, B.K., Kononov, J., Griffith, M.S., 2004. How Best to Rank Sites with Promise. Transportation Research Record, 1897. TRB, National Research Council, Washington, DC, pp. 48– 54. Horton, S., 2009. Success factors in the reduction of highwayrail grade crossing incidents.Volpe national transportation systems center. Huang, B., 2011. Integrating Pavement Engineering and Road Geometric Factors into Traffic Safety Management for High Speed Facilities.The University of Tennessee. Kononov, J., 2002. Identifying Locations with Potential for Accident Reductions: Use Of Direct Diagnostics and Pattern Recognition Methodologies.Transportation Research Record, 1784. TRB, National Research Council, Washington, DC, pp. 153–158. Lyon, C., Gotts, B., Wong, W.K.F., Persaud, B., 2007. Comparison of Alternative Methods for Identifying Sites with High Proportion of Specific Accident Types.Transportation Research Record, 2019. TRB, National Research Council, Washington, DC, pp. 212–218. Lyon, C., Persaud, B., 2008. Safety Effects of Targeted Program to Improve Skid Resistance.Transportation Research Record, 2068. TRB, National Research Council, Washington, DC, pp. 135–140. Hauer, E., Persaud, B.N., 1984. Problem of identifying hazardous locations using accident data.Transport. Res. Rec. 975, 36–43. Hauer, E., NG, J.C.N., Lovell, J., 1988. Estimation of safety at signalized intersections.Transport. Res. Rec. 1185, 48–61. Hauer, E., 1997. Observational BeforeAfter Studies in Road Safety.Pergamon, Tarrytown, NY. Higle, J.L., Witkowski, J.M., 1988. Bayesian identification of hazardous locations.Transport. Res. Rec. 1185, 24–36. Higle, J.L., Hecht, M.B., 1989. A comparison of techniques for the identification of hazardous locations.Transport. Res. Rec. 1238, 10–19. Kelton, W.D., Sadowski, R.P., Sturrock, D.T., 2003. Simulation with Arena. The McGrawHill Companies, Inc., NY. Kononov, J., 2002. Identifying locations with potential for accident reductions: use of direct diagnostics and pattern recognition methodologies. In: Transportation Research Record: Journal of the Transportation Research Board, No. 1784. TRB, National Research Council, Washington, DC, pp. 153–158. Kononov, J., Allery, B.K., 2004. Explicit consideration of safety in transportation planning and project scoping. In: Transportation Research Record: Journal of the Transportation Research Board, No. 1897. TRB, National Research Council, Washington, DC, pp. 116–125. Kononov, J., Janson, B.N., 2002. Diagnostic methodology for the detection of safety problems at intersections. In: Transportation Research Record: Journal of the Transportation Research Board, No. 1784. TRB, National Research Council, Washington, DC, pp. 51–56. Kononov, J., Allery, B., 2003. Level of service of safety: conceptual blueprint and analytical framework. In: Transportation Research Record: Journal of the Transportation Research Board, No. 1840. TRB, National Research Council, Washington, DC, pp. 57–66. Masliah, M., Bahar, G., 2006.Using basic collision data to manage road safety. In: Annual Conference of the Transportation Association of Canada, Charlottetown, PEI. Masliah, M., Bahar, G., Clayton, R., Hall, R., 2006.Managing road using basic crash data. In: Traffic Records Forum Association of Traffic Safety Information Professionals, (ATSIP).
Mollet, C.J., 2004. Developing a traffic safety improvement program: a review and comparison of different screening network approaches. In: Presented at Canadian Multidisciplinary Road Safety Conference XIV, Ottawa, Ontario. Maher, M.J., Mountain, L.J., 1988. The identification of accident blackspots: a comparison of current methods. Accident Anal. Prevent. 20 (2), 143–151. Multer, J., Raslear, Th., Yeh, M., 2012. Evaluating the Impact of Grade Crossing Safety Factors through Signal Detection Theory.Proceedings of the human factors and ergonomics society 56th annual meeting. MirandaMoreno, F., Fu, L., Ukkusuri, S., Lord, L., 2009. How to Incorporate Accident Severity and Vehicle Occupancy into the Hot Spot Identification Process? Journal of the Transportation Research Board, No. 2102, Transportation Research Board of the National Academies, Washington, D.C., 2009, pp. 53–60. Monsere, C., Todd, J., Dixon, K., Zheng, J., Van Schalkwyk, I., 2011. Assessment of Statewide Intersection Safety Performance, Final Report, FHWAORRD18.Oregon Department of Transportation, Federal Highway Administration. Montella, A., 2010. A comparative analysis of hotspot identification methods. Accident Analysis and Prevention 42, 571–581. MirandaMoreno, F., Fu, L.,Eluru, N.,Bagheri, M., 2012. A latent class modeling approach for identifying vehicle driver injury severity factors at highwayrailway crossings. Accident Analysis and Prevention. Office of Railroad Safety, 2010. Railroad Trespassing, Vandalism, and HighwayRail Grade Crossing Warning Device Violation Prevention Strategies. U.S. Department of Transportation. Ogden, B., 2007. RailroadHighway Grade Crossing Handbook. Washington: Institute of Transportation Engineers. Park, P., Parisien, J., Sahaji, R., Cozier, C., 2011. Development of geographic information system to identify potential high collision locations in Saskatoon. Saskatchewan Government Insurance, Interim Report. Persaud, B., 2001. Statistical Methods in Highway Safety Analysis.NCHRP Synthesis 295.Transportation Research Board, Washington, DC. Persaud, B., Lyon, C., Nguyen, T., 1999.Empirical Bayes Procedure for Ranking Sites for Safety Investigation by Potential for Improvement.Transportation Research Record, 1665. TRB, National Research Council, Washington, DC, pp. 7–12. Persaud, B.N., 1999. Empirical Bayes procedure for ranking sites for safety investigation by potential for safety improvement.Transport. Res. Rec. 1665, 7–12. PIARC, World Road Association, Technical Committee on Road Safety C13, 2004. TAC, Transportation Association of Canada, 2004. The Canadian Guide to InService Road Safety Reviews. Ottawa. Sayed, T., Navin, F., Abdelwahab, W., 1997. A countermeasure based approach for identifying and treating accident prone locations. Canadian Journal of Civil Engineering 24, 683–691. Saccomanno, F.F., Fu, L., Park, P., 2007. Decision support tool for prioritizing safety improvement programs at highrisk grade crossings. Department of Civil and Environmental Engineering university of Waterloo. Saccomanno, F.F., Park, P., Fu, L., 2007. Estimating countermeasure effects for reducing collisions at highway–railway grade crossings. Accident Analysis and Prevention 39 (2007) 406–416. Yeh, M., Multer, J., 2008. Driver behavior at highwayrailroad grade crossings: A literature review from 19902006. U.S. Department of Transportation. 
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Mathematics Learning Model of Open Problem Solving to Develop Students’ CreativityKetut Suastika
pp. 569577  Article Number: iejme.2017.031
Abstract The purpose of this research is to produce an open problem solving mathematics learning model to help students develop their creativity which meets the criteria of validity, practicality, and effectiveness. The components of instruction model used adopt Joyce and Weil. The quality of the developed products was evaluated based on the product development evaluation developed by Neeven, which includes validity by validators, practicality, and the effectiveness of field experiment by observers. The syntax realization of model consisted of five phases, namely: (1) Introduction, (2) Concept tracking, (3) Open problem presentation, (4) Work presentation, and (5) Closing. The model that had been declared valid by the validator was then tested to see the practicality and effectiveness. The practicality and effectiveness of the model were obtained after three trials. The process of model development is based on the theory of development of Plomp, which consists of three phases, namely: (1) preliminary research, (2) prototyping phase, and (3) assessment phase. The development result of this study is an open problem solving math learning model that can develop students’ creativity (PMT Model), which meets valid, practical, and effective criteria Keywords: Development, Learning Model of open Problem Solving, Creativity References Forrester, J.C. 2008. Thinking Creatively ; Thinking Critically. Asian Social Science, 4 (5): 100105, Hashimoto, Y. 1997. The Method of Fostering Creativity Through Mathematical Problem Solving. International Reviews on Mathematical Education,3 (29): 8687 Izzati, N. 2009. Berpikir Kreatif dan Kemampuan Pemecahan Masalah Matematis: Apa, Mengapa, dan Bagaimana Mengembangkannya Pada Peserta Didik. Prosiding Seminar Nasional Matematika dan Pendidikan Matematika, Bandung 19 Desember 2009, hal: 4960, Joyce, B., Weil, M., & Calhoun, E. 2009. Models of Teaching, Eighth Edition. Boston : Allyn and Bacon. Kontoyianni, K., Kattou, M., PittaPantazi, D.& Christou, C. 2013. Integrating mathematical abilities and creativity in the assessment of mathematical giftedness. Psychological Test and Assessment Modeling. 55 (3): 289315. Mann, E. L. 2009. The Search for Mathematical Creativity: Identifying Creative Potential in Middle School Students. Creativity Research Journal. 21(4), 338–348. Monahan, T. 2002. The DoItYourself Lobotomy: Open Your Mind to Greater Creative Thinking. New York: Published by John Wiley & Sons, Inc., Nadjafikhah, M., Yaftian, N., Bakhshalizadeh, S. 2012. Mathematical Creativity : Some Definitions and Characteristic. Procedia – Social and Behavioral Sciences. 31 (2012): 285 – 291. NCTM. 2000. Priciples and Standards for School Mathematics. Copyright by the National Council of Teachers of Mathematics, Inc. 1906 Association Drive, Reston, VA 20191–9988. Neeveen., N., Folmer, E. 2007. Educational Design Research. Dalam Plomp, T.&Neeven, N. (Eds), Formative Evaluation in Educational Design Research. Proceedings of the seminar conducted at the East China Normal University, Shanghai (PR China), November 23 – 26, 2007. Paparan Wamendikbud Bidang Pendidikan: Konsep dan Implementasi Kurikulum 2013. Pehkonen, E. 2007. Problem Solving in Mathematics Education in Finland. Finland: University of Helsinki Finland. Permendikbud no 65 tahun 2013 tentang Standar Proses Pendidikan Dasar dan Menengah. Plomp, T. 2007. Educational Design Research. Dalam Plomp, T.&Neeven, N. (Eds), Educational Design Research: An Introduction. Proceedings of the seminar conducted at the East China Normal University, Shanghai (PR China), November 23 – 26, 2007. Sharp, C. 2004. Developing young children’s creativity: what can we learn from research? Siswono, T.E.Y. 2007. Pembelajaran Matematika Humanistik yang Mengembangkan Kreativitas Siswa. Makalah disampaikan pada Seminar Nasional Pendidikan Matematika “Pembelajaran Matematika yang Memanusiakan Manusia” di Program Studi Pendidikan Matematika FKIP Universitas Sanata Dharma. Yogyakarta, 29–30 Agustus 2007. Stenberg, R. 2006. The Nature of Creativity. Creativity Research Journal. 18(1): 87–98. 
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The Use of Mathematical Module Based on Constructivism Approach as Media to Implant the Concept of Algebra OperationJazim, Rahmad Bustanul Anwar & Dwi Rahmawati
pp. 579583  Article Number: iejme.2017.032
Abstract Mathematical learning to implant the concept of algebra operation using constructivism approach is very important. Students should be actively involved in the process of building their understanding, so meaningful learning experiences can be to gained. This research was an experimental research involving 91 students of grade 8. This research applied constructivismbased mathematics module used by the students during studying the concept of algebra operation. The result showed that the use of constructivism based mathematics module was very effective in improving students' mathematical understanding on algebra operation material. This result was obtained by performing the initial test (pretest) before the use of modules and final test (posttest) after the use of module. Addition, the result of observation conducted during the learning activities showed that in the use of modules in learning mathematics, students with high academic ability tended to be more active in the discussion process. Keywords: module, constructivism approach, algebra operation References AnnSofi RöjLindberg. (2001). Active Learning of Mathematics. Experiential Learning for the Third Millenium. Vol. 2, 159168. Berger, M. (2005). Vygotsky’s Theory of Concept Formation and Mathematics Education. Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education, Vol. 2, pp. 153160. Bhowmik, M. (2014). Constructivism approach in mathematics teaching and assessment of mathematical understanding. Basic Research Journal of Education Research and Review ISSN 23156872 Vol. 4(1) pp. 0812 January 2015. Major, T. E., Mangope, B. (2012). The Constructivist Theory in Mathematics: The Case of Botswana Primary Schools. International Review of Social Sciences and Humanities Vol. 3, No. 2 (2012), pp. 139147. Mousley, J. (2005). What Does Mathematics Understanding Look Like? The Annual Conference held at RMIT. NCTM. (2000). Principles and Standars for School Mathematics. United States of America: The National Council of Teachers of Mathematics, Inc. Pepin, B. & Haggarty, L. (2005). Making Connections and Seeking Understanding. Sato, Manabu. (2007). Tantangan yang Harus Dihadapi Guru. Dalam Bacaan Rujukan untuk Lesson Study: Sistems (Strengthening Inservice Training of Mathematics and Science Education at Junior Secondary Level). Dirjen PMPTKDepdiknas dan JICA. Star, J. R., Caronongan, P., Foegen, A., Furgeson, J., Keating, B., Larson, M. R., Lyskawa, J., McCallum, W. G., Porath, J., & Zbiek, R. M. (2015). Teaching strategies for improving algebra knowledge in middle and high school students (NCEE 20144333). Washington, DC: National Center for Education Evaluation and Regional Assistance (NCEE), Institute of Education Sciences, U.S. Department of Education. Retrieved from the NCEE website: http://whatworks.ed.gov. Stylianides, A.J. & Stylianides, G.J. (2007). Learning Mathematics with Understanding: A Critical Consideration of the Learning Principle in the Principles and Standards for School Mathematics. The Montana Mathematics Enthusiast, (Online), 103114, Winkel. (2009). Psikologi Pengajaran. Yogyakarta : Media Abadi. Watson, A. (2007). Key Understandings in Mathematics Learning. Paper 6: Algebraic reasoning. University of Oxford. 
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26 
The Analysis of the Problem of Economic Mathematical Problems Reversed from the Ability of Logic Thinking in StudentsWahyuddin
pp. 585598  Article Number: iejme.2017.033
Abstract This study aims to determine the level of logical thinking skills of solving ability on math problem of the economy, and the effect on the ability of logical thinking ability in solving mathematical economics at Mathematics Education students Muhammadiyah University Makassar. This research is an expost facto nature of causality with total population were 245 people from 8 different classes. Samples invoved 58 students consisting of 2 classes using a sampling technique . The research instrument consists of logical thinking ability test as many as 30 items and problem solving test ability by 5 items were valid and reliable before use. Data were analyzed using descriptive and inferential statistics (correlation and regression analysis). The research findings shows that: (1) The ability to think logically masiswa are in good enough category with an average value of 69.13; (2) The level of mathematical problem solving ability for masiswa economy is in the category quite well with the average value of 74.03; (3) The level of logical thinking ability masiswa correlated with mathematical problem solving ability with great economy of 94.5% relationship where that is located on a well once; and (5) the ability to think logically positive effect on the ability of solving problems with the effect of 89.1% while the remaining 10.9% is influenced by other variables outside the model. On conslusion, the ability to think logically positive effect on the ability of settlement capability, it can be concluded that the higher of logical thinking skills possessed by the student means the student problemsolving abilities are higher. Keywords: Logical Thinking Skills, Problem Solving Ability, Mathematical Economics References Albrecht, K. (2009). Logical Thinking. http://www.audiblox2014.com/. Alexander, K.D. (2007). Effect of Intruction in Creative Problem Solving on Cognition, Creativity, and Satisfaction among Ninth Grade Students in An Introduction to World Agricultural Science and Technology Course. Dissertation. The Graduate Faculty of Texas Teach University. (Online) Tersedia: http://www.scirus.com. Arikunto, Suharsimi. (2002). Prosedur Penelitian Suatu Pendekatan Praktek. Jakarta: PT. Rineka Cipta. Bancong, H. (2013). Profil Penalaran Logis Berdasarkan Gaya Berpikir dalam Memecahkan Masalah Fisika Peserta Didik. Jurnal Pendidikan IPA Indonesia. 2 (2), hlm. 195202. ISSN: 23391286. Diakses di http ://journal.unnes.ac.id /nju/index.php/jpii. Cambell, Linda. (2006). Metode Praktis pembelajaran Berbasis Multiple Intelligences. Depok : Insuisi Press. CUPM (2004). Undergrad uate Program and Course in the Mathematical Sciences: CUPM Curriculum Guide. The Mathematical Association of America. Departemen Pendidikan Nasional. (2005). UndangUndang Nomor 14 Tahun 2005, Tentang Guru dan Dosen, Jakarta: Depdiknas. Fachrurrozie. (2009). Eams Games Tournament Sebagai Upaya Peningkatan Kemampuan Belajar Mahasiswa Pada Mata Kuliah Matematika Ekonomi. Jurnal Pendidikan Ekonomi. 4 (1), hlm. 5168. ISSN: 2541562X. Diakses di http://id.portalgaruda.org/?ref=browse&mod=viewarticle&article=136358. Hoerr, Thomas. R. (2007) Buku Kerja Multiple Intelle Gences : Pengalaman New City School di St. Louis, Missouri, As, Dalam Menghargai Aneka Kecerdasan Anak. Bandung : Mizan Media Utama. Kisworo, A. (2000). Pembelajaran Pemecahan Masalah pada Pembelajaran Geometri di Kelas I SMU Petra 5 Surabaya. Tesis. Surabaya : PPS Universitas Negeri Surabaya. Matlin, M.W. (2003). Cognition. Fifth Edition. New York : John Wiley & Son.Inc Maharani, Swasti. (2013). Profil Berpikir Logis Mahasiswa Calon Guru Matematika dalam Menyelesaikan Luas Daerah dengan Menggunakan Integral Lipat Dua. Jurnal Ilmiah Pendidikan Matematika. 2 (1), hlm. 16. ISSN : 23017929. Diakses di http://ejournal.ikippgrimadiun.ac.id/index.php/jipm/index. Nazan, Sezen, (2011). A scale on logical thinking abilities. Procedia Social and Behavioral Sciences. 15 (2011), hlm. 2476–2480 NCTM. (2000). Principles and Standards for School Mathematics . Virginia: NCTM, Inc Nelvin, Nool. R. (2012). Effectiveness of an Improvised Abacus in Teaching Addition of Integers. Journal of International Conference on Education and Management Innovation IPEDR..30 (2012), hal 307311. Diakses di http://www.ipedr.com/vol30/60ICEMI%202012M10060.pdf. Priatna, N. (2003). Kemampuan Penalaran dan Pemahaman Matematika Siswa Kelas 3 Sekolah Lanjutan Tingkat Pertama Negeri di Kota Bandung. Disertasi Doktor. PPS UPI Bandung: tidak diterbitkan. Ruseffendi, E.T. (2006). Pengantar Kepada Membantu Guru Mengembangkan Kompetensinya dalam Pengajaran Matematika untuk Meningkatkan CBSA. Bandung: Tarsito. Saragih, Sahat. (2006). Menumbuhkembangkan Berpikir Logis dan Sikap Positif terhadap Matematika Melalui Pendekatan Matematika Realistik. Jurnal pendidikan dan kebudayaan Departemen Pendidikan Nasional. Badan Penelitian dan Pengembangan, Edisi Juli 2006. Saragih, S. (2011). Menumbuh Kembangkan Berpikir Logis dan Sikap Positif Terhadap Matematika Melalui Pendekatan Matematika Realistik. Diakses di. www. Scribd. Com/ doc /4674 9184/aretical. Diakses pada 15 Oktber 2016. Scusa, T. and Yuma, C.O. (2008). Five Processes Of Mathematical Thinking: Math in the Middle Institute Partnership. University Of Nebraska Lincoln: Summative Projects For Ma Degree Siswono, Tatag. (2004). Identifikasi Proses Berpikir Kreatif Siswa dalam Pengajuan Masalah (Problem Posing) Matematika Berpandu dengan Model Wallas dan Creative Problem Solving (CPS). Buletin Pendidikan Matematika. 6 (2), hlm. 116. Diakses di https://tatagyes.files.wordpress.com/2009/11/paper04_wallascps1.pdf. Sumarmo, U. (2000). Pengembangan Model Pembelajaran Matematika untuk Meningkatkan Kemampuan Inteleqtual Tingkat Tinggi Siswa Sekolah Dasar. Laporan Penelitian FPMIPA IKIP Bandung. Tidak diterbitkan. Sumarmo, U (1994). Suatu Alternatif Pengajaran untuk Meningkatkan Kemampuan Pemecahan Masalah Matematika pada Guru dan Siswa SMP. Bandung: Pendidikan Matematika FPMIPA Bandung. Suriasumantri, J.S. (2009). Filsafat Ilmu Sebagai Pengantar Populer . Jakarta : Pustaka Sinar Harapan. Utari, Sumarmo. (2003). Berpikir dan Disposisi Matematik: Apa, Mengapa, dan Bagaimana dikembangkan pada Siswa Sekolah Dasar dan Menengah. Bandung: ITB. Walle, John A. Van De. (2008). Sekolah Dasar dan Menengah Matematika Pengembangan Pengajaran . Jakarta: Erlangga. Van De Walle, John A. (2003). Pengembangan Pengajaran Matematika. Jakarta: Erlangga. 
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27 
Gender Stereotype and Motivation in Learning Statistics among Tertiary Students in GhanaYarhands Dissou Arthur, Samuel AsieduAddo & Simon Kojo Appiah
pp. 599608  Article Number: iejme.2017.034
Abstract The present study has presented the effect of gender on tertiary students’ motivation, feeling of competence, relatedness and autonomy. The survey consists of cohort samples of 251 males and 78 females from tertiary institutions in Ghana. Nonparametric chisquare test of independence was used to assess the effect of gender on students’ motivation in learning statistics. The study results have indicated that students’ gender have no influence on the selfdetermination of student to learn statistics. The paper further revealed that students’ gender has no significant influence on the tertiary students’ need for competence, relatedness and autonomy. This study has established the fact that the tertiary students’ need for autonomy, relatedness and competence in learning statistics is independent of the students’ gender. Keywords: Relatedness, students’ motivation, competence, Ghana, statistics References Arthur, Y. D., AseiduAddo, S. & Annan, J. (2015). Student mathematics interest in Ghana: The role of parent interest, gender, basic school attended and fear of basic school mathematics teacher. Advances in Research, 5(5), 1–8. Bargh, J. A., Gollwitzer, P. M. & Oettingen, G. (2010). Motivation. Handbook of Social Psychology, 2, 268–316. Brown, L. I. & Kanyongo, G. Y. (2010). Gender differences in performance in Mathematics in Trinidad and Tobago:Examining affective factors. International Electronic Journal of Mathematics Education, 5, 113–130. Deci, E. L. (1992). The relation of interest to the motivation of behavior: A selfdetermination theory perspective. In The Role of Interest in Learnig and Development (pp. 43–70). Deci, E. L. & Ryan, R. M. (2000). The “ What ” and “ Why ” of Goal Pursuits: Human Needs and the SelfDetermination of Behavior. Psychological Inquiry, 11(4), 227–268. Deci, E., Vallerand, R., Pelletier, L., & Ryan, R. (1991). Motivation and Education: The SelfDetermination Perspective. Educational Psychologist, 26(3), 325–346. Eccles, J., Adler, T. F., Futterman, R., Goff, S. B., Kaczala, C. M. & Meece, J. et al. (1983). Expectancies, values and academic behaviors. In J. T. Spence (Ed.), Achievement and achievement motives: Psychological and Sociological Approaches (pp. 75–146). San Francisco,: Freeman. Fredricks, J. A. & Eccles, J. S. (2002). Children’s competence and value beliefs from childhood through adolescence: Growth trajectories in two malesextyped domains. Developmental Psychology, 38(4), 519–533. Frenzel, A. C., Goetz, T., Pekrun, R. & Watt, H. M. G. (2010). Development of Mathematics Interest in Adolescence: Influences of Gender, Family, and School Context. Journal of Research on Adolescence, 20(2), 507–537. Gottfried, A. E., Fleming, J. S. & Gottfried, A. W. (1994). Role of parental motivational practices in children’s academic intrinsic motivation and achievement. Journal of Educational, 86, 104–113. Gottfried, A. E., Marcoulides, G. a, Gottfried, A. W., & Oliver, P. H. (2013). Longitudinal Pathways from Math Intrinsic Motivation and Achievement to Math Course Accomplishments and Educational Attainment. Journal of Research on Educational Effectiveness, 6(1), 118131. Hannula, M. S. (2006). Motivation in mathematics: Goals reflected in emotions. Educational Studies in Mathematics, 63(2), 165–178. Harackiewicz, J. M., Barron, K. E., Carter, S. M., Lehto, A. T. & Elliot, A. J. (1997). Predictors and consequences of achievement goals in the college classroom: Maintaining interest and making the grade. Journal of Personality and Social Psychology, 73(6), 1284–1295. Honicke, T. & Broadbent, J. (2016). The influence of academic selfefficacy on academic performance: A systematic review. Educational Research Review, 17, 6384. Ijaz, M. A. (1975). Motivating students. Physics Today, 28(12), 6061. https://doi.org/10.1063/1.3069253 Jabor, M. K., Machtmes, K., Buntat, Y. & Kungu, K. (2011). The Influence of Age and Gender on the Students ’ Achievement in Mathematics. In International Conference on Social Science and Humanity, 5, 304–308. Kenrick, D. T., Neuberg, S. L., Griskevicius, V., Becker, D. V. & Schaller, M. (2010). GoalDriven Cognition and Functional Behavior: The FundamentalMotives Framework. Current Directions in Psychological Science, 19(1), 63–67. Krapp, A. (2005). Basic needs and the development of interest and intrinsic motivational orientations. Learning and Instruction, 15(5), 381–395. Lindberg, S. M., Hyde, J. S., Petersen, J. L., & Linn, M. C. (2010). New trends in gender and mathematics performance: A metaanalysis. Psychological Bulletin, 136(6), 1123–1135. Lubienski, S., Robinson, J., Crane, C. & Ganley, C. (2013). Girls’ and Boys' Mathematics Achievement, Affect, and Experiences: Findings from the ECLSK. Journal for Research in Mathematics Education, 44(4), 634–645. Pantziara, M. & Philippou, G. N. (2014). Students’ Motivation in the Mathematics Classroom. Revealing Causes and Consequences. International Journal of Science and Mathematics Education, 7(2), 1–27. Reeve, J. & Lee, W. (2014). Students’ classroom engagement produces longitudinal changes in classroom motivation. Journal of Educational Psychology, 106(2). 178189. Ryan, R., & Deci, E. (2000). Intrinsic and Extrinsic Motivations: Classic Definitions and New Directions. Contemporary Educational Psychology, 25(1), 54–67. Ryan, R. M., & Lynch, J. H. (1989). Emotional Autonomy Versus Detachment : Revisiting the Vicissitudes of Adolescence and Young Adulthood. Child Development, 60, 340–356. Skaalvik, S., & Skaalvik, E. M. (2004). Gender Differences in Math and Verbal SelfConcept, Performance Expectations, and Motivation. Sex Roles, 50(3), 241–252. Stevens, T., Olivarez, A., Lan, W. Y., & TallentRunnels, M. K. (2004). The Journal of Educational Research Role of Mathematics SelfEfficacy and Motivation in Mathematics Performance Across Ethnicity. The Journal of Educational Research, 974, 208–222. Van De Gaer, E., Pustjens, H., Van Damme, J. & De Munter, A. (2008). Mathematics participation and mathematics achievement across secondary school: The role of gender. Sex Roles, 59(78), 568–585. Wang, M.T. (2012). Educational and career interests in math: A longitudinal examination of the links between classroom environment, motivational beliefs, and interests. Developmental Psychology, 48(6), 1643–1657.

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Characteristics of Students Sensory Mathematical Imagination in Solving Mathematics ProblemTeguh Wibowo, Akbar Sutawidjaja, Abdur Rahman As’ari, I Made Sulandra
pp. 609619  Article Number: iejme.2017.035
Abstract This study aim to investigate the characteristics of students’ sensory mathematical imagination of in solving mathematics problems. This study includes qualitative research with two students of VIII grade junior high school used as subjects. To determine the characteristics of students sensory mathematical imagination who appeared in solving mathematics problems, researchers use the problem sheet as a supporting instrument in this study. The problem sheet consists of a question item that serves to stimulate appear of students sensory mathematical imagination. For accuracy of data using triangulation method of observation, students answers, and interviews. The results showed characteristics of students sensory mathematical imagination in solving mathematics problems is appear of the idea based on perception due to stimulate of the problem, actualization information by analogy according to what people think, the activity involves body movement (sensory motor), can be seen through visual representation. Keywords: Perception; sensory mathematical imagination References Carroll, M., Goldman, S., Britos, L., Koh, J., Adam, R., and Hornstein, M. (2010). Destination, Imagination and the Fires Within: Design Thinking in a Middle School Classroom. Journal Compilation ©, NSEAD/Blackwell Publishing Ltd. Chapman, O. (2008). Imagination as a Tool in Mathematics Teacher Education. Journal Mathematics Teacher Education, 11, 83–88. Creswell, J.W. (2014). Research Design: Qualitative, Quantitaive and Mixed Methods Approaches. California: Saga Publication. Currie, G. & Ravenscroft, I. (2002). Recreative Minds: Imagination in Philosophy and Psychology. Oxford: Oxford University Press. Ferrara, F. (2006). Remembering and Imagining: Moving back and forth between motion and its representation. Proceedings of the Thirtieth Conference of the International Group for the Psychology of Mathematics Education, (Vol.3, pp.65–72). Prague: Charles University. Kotsopoulos, D. & Cordy, M. (2009). Investigating Imagination as a Cognitive Space for Learning Mathematics. Educ Stud Math, 70, 259–274, DOI 10.1007/s 1064900891540. Muir, T., Beswick, K., Williamson, J. (2008). “I’m not very good at solving problems”: An exploration of students’ problem solving behaviours. Journal of Mathematical Behavior, 27, 228–241. Nemirovsky, R. & Ferrara, F. (2008). Mathematical Imagination and Embodied Cognition. Journal Educational Studies in Mathematics, 70, 159–174. Samli, A.C. (2011). From Imagination to Creativity. From Imagination to Innovation: New Product Development for Quality of Life, DOI 10.1007/9781461408543_2, © Springer Science + Business Media, LLC. Solso, R., Maclin, O. & Maclin, M. (2008). Psikologi Kognitif Edisi Kedelapan. Jakarta: Erlangga. Swirski, T. (2010). Unleashing the imagination in learning, teaching and assessment: design perspectives, innovative practices and meaning making. Ph.D candidate, Macquarie University. van Alphen, P. (2011). Imagination as a transformative tool in primary school education. RoSE  Research on Steiner Education, 2 (2), ISSN 18916511. Wibowo, T. and As'ari, A.R. (2014). Type Imagination Student Mathematical In Mathematical Problem Solving. Proceedings of the National Seminar on Education Mathematics II. Math P4TK Yogyakarta. Wilke, J. (2010). Using Imagination in the Math Classroom. Journal of Educational Perspectives, 39(2).

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Students’ Reflective Abstraction in Solving Number Sequence ProblemsMohammad Djasuli, Cholis Sa’dijah, I Nengah Parta, Tjang Daniel Chandra
pp. 621632  Article Number: iejme.2017.036
Abstract This study is qualitative in nature, aims to describe students’ reflective abstraction in solving problems related to number sequence. As subjects of this study are 6 students, composed of 3 students (2 female and one male) from State Senior High School (SMAN) 1 Pasuruan, and 3 students (2 male and 1 female) from SMAN 1 Pandaan, East Java, Indonesia. In this study, the researchers were acted as human instruments. Narrative description was compiled by assembling descriptions of reflective abstraction stages associated with the criteria of high, intermediate, or low thinking processes, and the cognitive levels including knowledge application and reasoning. The results suggest that students’ strategies of problem solving are not directly proportional to their level of reflective abstraction. It was also found that students’ reflective abstraction furnish students’ individually unique solution, simply complicated, while interventions are important in its attainments. Keywords: Stages and levels of reflective abstraction, high school students, number sequence References Abrahamson, D. (2006). Exposing Piaget’s Scheme: Empirical Evidence for the Ontogenesis of Coordination in Learning a Mathematical Concept. University of California, Berkeley. Belbase, S. (2010). A Reflective Journey through Theory and Research in Mathematical Learning and Development. Retrieved from http://files.eric.ed.gov/fulltext/ED514497.pdf Beth, E. W., & Piaget, J. (1966). Mathematical Epistemology and Psychology. Dordrecht, The Netherlands: D. Reidel. Bowie, L. 1998. A Learning Theory Approach to Students’ Misconceptions in Calculus. Thesis. University of Cape Town, South Africa. Retrieved from https://open.uct.ac.za/bitstream/ handle/11427/9556/thesis_sci_1998_bowie_l.pdf?sequence=1 Carter, P. & Russel, K. (2004). The Complete Book of Fun Maths, 250 Confidence Boosting Tricks, Test and Puzzles. New York, NY: John Wiley & Sons. Retrieved from http://as.wiley.com/WileyCDA/WileyTitle/productCd0470870915.html Clark, D.A. (2014). The Wiley Handbook of Cognitive Behavioral Therapy. First Edition. New York, NY: Guilford Press. Copley, J. (2013). Mathematical Thinking. Retrieved from http://images.pearsonclinical.com/images/ Assets/WSS_5/Research Summary_Mathematical_Thinking_FNL.pdf Creswell, J.W. (2014). Research Design: Qualitative, Quantitative, and Mixed Methods Approaches. Fourth Edition. Sage Publications. Chrisopher, J.C. & Campbell, R.L. (2008). An InteractivistHermeneutic Metatheory for Positive Psychology. Theory & Psychology. Vol. 18(5), 675–697. Sage Publications. DOI: 10.1177/ 0959354308093401 Retrieved from http://tap.sagepub.com. Dubinsky, Ed. (1992). Reflective Abstraction in Advanced Mathematical. In Advanced Mathematical Thinking. David Tall (ed), 95123. Dordrecht, The Netherlands: Kluwer Academic Publisher. Ferrari, P.L. (2003). Abstraction in Mathematics. Philosophical Transactions of the Royal Society B: Biological Sciences. Vol. 358(1435): 1225–1230. doi: 10.1098/rstb.2003.1316 Glasersfeld, Ernst von. (1991). Abstraction, RePresentation, and Reflection. In Epistemological foundations of mathematical experience. L.P. Steffe (Ed). New York, NY: Springer. Goedecke, J. (2013). Abstraction in Mathematics. A course material on powerpoint file. Queen’s College. Retrieved from https://www.dpmms.cam.ac.uk/~jg352/pdf/TMSTalk.pdf Gray, E. & Tall, D. (2001). Relationships between Embodied Objects and Symbolic Procepts: An Explanatory Theory of Success and Failure in Mathematics. Retrieved from http://homepages.warwick.ac.uk/staff/David.Tall/pdfs/dotpme25pintotall.pdf Hazzan, O & Zazkis, R. (2005). Reducing Abstraction: The Case of School Mathematics. Retrieved from http://www.sfu.ca/~zazkis/publications/Reducing%20Abstraction.pdf Kasali, R. (2006). Change! Cetakan ke delapan. Jakarta: PT Gramedia Pustaka Utama. Kumar, R. (2011). Research Methodology: a stepbystep guide for beginners. Third Edition. Sage Publications, Inc. Marlow, E. (1990). Psychological Foundations in Teaching Mathematics. Retrieved from http://files.eric.ed.gov/fulltext/ED431606.pdf Mason, J., Burton, L. & Stacey, K. (2010), Thinking Mathematically. Second Edition. England: Pearson Education Limited. Michelmore, M & White, P. (2004). Abstraction in Mathematics and Mathematics Learning. In Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education. Vol 3, 329–336. Retrieved from https://www.emis.de/ proceedings/PME28/RR/RR031_Mitchelmore.pdf Mitchelmore, M. & White, P. (2007). Abstraction in Mathematics Learning. In Mathematics Education Research Journal. Vol 19(2), 19. Mousoulides, N. & Gagatsis, A. (2004). Algebraic and Geometry. Approach in Function Problem Solving. Retrieved from http:// files.eric.ed.gov/fulltext/ED489596.pdf Ozmantar, F. M. & Monaghan, J. (2007). A Dialectical Approach to Formation of Mathematical Abstractions. Mathematics Education Research Journal,Vol.19 (2), 89112. Panasuk, R. M. (2011). Taxonomy for Assessing Conceptual Understanding in Algebra Using Multiple Representation. College Student Journal, Vol. 45 (2), 219232. Spring Hill Station, Mobile, AL. Retrieved from http://jasonadair.wiki.westga.edu/file/view/Taxonomy+for+ assessing+conceptual+understanding+in+Algebra+using+multiple+representations.pdf Paschos, T. & Farmaki, V. (2006). The Reflective Abstraction in the Construction of the Concept of the Definite Integral: A Case Study. Retrieved from ftp://ftp.math.ethz.ch/EMIS/proceedings/ PME30/4/337.pdf), Ruch, F.L. (1967). Psychology and Life. Glenview, IL: Scott Foresman. Schoenfeld, A.H. (1992). Learning to Think Mathematically: Problem Solving, Metacognition, and Sense Making in Mathematics. In: D. Grouws (Ed). Handbook for Research on Mathematics Teaching and Learning. New York, NY: MacMillan. Silver, H.F., Brunsting, J.R., Walsh, T. & Thomas, E.J. (2012). Math Tools, Grades 3–12. 60+ Ways to Build Mathematical Practices, Differentiate Instruction, and Increase Student Engagement. Second Edition. Sage Publishing. Solso, R.L, MacLin, O.H. & MacLin, M.K. (2008) Cognitive Psychology. Eighth Edition. Pearson. Stacey, K. (2014) What is mathematical thinking and why is it important? Retrieved from https://www.researchgate.net/publication/254408829 Tall, D. (2002) Advanced Mathematical Thinking. New York, NY: Kluwer Academic Publishers. Tall, D. (2009) The Development of Mathematical Thinking: ProblemSolving and Proof. Retrieved from http://homepages.warwick.ac.uk/staff/David.Tall/pdfs/dot2009dpaperforjohn mason.pdf Turnau, S. (Ed) (2008). Handbook of Mathematics Teaching Improvement:Professional Practices that Address PISA. Output of the Krygowska Project. “Professional Development of TeacherResearchers” 20052008. University of Rzeszów. KSERKOP, Kraków, Poland: Drukarnia Cyfrowa. Walle, J. A.V. (2007). Elementary and Middle School Mathematics. Cetakan ketujuh. Jakarta: Penerbit Erlangga. Zimbardo, P.G. & Ruch, F.L. (1977). Psychology and Life. Ninth Edition. Chicago, Illinois: Pearson Scott Foresman. Zull, J. E. (2002). The Art of Changing the Brain. Sterling, VA: Stylush Publishing. 
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Investigation into Selfregulation, Engagement in Learning Mathematics and Science and Achievement among Bahrain Secondary School StudentsMasooma Ali Al Mutawah, Ruby Thomas & Myint Swe Khine
pp. 633653  Article Number: iejme.2017.037
Abstract Students’ view on themselves is the root of selfregulatory skills, and it will serve as an evaluator of their capability to succeed. This study attempts to find the relationship between students’ selfregulation in learning and academic achievements in Mathematics and Science in the secondary schools in Bahrain. ‘Engagement in Mathematics/Science Learning and SelfRegulation’ questionnaires adopted from TIMSS (2011) and administered to different sets of students. The data was analyzed to explore the reliability of the questionnaires and the association between selfregulation and academic achievement. The study found that there is a positive correlation between them in both cases. Keywords: Selfregulation, Engagement, Academic achievement and Reliability References Bandura, A. (1997). Selfefficacy: The exercise of control. New York: Freeman. Baumeister, R. F. & Vohs, K. D. (2004). Handbook of selfregulation: Research, theory, and applications. New York, NY: Guilford Press. Becker, D. R., McClelland, M. M., Loprinzi, P., & Trost, S. G. (2014). Physical activity, selfregulation, and early academic achievement in preschool children. Early Education & Development, 25, 56–70. doi: 10.1080/10409289.2013.780505. Bembenutty, H., & Zimmerman, B. J. (2003, April). The relation of motivational beliefs and selfregulatory processes to homework completion and academic achievement. Paper presented at the Annual Meeting of the American Educational Research Association, Chicago, IL. BernierClarebout, G., Horz, H., & Schnotz, W. (2010). The relations between selfregulation and the embedding of support in learning environments. Educational Technology Research and Development, 58 (5), 573587. Boekaerts, M. (1996). Selfregulated learning at the junction of cognition and motivation. European Psychologist, 1, 100–112. Boekaerts, M., & Corno, L. (2005) Selfregulation in the classroom: A perspective on assessment and intervention. Applied Psychology: An International Review, 54(2), 199231. Bull, R. & Scerif, G. (2001) Executive functioning as a predictor of children’s mathematics ability: inhibition, switching, and working memory. Developmental Neuropsychology, 19, 273–293. Butler, D. L., & Winne, P.H. (1995). Feedback and selfregulated learning: A theoretical synthesis. Review of Educational Research, 65(3), 245281. Canca, D. (2005). Cinsiyete gore universite oğrencilerinin kullandıklarıbilişsel ve bilişustu oğrenme stratejileri ve akademik başarıları arasındaki ilişkilerin incelenmesi. Yayınlanmamış yüksek lisans tezi, Yıldız Teknik Üniversitesi, Sosyal Bilimler Enstitüsü, İstanbul. Cantwell, R. H. (1998). The development of beliefs about learning from mid to late adolescence. Educational Psychology, 18(1), 2740. Corno, L. (2001). Volitional aspects of selfregulated learning. In B. J. Zimmerman & D. H. Schunk (Eds.), Selfregulated learning and academic achievement: Theoretical perspectives (2nd ed., pp. 191226). Mahwah, NJ: Lawrence Erlbaum Associates. Crawford, K., Gordon, S., Nicholas, J., & Prosser, M. (1998). University mathematics students’ conceptions of mathematics. Studies in Higher Education, 23, 8794. Davis, D. (2011). NonCognitive Constructs and SelfReported Creativity by Domain. Journal of Creative Behavior, Volume 45 Number 3 Third Quarter 2011, 188198. De Backer, T. K., & Nelson, R. M. (1999). Variations on an expectancyvalue model of motivation in science. Contemporary Educational Psychology, 24, 71–94. De Bruin, A.B., Thiede, K.W., & Camp, G. (2011). Generating keywords improves metacomprehension and selfregulation in elementary and middle school children. Journal of Experimental Child Psychology, 109 (3), 294310. De Corte, E., Mason, L., Schraw, G., Crippen, K., & Hartley, K. (2006). Promoting selfregulation in science education: metacognition as part of a broader perspective on learning. Research in Science Education, 36, 111139. De Corte, E., Op’t Eynde, P., & Verschaffel, L. (2002). ―Knowing what to believe: Therelevance of students’ mathematical beliefs for mathematics education. In B. K. Hofer & P. R. Pintrich (Eds.), Personal epistemology: The psychology of beliefs about knowledge and knowing (pp. 297 320). De corte, E., Verschaffel, L., & Op’teynde, P. (2000). Selfregulation: A characteristic goal of mathematics education. In M. Boekaerts, P. R. Pintrich, & M. Zeidner (Eds.), Handbook of selfregulation: Theory, research, and applications (pp. 687722). San Diego, CA: Academic Press. Deci, E. L., & Ryan, R. M. (2002). Handbook of self determination research. Rochester, NY: University of Rochester Press. Eilam B., Zeidner M. and Aharon, I. (2009) Student conscientiousness, selfregulated learning, and science achievement: an explorative field study. Psychology in the Schools, 46 (5), 420  432. www.interscience.wiley.com. DOI: 10.1002/pits.20387. Eom, Y., & Reiser, R. A. (2000). The effects of self regulation and instructional control on performance and motivation in computerbased instruction. International Journal of Instructional Media, 27(3), 247261. Ergöz, G. (2008). Investigation of selfregulated learning and motivational beliefs mathematics achievement Yayınlanmamış yüksek lisans tezi, Middle East Technical University, Department of Secondary Science and Mathematics Education, Ankara. Eshel, Y., & Kohavi, R. (2003). Perceived classroom control, selfregulated learning strategies, and academic achievement. Educational Psychology, 23, 249260. Forgas, J. P., Baumeister, R. F., & Tice D. M. (2009). Psychology of selfregulation. Cognitive, affective and motivational processes. New York: Psychology Press Tylor & Francis Group. Fox, K. R., & Wilson, P. M. (2008).Selfperceptual systems and physical activity. In T.S. Horn (Ed.), Advances in sport psychology (pp. 4964). Champaign, IL: Human Kinetics. Garavalia, L. S., & Gredler, M. E. (2002). An exploratory study of academic goal setting, achievement calibration and selfregulated learning. Journal of Instructional Psychology, 29 (4), 221230. Glaser, C., & Brunstein, J. C. (2007). Improving fourthgrade students’ composition skills: Effects of strategy ınstruction and selfregulation procedures. Journal of Educational Psychology, 99 (2), 297310. Gollwitzer, P. M., & Brandstätter, V. (1997). Implementation intentions and effective goal pursuit. Journal of Personality and Social Psychology, 73(1), 186199. Grouws, D. A., Howald, C. L., & Colangelo, N. (1996, April). Student conceptions of mathematics: A comparison of mathematically talented students and typical high school algebra students. Paper presented at the American Educational Research Association, New York, NY. Hannula M., Evans J., Philippou, G., and Zan R. (2004) Affect in mathematics education – exploring theoretical frameworks. Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education, l, 107–136. Harris, K. & Graham, S. (1999). Programmatic intervention research: Illustrations from the evolution of selfregulated strategy development. Learning Disability Quarterly, 22, 251262. Harris, K. R., Friedlander, B.D., Saddler, B., Frizzelle, R. & Graham, S. (2005). Self monitoring of attention versus selfmonitoring of academic performance: Effects among students with ADHD in the general education classroom. Journal of Special Education, 39 (3), 145156 Haşlaman, T. (2005). Programlama dersi ile ilgili ozduzenleyici oğrenme stratejileri ve başarı arasındaki ilişkilerin incelenmesi: Bir yapısal eşitlik modeli. Yayınlanmamış yüksek lisans tezi, Hacettepe Üniversitesi, Fen Bilimleri Enstitüsü, Ankara. Hofer, S.M.(1999. Assessing personality structure using factorial invariance procedure, in I.Mervielde, I.J. Deary, F. De Fruyt and F. Osterndof (eds) Personality Psychology in Europe, vol. 7, pp. 3549. Tilburg, Netherlands: Tilburg University Press. IranNejad, A. (1990). Active and dynamic self regulation of learning processes. Review of Educational Research, 60, 573602. Kenney, P. A., & Silver, E. A. (Eds.). (1997, November). Results from the sixth mathematics assessment of the National Assessment of Educational Progress. Kinney, D. P. (2001). Developmental theory: Application in a developmental mathematics program. Journal of Developmental Education, 25(2), 1012, 14, 16,18, 34. Kitsansas, A., Sten, S., & Huie, F. (2009). The role of selfregulated strategies and goal orientation in predicting achievement of elementary school children. International Electronic Journal of Elementary Education, 2 (1), 6581. Koller, O. (2001). Mathematical world views and achievement in advanced mathematics in Germany: Findings from TIMSS population 3. Studies in Educational Evaluation, 27, 6578. Kolovelonis, A., Goudas, M., & Dermitzaki, I. (2011). The effect of different goals and selfrecording on selfregulation of learning a motor skill in a physical education setting. Learning and Instruction, 21 (3), 355364. Kuhl, J., & Fuhrmann, A. (1998). Decomposing selfregulation and selfcontrol: The volitional components inventory. In J. H. C. S. Dweck (Ed.), Motivation and selfregulation across the life span (pp. 1549). Cambridge: Cambridge University Press. Labuhn, A.S., Zimmerman, B.J., & Hasselhorn, M. (2010). Enhancing students’ self regulation and mathematics performance: The influence of feedback and self evaluative standards Metacognition and Learning, 5 (2), 173194. Lampert, M. (1990). When the problem is not the question and the solution is not the answer: Mathematical knowing and teaching. American Educational Research Journal, 27, 2963. Leininger, L. J. and Khalil, A. (2008) Cognitive and NonCognitive Predictors of Success in AEP. Journal of Policy Analysis and Management, 27(3), 521535. DOi: 10.1002/pam.20357. Mahwah, NJ: Erlbaum Muis, K. R. (2004). Personal epistemology and mathematics: A critical review and synthesis of research. Review of Educational Research, 74, 317377. McClelland, M. M., Cameron Ponitz, C. E., Connor, C. M., Farris, C. L., Jewkes, A. M., & Morrison, F. J. (2007). Links between behavioral regulation and preschoolers’ literacy, vocabulary, and math skills. Developmental Psychology, 43, 947–959. doi:10.1037/00121649.43.4.947. McClellan, E. (1999). Moral education in America: Schools and the shaping of character from colonial times to the present.New York, NY: Teachers College Press. Moffitt, T. E., Arseneault, L., Belsky, D., Dickson, N., Hancox, R. J., Harrington, H., Houts, R., Poulton, R., Roberts, B.W., Ross, S.,Sears, M. R., Thomson, W. M. & Caspi, A. (2011) A gradient of childhood selfcontrol predicts health, wealth, and public safety. Proceedings of the National Academy of Sciences of the United States of America, 108, 2693–2698. Nicholls, J. G. (1989). The competitive ethos and democratic education. Cambridge, MA: Harvard University Press. Nota, L., Soresi, S., & Zimmerman, B. J. (2004). Selfregulation and academic achievement and resilience: A longitudinal study. International Journal of Educational Research, 41(3), 198215. Pajares, F. (2002) Gender and Perceived SelfEfficacy in SelfRegulated Learning, Theory Into Practice, 41(2), 116125. http://dx.doi.org/10.1207/s15430421tip4102_8. Pape, S. J., & Smith, C. (2002). Selfregulating mathematics skills. Theory into Practice, 41, 93101. Paulsen, M. B., & Feldman, K. A. (2007). The conditional and interaction effects of epistemological beliefs on the selfregulated learning of college students: Cognitive and behavioral strategies. Research in Higher Education, 48, 353401. Pintrich, P. R. (2000). The role of goal orientation in selfregulated learning. In M. Boekaerts, P. Pintrich, & M. Zeidner (Eds.), Handbook of selfregulation (pp. 451–502). San Diego, CA: Academic Press. Pintrich, P. R., & Schunk, D. H. (2002). Motivation in education: Theory, research, and applications. Columbus, OH: Merrill. Pintrich, P. R., & De Groot, E. (1990). Motivational and selfregulated learning components of classroom academic performance. Journal of Educational Psychology, 82(1), 3350. Pintrich, P., R., Smith, D. A. F., Garcia, T., & McKeachie, W. J. (1991). A manual for the use of the motivated strategies for learning questionnaire (MSLQ). National Center for Research to Improve Postsecondary Teaching and Learning, Ann Arbor: Michigan, ED 338 122. Pokay, P., & Blumenfeld, P. C. (1990). Predicting achievement early and late in the semester: The role of motivation and use of learning strategies. Journal of Educational Psychology, 82, 4150. Ruban, L., & Reis, S. M. (2006). Patterns of selfregulatory strategy use among lowachieving and high achievming university students, Roeper Review, 28 (3), 148156. Schmeichel, B.J.; Baumeister. (2006) Selfregulatory processes defend against the threat of death: Effects of selfcontrol depletion and trait selfcontrol on thoughts and fears of dying. Journal of Personality and Social Psychology, 91(1), 4962. Schoenfeld, Alan H.(1992). "Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics." Handbook of research on mathematics teaching and learning: 334370. Schoenfeld, A. H. (1987). What’s all the fuss about metacognition? In A. H. Schoenfeld (Ed.), Cognitive science and mathematics education (pp. 189215). Hillsdale, NJ:Lawrence Erlbaum Associates. Schoenfeld, A. H. (1989). Explorations of students’ mathematical beliefs and behavior. Journal for Research in Mathematics Education, 20,338355. SchommerAikins, M., Duell, O. K., & Hutter, R. (2005). Epistemological beliefs, mathematical problemsolving beliefs, and academic performance of middle school students. The Elementary School Journal, 105, 289304. Schunk, D. H. (1986). Verbalization and children’s selfregulated learning. Contemporary Educational Psychology, 11, 347–369. Schunk, D. H. (1996). Goal and selfevaluative influences during children’s cognitive skill learning. American Educational Research Journal, 33, 359–382. Seider, S. and Soutter, M. (2013) College Access, Student Success, and the New Character Education. Journal of College & Character, 14(4), 351 356. doi:10.1515/jcc20130044. Schunk, D. H. (2000). Coming to terms with motivational constructs. Contemporary Educational Psychology, 25, 116–119. Shunk, D. (1996). Goal and selfevaluative influences during children’s cognitive skill learning. American Educational Research Journal, 33, 359382. Schunk, D. H. (1995). Selfefficacy and education and instruction. In J. E. Maddux (Ed.), Selfefficacy, adaptation, and adjustment: Theory, research, and application(pp. 281303). New York: Plenum Press. Sparkman, L., Maulding, W. S. and Roberts, J. G. (2002) Noncognitive predictors of student success in college. College Student Journal, 642652. Strayhorn, T. (2015) Factors Influencing Black Males’ Preparation for College and Success in STEM Majors: A Mixed Methods Study. The Western Journal o f Black Studies, 39(1), 4563. Trainin, G., & Swanson, H. L. (2005). Cognition, metacognition, and achievement of college students with learning disabilities. Learning Disability Quarterly, 28(4), 261272. Uredi, I. ve Uredi, L. (2005). İlkoğretim 8. sınıfoğrencilerinin oz duzenleme stratejileri ve motivasyonel inanclarının matematik başarısını yordama gucu. MersinÜniversitesi Eğitim Fakültesi Dergisi, 1(2), 250260. Valiente, C., LemeryChalfant, K., Swanson, J. & Reiser, M. (2008) Prediction of children’s academic competence from their effortful control, relationships, and classroom participation. Journal of Educational Psychology, 100, 67–77. Velayutham S., Aldridge S. J., and Fraser B. (2011) Development and Validation of an Instrument to Measure Students’ Motivation and Self Regulation in Science Learning. International Journal of Science Education, 33(15), 2159 – 2179. http://dx.doi.org/10.1080/09500693.2010.541529. Velayutham S., Aldridge S. J., and Fraser B. (2012) Gender differences in student motivation and selfregulation in science learning: a multigroup structural equation modeling analysis. International journal of science and mathematics education, 10, 13471368. Winne, P. H. (2000). Information processing models of selfregulated learning. In B. J. Zimmerman & D. H. Schunk (Eds.), Selfregulated learning and academic achievement: Theory, research, and practice. New York: Longman. Wolters, C.A. (2011). Regulation of motivation: Contextual and social aspects. Teachers College Record, 113 (2), 265283. Zhou, Q., Main, A. & Wang, Y. (2010) The relations of temperamental effortful control and anger/frustration to Chinese children’s academic achievement and social adjustment: a longitudinal study. Journal of Educational Psychology, 102, 180–196. Zimmerman, B. J. (1995). Selfefficacy and educational development. In A. Bandura (Ed.), Selfefficacy in changing societies (pp. 202–231). New York: Cambridge University Press. Zimmerman, B. J. (2006). Development and adaptation of expertise: The role of selfregulatory processes and beliefs. In K. A. Ericsson, N. Charness,P. J. Feltovich & R. R. Hoffman (Eds.), The Cambridge handbook of expertise and expert performance (pp. 705722). New York, NY: Cambridge University Press. Zimmerman, B. J., & Kitsantas, A. (2005). Homework practices and academic achievement: The mediating role of selfefficacy and perceived responsibility beliefs. 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The Effectiveness of OpenEnded Problems Based AnalyticSynthetic Learning on the Mathematical Creative Thinking Ability of PreService Elementary School TeachersYeni Yuniarti, Yaya S. Kusumah, Didi Suryadi & Bana G. Kartasasmita
pp. 655666  Article Number: iejme.2017.038
Abstract This study aims to analyze the achievement of mathematical creative thinking ability of preservice elementary school teachers who received openended problems based analyticsynthetic learning and conventional learning. This study is a quasiexperimental research with pretestposttest control group design to preservice elementary school teachers in a state university of West Java with 136 students divided into two groups of research subjects, of 68 students each. The instrument used in this research are prior mathematical knowledge test, mathematical creative thinking ability tests, and interview guidance. The results of data analysis using statistic of parametric and nonparametric showed that: 1) The Achievement mathematical creative thinking ability of students who received openended problems based learning analyticsynthetic better than those conventional learning is reviewed whole and each level prior mathematical knowledge as well; 2) the effect size of openended problems based analyticsynthetic learning on the achievement of students' mathematical creative thinking ability in high category. The research recommended that openended problems based analyticsynthetic learning can be used achievement of mathematical creative thinking ability. Keywords: Creative thinking, openended, analyticsynthetic learning References Arikunto, S. (2005). Dasardasar Evaluasi Pendidikan. Jakarta: Bumi Aksara. Badan Standardisasi Nasional Pendidikan (BSNP). (2006). Pedoman penyusunan kurikulum tingkat satuan pendidikan. Jakarta: Depdiknas. Celik, D. & dan Arslan, A.S. (2012). The Analysis of Teacher Candidates’ Translating Skills in Multiple Representations. Elementary Education Online, 11(1), 239250. Chamberlin, S.A. & Moon, S.M. (2005). Modeleliciting activities as tool to develop and identify creativity gifted mathematicians. Journal of Secondary Gifted Education, 17(1), 37–47. Chareka, O. (2010). A matter of prior knowledge: Canadian young children’s conceptions about the future in the global community. International Electronic Journal of Elementary Education, 2(2), 287303. Craig, J. (2015). Assessing the Relationship between Questioning and Understanding to Improve Learning and Thinking (QUILT) and Student Achievement in Mathematics: A Pilot Study. Virginia: Charleston. Hailikari, T. (2009). Assessing University Students’Prior Knowledge. Implications for Theory and Practice. Helsinki: Helsinki University Print. Hyman, B. (1993). Measuring What Counts: A Conceptual Guide for Mathematics Assessment. Washington: National Academies Press. Kartini. (2011). Peningkatan Berpikir Kritis dan Kreatif serta Belief Matematis Siswa Sekolah Menengah Atas melalui Pembelajaran Inkuiri Model Alberta. Diterbitkan: SPS UPI. Khoiri, W., Rochmad, A. & Cahyono, A.N. (2013). Problem Based Learning berbantuan Multimedia dalam Pembelajaran Matematika untuk meningkatkan Kemampuan Berpikir Kreatif. Unnes Journal of Mathematics Education, 2(1), 114121. Kumiati. (2014). Peningkatan Kemampuan Berpikir Kritis dan Kreatif Matematis serta Soft Skill Mahasiswa Pendidikan Guru SD melalui Pendekatan Pembelajaran Kontekstual. Diterbitkan: SPS UPI. Kwon, O.N., Park, J.S & Park, J.H. (2006). Cultivating Divergent Thinking in Mathematics through an OpenEnded Approach. Asia Pacific Education Review, 7(1), 5161. Lee, I.R. & Kemple, K. (2014). Preservice Teachers' Personality Traits and Engagement in Creative Activities as Predictors of Their Support for Children's Creativity. Creativity Research journal. 26(1). 8294. Mann, E.L. (2005). Mathematical Creativity and School Mathematics: Indicators of Mathematical Creativity in Middle School Students. Direct access: http://www.gifted. uconn.edu/Siegle/ Mann, E.L. (2006). Creativity: The Essence of Mathematics. Journal for the Education of the Gifted, 30(2), 236–260. Mulyana, T. (2008). Pembelajaran Analitik Sintetik untuk Meningkatkan Kemampuan Berpikir Kritis dan Kreatif Matematik Siswa Sekolah Menengah Atas. Diterbitkan: SPS UPI. Munandar, U. (2014). Pengembangan Kreativitas Anak Berbakat. Jakarta: Rineka Cipta. Munandar, U. (2003). Kreativitas & Keberbakatan. Strategi Mewujudkan potensi kreatif & Bakat. Jakarta: PT Gramedia Pustaka Utama. Nadjafikhah, M. & Yaftian, N. (2013). The frontage of Creativity and Mathematical Creativity. Procedia  Social and Behavioral Sciences, 90, 344350. Nadjafikhah, M., Yaftian, N. & Bakhshalizadeh, S. (2012). Mathematical creativity: some definitions and characteristics. Procedia  Social and Behavioral Sciences, 31, 285291. National Research Council. (2012). Education for Life and Work: Developing Transferable Knowledge and Skills in the 21st Century. Committee on Defining Deeper Learning and 21st Century Skills, James W. Pellegrino and Margaret L. Hilton, Editors. Board on Testing and Assessment and Board on Science Education, Division of Behavioral and Social Sciences and Education. Washington: The National Academies Press. Neumann, C.J. (2007). Fostering creativity—A model for developing a culture of collective creativity in science. EMBO Reports, 8(3), 202–206. Noer, S.H. (2011). Kemampuan Berpikir Kreatif Matematis dan Pembelajaran matematika Berbasis masalah OpenEnded. Jurnal Pendidikan Matematika, 5(1), 104 – 111. Nohda, N. (2000). Teaching by OpenApproach Method in Japanese Mathematics Classroom. Proceedings of the Conference of the International Group for the Psychology of Mathematics Education, 1, 2327. Risnanosanti. (2010). Kemampuan Berpikir Kreatif Matematis dan Self Efficacy terhadap Matematika Siswa Sekolah Menengah Atas (SMA) dalam pembelajaran Inquiri. Diterbitkan: SPS UPI. Shahrill, M. & Clarke, D.J. (2014). Brunei Teachers’ Perspectives on Questioning: Investigating the Opportunities to “Talk” in Mathematics Lessons. International Education Studies, 7(7), 117. Sriraman, B. (2005). Are giftedness & creativity synonyms in mathematics? An analysis of constructs within the professional and school realms. The Journal of Secondary Gifted Education, 17, 20–36. Starko, A.J. (2014). Creativity in the Classroom Schools of Curious Delight. New York: Routledge. Sternberg, R.J. (2006). The Nature of Creativity. Creativity Research Journal. 18(1), 87–98. Suastika, K. (2017). Mathematics Learning Model of Open Problem Solving to Develop Students’ Creativity. International Electronic Journal of Mathematics Education. 12(6), 569577. Supriadi. (2014). Mengembangkan Kemampuan dan Disposisi Pemodelan serta Berpikir Kreatif Matematis Mahasiswa PGSD melalui Pembelajaran Kontekstual Berbasis Etnomatematika. Diterbitkan: SPS UPI. Suryana, A. (2016). Meningkatkan Advanced Mathematical Thinking dan Self Renewal Capacity Mahasiswa melalui Pembelajaran Model PACE. Pendidikan: Universities Pendidikan. Trilling, B. & dan Fadel, C. (2009). 21 st Century Skill: Learning for Life in Our Times. San Francisco: JosseyBass A Wiley Imprint. Yaqoob, M. (2012). Developing Creative Thinking: Using a Cognitive Teaching Model in Literature Classroom. The International Journal of Learning. 18(6), 7182. 
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Are Word Problems Really More Difficult for Students with Low Language Proficiency? Investigating Percent Items in Different Formats and TypesBirte Pöhler, Ann Cathrice George, Susanne Prediger, Henrike Weinert
pp. 667687  Article Number: iejme.2017.039
Abstract Achievement gaps between students with low and high language proficiency appear for word problems, but is this due to their text format or their conceptual challenges? A test with percent problems of different types and in pure, text and visual format was conducted with N=308 seventh graders. Students’ scores were analyzed statistically by a cognitive diagnosis model. Unlike expected, the probability for students with low language proficiency to solve items in text format is not lower than in pure format. These results are interpreted as indication that conceptual challenges might impact stronger than reading challenges. Keywords: Percentages, word problems, cognitive diagnosis model, DINA, visual models, language proficiency References Abedi, J. (2004). Will You Explain the Question?. Principal Leadership, 4(7), 2731. Abedi, J. (2006). Language issues in itemdevelopment. In S. M. Downing & T. M. Haldyna (Eds.), Handbook of test development (pp. 377398). Mahwah: Erlbaum. Abedi, J., & Lord, C. (2001). The language factor in mathematics tests. Applied Measurement in Education, 14(3), 219234. Behr, M. J., Harel, G., Post, T. R., & Lesh, R. (1992). Rational number, ratio, and proportion. In D. A. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning (pp. 296–332). New York: Macmilian. Carpenter, T. P., Corbitt, M. K., Kepner, H. S., Lindquist, M. M., & Reys, R. E. (1980). NAEP note: Problem solving. The Mathematics Teacher, 73(6), 427433. de la Torre, J. (2009). DINA model parameter estimation: A didactic. Journal of Educational and Behavioral Statistics, 34(1), 115–130. de La Torre, J. & Minchen, N. (2014). Cognitively Diagnostic Assessments and the Cognitive Diagnosis Model Framework. Psicología Educativa, 20(2), 89–97. de la Torre, J., & Lee, Y.S. (2010). A note on the invariance of the DINA model parameters. Journal of Educational Measurement, 47(1), 115–127. DiBello, L., Roussos, L., & Stout, W. (2007). Review of cognitively diagnostic assessment and a summary of psychometric models. In C. R. Rao & S. Sinharay (Eds.), Handbook of Statistics, Volume 26, Psychometics (pp. 979–1030). Amsterdam: Elsevier. Dole, S., Cooper, T.J., Baturo, A.R., & Conoplia, Z. (1997). Year 8, 9 and 10 students’ understanding and access of percent knowledge. In A. Begg (Ed.), People in mathematics education. Proceedings of 20th MERGA (pp. 711). Rotorua: Merga. Duarte, J., Gogolin, I. & Kaiser, G. (2011). Sprachlich bedingte Schwierigkeiten von mehrsprachigen Schülerinnen und Schülern bei Textaufgaben. In S. Prediger & E. Özdil (Eds.), Mathematiklernen unter Bedingungen der Mehrsprachigkeit (pp. 3553). Münster: Waxmann. Fischer, G.H. & Molenaar, I.W. (1995). Rasch models: foundations, recent developments and applications. New York: Springer. George, A. C. & Robitzsch, A. (2014). Multiple group cognitive diagnosis models, with an emphasis on differential item functioning. Psychological Test and Assessment Modeling, 56(4), 405–432. George, A. C. & Robitzsch, A. (2015). Cognitive diagnosis models in R: A didactic. The Quantitative Methods for Psychology, 11(3), 189–205. George, A. C., Robitzsch, A., Kiefer, T., Groß, J., & Ünlü, A. (2016). The R Package CDM for cognitive diagnosis modeling. Journal of Statistical Software, 74(2), 1–24. Haag, N., Heppt, B., Roppelt, A., & Stanat, P. (2015). Linguistic simplification of mathematics items: effects for language minority students in Germany. European Journal of Psychology of Education, 30(2), 145167. Haag, N.,Heppt, B., Stanat, P.,Kuhl, P.,& Pant, H. A. (2013). Second language learners'performance in mathematics: Disentangling the effects of academic language features. Learning and Instruction, 22(28), 24–34. Haertel, E. H. (1989). Using restricted latent class models to map the skill structure of achievement items. Journal of Educational Measurement, 26, 301–323. Hafner, T. (2012). Proportionalität und Prozentrechnung. Wiesbaden: Vieweg + Teubner. Hirsch, E. D. (2003). Reading Comprehension Requires Knowledge  of Words and the World. Scientific Insights into the FourthGrade Slump and the Nation’s Stagnant Comprehension Scores. American Educator, 4(1), 1044. Jitendra, A. K., & Star, J. R. (2012). An exploratory study contrasting high and lowachieving students' percent word problem solving. Learning and Individual Differences, 22(1), 151158. Johnson, M., Lee, Y.S., Sachdeva, R. J., Zhang, J., Waldman, M., & Park, J. Y. (2013, March). Examination of gender differences using the multiple groups DINA model. Paper presented at the 2013 Annual Meeting of the National Council on Measurement in Education, San Francisco CA. Koedinger, K.R. & Nathan, M. J. (2004). The real story behind the story problems. Effects of representations on quantitative reasoning. The Journal of the Learning Sciences, 13(2), 129164. Kouba, V., Brown, C., Carpenter, T., Lindquist, M., Silver, E., & Swafford, J. (1988). Results of 4th NAEP Assessment of Mathematics. Arithmetic Teacher, 35(8), 1419. Martiniello, M. (2008). Language and the performance of Englishlanguage learners in math word problems. Harvard Educational Review, 78(2), 333–368. MaydeuOlivares. (2013). Goodnessoffit assessment of item response theory models. Measurement: Interdisciplinary Research and Perspectives, 11, 71–137. Moschkovich, J. (2013). Principles and Guidelines for Equitable Mathematics Teaching Practices and Materials for English Language Learners. Journal of Urban Mathematics Education, 6(1), 4557. OECD (2007). PISA 2006. Vol. 2: Data. Paris: OECD. Parker, M. & Leinhardt, G. (1995). Percent: A Privileged Proportion. Review of Educational Research, 65(4), 421481. Paulus (2009). Die Bücheraufgabe zur Bestimmung des kulturellen Kapitals bei Grundschülern. URL: http://psydok.sulb.unisaarland.de/volltexte/2009/2368/. Pöhler, B., & Prediger, S. (2015). Intertwining lexical and conceptual learning trajectories  A design research study on dual macroscaffolding towards percentages. Eurasia Journal of Mathematics, Science & Technology Education, 11(6), 16971722. Pöhler, B., Prediger, S., & Neugebauer, P. (2017, in press). Content and language integrated learning: A field experiment for percentages. To appear in Proceedings of the 41st Annual Meeting of the International Group for the Psychology of Mathematics Education (PME 41). Singapore: PME. Pöhler, B., Prediger, S., & Weinert, H. (2016). Cracking percent problems in different formats  The role of texts and visual models for students with low and high language proficiency. In K. Krainer & N. Voundrová (Eds.), CERME 9. Proceedings of the Ninth Congress of the European Society for Research in Mathematics Education (pp. 331338). Prague: Charles University / ERME. Prediger, S., Renk, N., Büchter, A., Gürsoy, E. & Benholz, C. (2013). Family background or language disadvantages? Factors for underachievement in high stakes tests. In A. Lindmeier & A. Heinze (Eds.), Proceedings of 37th PME (4, 4959). Kiel: PME. Prediger, S., Wilhelm, N., Büchter, A., Gürsoy, E., & Benholz, C. (2015). Sprachkompetenz und Mathematikleistung–Empirische Untersuchung sprachlich bedingter Hürden in den Zentralen Prüfungen 10. Journal für MathematikDidaktik, 36(1), 77104. R Core Team (2015). R: A language and environment for statistical computing. R Foundation for Statistical Computing. Vienna, Austria. Retrieved from http://www.Rproject.org Redder, A. & Wagner, J. (2015): BispraTest. Project internal test development, adapted from Uesseler et al. 2015. Robitzsch, A., Kiefer, T., George, A. C. & Ünlü, A. (2016). CDM: Cognitive Diagnosis Modeling. R Package version 3.114. Retrieved from http://CRAN.Rproject.org/package=CDM. Secada, W. G. (1992). Race, ethnicity, social class, language and achievement in mathematics. In D. A. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning (pp. 623–660). New York: MacMillan. Tatsuoka, K. K. (Ed). (1984). Analysis of errors in fraction addition and subtraction problems. Final Report for Grant No. NIEG810002. Urbana, IL: University of Illinois. Uesseler, S., Runge, A., & Redder, A. (2013). „Bildungssprache“ diagnostizieren. Entwicklung eines Instruments zur Erfassung von bildungssprachlichen Fähigkeiten bei Viert und Fünftklässlern. In A. Redder & S. Weinert (Eds.), Sprachförderung und Sprachdiagnostik. Interdisziplinäre Perspektiven (pp. 4267). Münster: Waxmann. Van den HeuvelPanhuizen, M. (2003). The didactical use of models in realistic mathematics education. Educational Studies in Mathematics, 54(1), 935. Van den HeuvelPanhuizen, M. (2005). The role of contexts in assessment problems in mathematics. For the Learning of Mathematics, 25 (2), 29. Walkington, C., Cooper, J., & Howell, E. (2013). Effects of visual representations and interestbased personalization on solving percent problems. In Martinez, M. & Castro Superfine, A. (Eds.), Proceedings of 35th PMENA (pp. 533536). Chicago: University of Illinois. Walzebug, A. (2014). Is there a languagebased social disadvantage in solving mathematical items? Learning, Culture and Social Interaction 3 (2), 159169. Wolf, M. K., & Leon, S. (2009). An Investigation of the Language Demands in Content Assessments for English Language Learners. Educational Assessment, 14(34), 139159. Xu, X. & von Davier, M. (2008). Comparing multiplegroup multinomial loglinear models for multidimensional skill distributions in the general diagnostic model (rr0835). Educational Testing Service. 
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The influence of learning model and learning independence on mathematics learning outcomes by controlling students' early abilityDodik Mulyono
pp. 689708  Article Number: iejme.2017.040
Abstract The aims of this research are; (1)Differences in mathematics learning outcomes of students learning with reciprocal teaching and student facilitator and explaining, (2)The effect of interaction between learning model and learning independence on mathematics learning outcomes in students, (3)Differences in student learning outcomes that have high learning independence by learning model reciprocal teaching and student facilitator and explaining, (4)Differences in learning outcomes of students who have low learning independence who learn with reciprocal teaching and learning with student facilitator and explaining. The research method used is experimental method. The result of hypothesis, (1)testing shows that H0 is rejected, (2)testing shows that H0 is rejected, (3)testing shows that H0 is rejected, (4)testing shows that H0 is rejected. Keywords: Learning Independence, Learning Models, Initial Abilities References Alisha Francis and Abraham Flanigan, SelfDirected Learning and Higher Education Practices: Implications for Student Performance and Engagement, The International Journal of the Scholarship of Teaching and Learning v. 7 n. 3, 2012. Arend, I Arend, (2012), Learning to Teach, 9th Editions, New York: McGrawHillCompanies. ISBN 9780078024320 Dick, Walter, Carey, Lou, Carey , James O, (2009), The Systematic Design of Instruction, New Jersey: Pearson Education, Inc. ISBN 9780132824859 Elaine B. Johnson, (2009), Contextual Teaching & Learning,terjemahan IbnuSetiawan, Bandung: Mizan Learning Center. ISBN 076197864X (c) Emzir, (2008), Metodologi Penelitian Pendidikan Pendekatan Kuantitatif dan Kualitatif, Jakarta: PT Raja Grafindo Persada. ISBN 9797691624 Fridani, Lara. (2009), Ape Lestari,Inspiring Education: Kisah Inspriratis Pembelajran Anak Usia Sekolah Dasar, Bandung: Alex Media Komputindo. ISBN 979273998X Harvey. S. Virginia and Wolfe, A. Chickie Louise, (2007), Fostering independent learning : practical strategies to promote student successs, New York: TheGuilford Press. ISBN13: 9781593854515 Jubeir Suleiman Samir AlHarby, The Effect of ReciprocalTeaching Strategy on LearningOutcomes and Attitudes of QassimUniversity Students in “Islamic Culture”, Journal of Education and Practice, Vol.7, No.6, 2016 Lie, Anita. (2010), Cooperative Learning, Jakarta: PT. Grasindo. ISBN 9789790253209 Oczkus. Lori D. (2010),Reciprocal teaching at work: powerful strategies and lessons for improving reading comprehension, Newyork: International ReadingAssociation. ISBN 9780872075078 Pallinscar, Anne marle S. and Ann L. Brown, Reciprocal Teaching Of Comprehension Fostering and Comprehension Monitoring Activities, Washington D.C: llionisUniversity Of liionis at OrbanaChampion, Cognition and Instruction I, 2007. Robyn M. Gillies and Adrian F. Ashman, (2003),Cooperative Learningthe; social and intellectual outcomes of learning in groups, New York: Routledge Falmer. ISBN 0203465261 Master ebook ISBN Seyyed Ali OstovarNamaghi and MohammadReza Shahhosseini, On the Effect of Reciprocal Teaching Strategy on EFL Learners’ Reading Proficiency, Journal of Language Teaching and Research, Vol. 2, No. 6, 2011 Siska Ryane Muslim, Pengaruh Penggunaan Metode Student Facilitator And Explaining Dalam Pembelajaran Kooperatif Terhadap Kemampuan Pemecahan Masalah Matematik Dan Kemampuan Berpikir Kritis Matematik Siswa SMK Di Kota Tasikmalaya, Jurnal Pendidikan dan Keguruan Vol. 1 No. 1, 2014. Wiliams, Jill. (2003),Promoting independent learning in the primary classroom, Buckingham: Open University Pres. ISBN 0335200168 
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The Teaching and Learning Process of Mathematics in the Primary Education Stage: a Constructivist Proposal within the Framework of Key CompetencesLuis Del Espino Díaz
pp. 709713  Article Number: iejme.2017.041
Abstract This paper aims to analyze the importance of acquiring mathematical skills in the primary education stage within the framework of the key competences highlighting their contribution to the development of a mathematical culture of society, hence the importance of the issues addressed in this paper. After giving a description of what the competence approach entails in education, we will focus on the constructivist methodology applied to the area of mathematics to finalize with the elaboration of pedagogical guidelines that facilitate the teaching and learning process of mathematics in the stage of primary education. Keywords: teaching mathematics; constructivism; curriculum; mathematical competence; primary education References Alsina, Á. (2015). Cómo fomentar el aprendizaje de las matemáticas en el aula. Ideas clave para la Educación Primaria. Barcelona: Editorial Casals. Baro, A. (2011). Metodologías activas y aprendizaje por descubrimiento. Revista Innovación y experiencias educativas. 40. Bhowmik, M. (2015). Constructivism approach in mathematics teaching and assessment of mathematical understanding. Basic Research Journal of Education Research and Review, 4(1), 0812. DíazBarriga, F. y Hernández, G. (2002). Constructivismo y aprendizaje significativo. Mexico: Mc Graw Hill. Garmendia Mujika, M., & Guisasola Aranzabal, J. (2015). Alfabetización científica en contextos escolares: El Proyecto Zientzia Live!. Revista Eureka sobre Enseñanza y Divulgación de las Ciencias, 12(2). Guirles, J. R. G., & Ramón, J. (2002). El constructivismo y las matemáticas. Sigma: Revista de Matemáticas, Vitoria, (2), 113129. Jazim, Anwar, R.B. & Rahmawati, D. (2017). The Use of Mathematical Module Based on Constructivism Approach as Media to Implant the Concept of Algebra Operation. IEJMEMathematics Education, 12(6), 579583. Major, T. E., Mangope, B. (2012). The Constructivist Theory in Mathematics: The Case of Botswana Primary Schools. International Review of Social Sciences and Humanities, 3(2) (2012), 139147. Martín, Y. (2013). Una propuesta constructivista, creativa y motivadora para el aprendizaje de las matemáticas en educación infantil. (Trabajo de Fin de Grado). UVA, Valladolid. Piñero, M. A. C., Pulido, J. R., & Falcón, J. A. A. (2017). El enfoque competencial educativo en el contexto europeo. El Guiniguada. Revista de investigaciones y experiencias en Ciencias de la Educación, 26, 6276. Rico, L. (2006). La competencia matemática en PISA. PNA, 1(2), 4766. Romero, F. (2009). Aprendizaje significativo y constructivismo. Revista digital Temas para la educación. 3 UNESCO (1996). La educación encierra un tesoro. Madrid: Editorial Santillana. Vigotsky, L. (1988). El desarrollo de los procesos psicológicos superiores. México: Editorial Crítica, Grupo editorial Grijalbo. 
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Patterns Change of Awareness Process, Evaluation, and Regulation on Mathematics StudentDwi Purnomo, Susilo Bekti
pp. 715733  Article Number: iejme.2017.042
Abstract This paper describe the change patterns in the process of awareness, evaluation, and regulation of mathematics students in solving mathematical problems. The patterns of change is reveled done by observation of the emergence of activity and indicators awareness, evaluation, and regulation of students. Student metacognition activities and indicators are outlined in 5 activities with 30 indicators of awareness process, 5 activities with 23 indicators of evaluation process, and 4 activities with 19 indicators of regulation process. The subjects of the study were students of mathematics education who had taken Differential Calculus and subjects were given mathematical problems. Mathematical problem solving is done through thinkaloud. In addition to thinkaloud research subjects were given metacognition questionnaires, observed using observation sheets, and interviews. The data include student work, thinkaloud, metacognition questionnaire, interview, and observation were analyzed using fixed comparison method. The result show that the change pattern of awareness, evaluation, and regulation processes of mathematics students were categorized into complete sequenced metacognition process, complete unsequenced metacognition and incomplete metacognition. Keywords: Componen of Metacognition, Pattern, Complete Sequenced, Complete Unsequenced, Incomplete References Anderson, L.W. & Krathwohl, D.R. (2001). A Taxonomy for learning, teaching, and assessing (A Revision of Bloom’s taxonomy of educational objectives). New York: Addision Wesley Longman, Inc. Baker, L. & Brown, A. L. (1984). Metacognitive skills and reading. In Douglas J. Hacker, John Dunlosky and Arthur C. Graesser (Eds.) Handbook of metacognition in eucation. (pp. 725). New York: Routledge. Biryukov, P. (2003). Metacognitive aspects of solving combinatorics problem kaye College of Education. Direct access:http://www.cimt.org.uk/journal/biryukov.pdf. Cromley, J.G. (2005). Metacognition, cognitive strategy instruction, and reading in adult literacy. Direct access: http://www.ncsall.net/index.html@id=782.htm. Davidson J. E., Deuser R. & Sternberg R. J. (1994). The Role of Metacognition in problem solving. In J. Metcalfe and A. R. Shimamura (Eds.), Metacognition: knowing about knowing (pp. 207226). Cambridge, MA: MIT Press. Davidson, J. E. & Sternberg, R. J. (1998). Smart problem solving: How metacognition helps. In D. J. Hacker., J. Dunlosky, A. C. Graesser (Eds.), Metacognition in educational theory and practice (pp. 4768). Mahweh, NJ: Lawrence Erlbaum Associates. Desoete, A., Roeyers, H. & Buysse, A. (2001). Metacognition and mathematical problem solving in grade 3. Journal of Learning Disabilities; SepOct 2001; 34, 5; Academic Research Library.pp 435. Direct access:http://www.fi.uu.nl Flavell, J. (1976). Metacognitive aspects of problem solving. in L. Resnick (Ed), In the Natrure of Intelligence. Direct access:http://www.library.edu. In’am, A., Sa’ad, N. & Ghani, S.A. (2012).A Metacognitive approach to solving Algebra problems. International Journal of Independent Research and Studies. University Pendidikan Sultan Idris, Malaysia. Direct access:http://www. aiars.org/ijirs...20120195.pdf. Jayapraba, G. (2013). Metacognitive instruction and cooperative learning strategi for Ppomoting insightful learning in Science. International Journal on New Trends in Education and Their Implications. Direct access:http://www:ijonte.org. Karan, E. P. & Irizarry, J. (2011). Effects of metacognitive strategies on problem solving ability in construction education. Direct access:http://www.ascpro.ascweb.org. Kuntjoyo, (2009). Metakognisi dan keberhasilan peserta didik. Direct access:http://www.ebekunt.wordpress.com/2009/.../metakognisidankeberhasilan_peserta_didik. Kuzle, A. (2011). Patterns of metacognitive behavior during mathematics problem solving in a dynamic Geometry environment. Direct access: http://www.jwilson.coe.uga.edu, Lioe, L.T., Fai H. K. & Hedberg, J.G. (2006). Students’ metacognitive problem solving strategies in solving openended problems in pairs. Direct access: http://www.math.ecnu.edu.cn/.../tsg205.doc. Livingstone, J.A. (1997). Metecognition on overview. Direct access:http:// www. gse.buffaloedu/fas/shuell/cep564/Metacog.htm. Magiera, M. T. & Zawojewski, J. S. (2011). Characterizations of socialbased and selfbased contexts associated with students’ awareness, evaluation, and regulation of their thinking during smallgroup mathematical modeling. Journal for Research in Mathematics Education. Number 5, Volume 42 November 2011. pp. 486516. Mariam, A. M. & Idrus, N. M. (2013). Metacognitive strategies in quadratic equation word problem. Jurnal Pendidikan Sains dan Matematik Malaysia. Volume 3 Number 2 ISSN 22320393. Direct access: http://www .pustaka2.upsi.edu.my/.../metacognitive. Marrongelle, K. (2007). The role of physics in students’ conceptualization of calculus consepts: Implications of research on teaching practice. Direct access, http://www.Math.Uoc.Gr/~Ictm2/Proceedings/Pap153.Pdf. Mokos, E. & Kafoussi, S. (2013). Elementary students' spontaneous metacognitive functions different types of mathematical problems. Journal Research in Mathematics Education. Volume 2 number 2, June 2013. pp 242267. Direct access: http://www.hipatiapress.com. Peraturan Menteri Pendidikan dan Kebudayaan Republik Indonesia Nomor 54 Tahun 2013 tentang Standar kompetensi lulusan pendidikan dasar dan menengah. Peraturan Menteri Pendidikan dan Kebudayaan Republik Indonesia Nomor 69 Tahun 2013 tentang Kerangka dasar dan struktur kurikulum sekolah menengah atas/madrasah aliyah. 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(2017), The characteristic of the process of students’metacognition in solving Mathematics problems. International Educational Studies (IES) Journal. ISSN 19139020 EISSN 19139039. Volume 10, Number 5. Sabella, M.S. & Redish E.F. (2003). Student understanding of topics in calculus. Direct access:http://www.physics.umd.edu/perg/plinks/calc.htm. Schoenfeld, A. H. (1992). Learning to think mathematically: problem solving, metacognition, and sensemaking in mathematics. Direct access: http://www.math.ubc.ca. Schoenfeld. A.H., Elizabeth & Corner, E. (1992). Learning to think mathematically: problem solving metacognition, and sensemaking in mathematics. Berkeley, CA. Reston: NCTM Schoenfeld, A. H. (1994). Mathematical thinking and problem solving. New Jersey: School Mathematics. Reston: NCTM Sengul, S. & Katranci, Y. (2012). Metacognitive aspects of solving function problems. ProcediaSocial and Behavioral Sciences 46 ( 2012 ) 2178 – 2182. Directaccess: http://www.sciencedirect.com/science/article/pii/S1877042815042068. Stillman, G. A. & Galbraith, P. L. (1998). Applying mathematics with real world connections: Metacognitive characteristics of secondary students. Educational Studies in Mathematics 36(2), 157195. Tan, O. S. (2004). Cognition, metacognition, and problembased learning, in enhancing thinking through problembased learning approaches. Singapore: Thomson Learning. Veenam, M.V.J., Wilhelm, P. & Beishuizen, J. J. (2004). The relation between intellectual and metacognitive skills from a developmental perspective. Direct access: http://www.ww4.ncsu.edu/.../Veenman,%20Wilhelm ,%20%26%20Beishuizen%2004.pdf. Wilson, J. (1997). Beyond the basics: Assessing students' metacognition. Paper Presented at the 14th Annual Hong Kong Educational Research Association Conference. Hong Kong. November, 1997. Direct access: http://www.files .eric.ed.gov.fulltext/ED415244.pdf. Wilson, J. & Clarke D. (2002). Monitoring mathematical metacognition. Paper presented at the Anual Meeting for the American Education Research Assosiation, New Orleeans, LA. Wilson, J. & Clarke D. (2004). Towards the modelling of mathematical metacognition. Mathematics Education Research Journal. 16(2) pp. 2548. Direct access: http://www.files.eric.ed.gov/fulltext/EJ747867. Wong Khoon Yoong, (2007). Metacognitive awareness of problem solving among primary and secondary school students. Direct access: http: // www .math. nie.edu.sg. Zainal, Z. & Tajudin, N. M. (2013). Metacognitif process in solving nonroutin mathematics problems. Direct access: http://www.psmm.upsi.edu.my. Zechmeister, E.B. & Neyberg, S.E. (1982). Human memory: An introduction to research and theory. Monterey, C.A: Brooks/Cole Publishing Company. 
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The Effects of ‘Geometry Sketchpad’ on Grade 12 Learners’ Performance in GeometryLeena Ngonyofi Kanandjebo & Elizabeth Ndeukumwa Ngololo
pp. 735747  Article Number: iejme.2017.043
Abstract Learners at Grade 12 level persistently show a weak conceptual understanding of geometric concepts (DNEA, 2011, 2012, 2014). The study was guided by Bruner’s (1960) Constructivist Theory, using Understanding by Design teaching approach to explain Geometrical concepts. The study was qualitative, using nonequivalent pretest and posttest quasiexperimental design. Cluster random sampling was used to select a sample of 176 Grade 12 learners from two purposively selected secondary schools. The findings revealed that at 95% confidence level Keywords: ICTdriven pedagogy, Geometry, performance, Geometer’s Sketchpad (GSP), Understanding by Design (UbD) References Bruner, J. (1960). The process of Education. Cambridge, MA: Harvard University Press. Retrieved from, http://ti.psychology.org/bruner.html Clayton, S. (2011). Understanding by Design: Designing Learning, Assessment and Teaching for Understanding. Retrieved from, http://www.ascdsingapore.org/images/Vol16pg6366.pdf Cohen, L., Manion, L., & Morrison, K. (2011). Research Methods in education (7th ed.). Canada: Routledge. DNEA. (2011). Examiner’s report: Mathematics NSSC core and extended examinations. Windhoek: DNEA. DNEA. (2012). Examiner’s report: Mathematics NSSC core and extended examinations. Windhoek: DNEA. DNEA. (2013). National and regional Distribution of Symbols November 2012 NSSC Ordinary level (Gd. 12) Full Time. Retrieved from, http://www.dnea. gov.na/stats/ Reports/201312/Ordinary/distr_4.pdf DNEA. (2014). Examiner’s report: Mathematics NSSC core and extended examinations. Windhoek: DNEA. DNEA. (2014). National and regional Distribution of Symbols November 2014 NSSC Ordinary level (Gd. 12) Full Time. Retrieved from, http://www.dnea. gov.na/stats/ Reports/201412/Ordinary/distr_4.pdf EMIS. (2014). Education statistics. Windhoek: Directorate of Planning and Development: Ministry of Education. Gay, L. R., Mills, G. E., & Airasian, P. (2009). Educational research. Competencies for analysis and applications (9th ed.). New Jersey, USA: Pearson Education Inc. Idris, N. (2009). The Impact of Using Geometers’ Sketchpad on Malaysian Learners’ Achievement and Van Hiele Geometric Thinking. Journal of Mathematics Education. 2(2), 94107. Karue, N., & Amukowa, W. (2013). Analysis of Factors that Lead to Poor Performance in Kenya Certificate of Secondary Examination in Embu District in Kenya. Retrieved from, http://www.tijoss.com/TIJOSS%2013th%20Volume/Amukowa.pdf Keskin, S. (2006). Comparison of several Univariate normality tests regarding Type I Error and power of the test in simulation based small samples. Journal of Applied Science research 2(5), 296300. Mateya, M. (2008). Using the Van Hiele theory to analyse geometrical conceptualisation in Grade 12 learners: A Namibian perspective. Published Master’s thesis, Rhodes University, Johannesburg. McTighe, J., & Wiggins, G. (2012). Understanding by Design framework. Retrieved from http://www.ascd.org/ASCD/pdf/siteASCD/publications/UbD_WhitePaper0312.pdf Myers, R.Y. (2009). The Effects of the Use of Technology In Mathematics Instruction on Learner Achievement. Published PhD Dissertations. Florida International University. Retrieved from http://digitalcommons.fiu.edu/etd/136. National Institute for Educational Development (NIED). (2010). Namibian Secondary School Certificate Mathematics Syllabus Ordinary level. Okahandja: NIED. Ngololo, E. N., Howie, S. J., & Plomp, T. (2012). An evaluation of the implementation of the National ICT Policy for Education in Namibian rural science classrooms. African Journal of Research in MST Education,16(1), 4–17. Ogdol, E.,R., & Lapinid, M., R. (2013). Developing students’ Mathematical understanding on linear equations in two variables using a UbD unit plan. Paper Presented at Research Congress, March 79, 2013. De La Salle University Manila. Retrieved from http://www.dlsu.edu.ph/conferences/dlsu_research_congress/2013/_pdf/LLI/LLIII014.pdf Pearson, E., Dorrian, J., & Litchfield, C. (2011). Harnessing Visual Media in Environmental Education: Increasing Knowledge of Orangutan Conservation Issues and Facilitating Sustainable Behaviour through Video Presentations. Environmental Education Research, 17(6), 751767. Perry, M. J. M. (2013). Effects of Visual Media on Achievement and Attitude in a Secondary Biology Classroom. Published Master’s thesis. Ohio University. Roblyer, M. D., Edwards, J., & Havriluk, M. A. (2010). Integrating educational technology in teaching. Colombus, OH: Merrill. Simataa, A., & Simasiku, L. (2012). An analysis of the management of the Namibian information communication technology school curriculum planning. International Journal of Global education, 1(2), 714. Social Studies Center for Educator Development (SSCED). (1999). Texas Social Studies Framework, KindergartenGrade 12: Research and Resources for Designing a Social Studies Curriculum. Austin, TX: Texas Education Agency. United Nations. (2015). Sustainable Development Goal 4: Ensure inclusive and equitable quality education and promote lifelong learning opportunities for all. Retrieved from, https://sustainabledevelopment.un.org/sdg4 Wenglinsky, H. (1998). Does it compute? The relationship between educational technology and student achievement in Mathematics. New Jersey: Educational Testing Service. Wiggins, G., & McTighe, J. (2003). Understanding by Design framework. Retrieved from, http://www.ascd.org/readingroom/books/wiggins98book.html#chap1 Wiggins, G., & McTighe, J. (2005). Understanding by design. Alexandria, VA: ASCD. 
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On the Teaching and Learning of Fractions through a Conceptual Generalization ApproachBojan Lazić, Sergei Abramovich, Mirela Mrđa & Daniel A. Romano
pp. 749767  Article Number: iejme.2017.044
Abstract This paper deals with precursory (propaedeutic) learning of the concept of number in the elementary mathematical education. The authors’ objective is to suggest a method allowing for the increase of the effectiveness of interactive expansion of the concept of number by using a gradeappropriate learning framework for elementary mathematical education content. A theoretical background for the creation of this method is based on the description of various characteristics of precursory learning and interactive teaching of mathematics as well and the flexible differentiation approach. The paper especially emphasizes the possibilities of propaedeutic understanding of the concept of fraction and examine the effects of such approach in terms of student achievement in elementary mathematics education, on the basis of a methodological approach. Results obtained during the experimental research suggest that under the influence of the methodological approach of introducing fractions through propaedeutic learning, students achieve significantly better results in learning compared to students who have not used this method. Keywords: Fractions ∙ Propaedeutic learning ∙ Methodological approach ∙ Flexible differentiation ∙ Empirical evaluation References Abramovich, S., Easton, J. & Hayes, V.O. (2012). Parallel structures of computer – assisted signature pedagogy: the case of integrated spreadsheets, Computers in the Schools, 29(12), 174190. Amato, S. A. (2005). Developing students‘understanding of the concept of fractions as numbers. In H. L. Chick & J. L. Vincent (Eds.), Proceedings of the 29th PME International Conference, 2, 49–56. Behr, M., Lesh, R., Post, T. & Silver, E. (1983). Rational Number Concepts. In R. Lesh & M. Landau (Eds.), Acquisition of Mathematics Concepts and Processes, (pp. 91125). New York: Academic Press. Behr, M., Harel, G., Post, T. & Lesh, R. (1993). Rational Numbers: Toward a Semantic AnalysisEmphasis on the Operator Construct. In T. P. Carpenter, E. Fennema, & T.A. Romberg, (Eds.), Rational Numbers: An Integration of Research (pp. 1347). NJ: Lawrence Erlbaum. Berlin, D. F. & White, A. L. (1995). ,,Connecting School Science and Mathematics”. In: Connecting Mathematics across the Curriculum, Ed. House, P. A. & Coxford, A. F., National Council of Teachers of Mathematics, 1995. Yearbook, Reston, Virginia. Charalambous, C.Y. & PittaPantazi, D. (2005), Revisiting a theoretical model on fractions: Implications for teaching and researching, In Chick, H. L. & Vincent, J. L. (Eds.). Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education, (Vol. 2, pp. 233240), Melbourne: PME. Charalambous, C.Y. & PittaPantazi, D. (2007), Drawing on a theoretical model to study students’ understanding of fractions, Educational Studies in Mathematics, 64(3): 293–316. Fosnot, C. (2007). Field Trips and Fund Raisers: Introducing Fractions. Portsmouth: Heineman. Galen, F., Feijs, E., Figueiredo, N., Gravemeijer, K., Herpen, E. & Keijzer, R. (2008). Fractions, percentages, decimals and proportions: A learningteaching trajectory for grade 4, 5 and 6. Rotterdam: Sense. Gleizer, D. G. (1997). Geometry in the school: problems and judgments. Norma, 3 (12), 920. Hackenberg, A.J. (2010). Students’ reasoning with reversible multiplicative relationships. Cognition and Instruction, 28(4), 383342. Hasegawa, J. (2000). Classroom discussion on the representation of quantity by frаctions: Stability of misconcepuon and implications to practice. In T. Nakahara & M. Koyama (Eds.). Proceedings of the 24th PME International Conference, 3, 41–48. Kieren, T.E. (1976). On the mathematical, cognitive, and instructional foundations of rational numbers. In R. Lesh (Ed.), Number and Measurement: Papers from a Research Workshop (pp. 101144). Columbus, OH: ERIC/SMEAC. Kieren, T.E. (1995), Creating Spaces for Learning Fractions. In: J. T. Sowder & B. P. Schappelle (Eds.), Providing a Foundation for Teaching Mathematics in the Middle Grades, (pp. 3166). Albany: State University of New York Press. Klippert, H. (2001). How to successfully teach the team. Zagreb: Eduka. Lamon, S.J. (2012). Teaching Fractions and Ratios for Understanding: Essential Content Knowledge and Instructional Strategies for Teachers. New York, NY and London, UK. Routledge. Lazić, B. (2015). Propaedeutic Introduction of Fractions in Arithmetics for Lower Grades of Primary School, Ph.D. Thesis, University of Belgrade, Teaching Training Faculty. Lazić, B. & Maričić, S. (2015). Propaedeutic formation of the concept of fraction in elementary mathematics education; In: Novotná, J. & Moraová, H. (Eds.), Proceedings if Developing Mathematical Language and Reasoning, (pp. 212221), Charles University, Faculty of Education, Prague. Lazić, B., Milinković, J. & Petojević, A. (2012). Connecting mathematics in propaedeutic exploration of the concept of fraction in elementary grades, In: Brankovic, N. (Ed.), Theory and Practice of Connecting and Integrating in Teaching and Learning Process (pp. 123–137). Sombor: Faculty of Education in Sombor. Mamede, E., Nunes, T. & Bryant, P. (2005). The equivalence and ordering of fractions in partwhole and quotient situations. In H. L. Chick & J. L. Vincent (Eds.). Proceedings of the 29th PME International Conference, 3, 281–288. Marshall, S.P. (1993). Assessment of rational number understanding: A schemabased approach, in T.P. Carpenter, E. Fennema & T.A. Romberg (Eds.), Rational Numbers: An Integration of Research, (pp. 261–288) Lawrence Erlbaum Associates, New Jersey. Milinković, J. (2007). Methodological aspects of the introduction to probability and statistics. Belgrade: Faculty of Pedagogy. Mrdja, M., Crvenković, S. & Milovanovic, J. (2015). The increase in efficiency of interactive learning of mathematics through the implementation of mini exemplary teaching, IMVI Open Mathematical Education Notes, 5(2): 87–99. Petrovic, N., Mrdja, M. & Lazic, B. (2011). Models of differentiated interactive classroom teaching of mathematics. Norma, 15(2): 211228. PittaPantazi, D., Gray, E. M. & Christou, C. (2004). Elementary school students’ mental representations of fractions. In M. J. Hoines & A. D. Fuglestad (Eds.). Proceedings of the 28th PME International Conference, 4, 41–48. Prediger, S. (2013). Focussing structural relations in the bar board – a design research study for fostering all students’ conceptual understanding of fractions. In B. Ubuz, C. Haser & M. A. Mariotti (Eds.), Proceedings of the 8th Congress of the European Society for Research in mathematics Education, Antalya, 343–352. Rasmussen, P. (2004). Towards flexible differentiation in higher education?: recent changes in Danish higher education, In Fägerlind, I. and Strömqvist, G. (Eds.), Reforming higher education in the Nordic countries –studies of change in Denmark, Finland, Iceland, Norway and Sweden, International Institute for Educational Planning, Paris. Santos, D.A. (2008). Andragogic propaedeutic mathematics, Available online at: http://www.freemathtexts.org/Santos/PDF/Arithmetic(2008).pdf.. Schon, D.A. (1963). Invention and the evolution of ideas. London: Social science paperbacks. Shulman, L. S. (2005). Signature pedagogy in the professions. Daedalus, 134(3): 5259. Siegler, R.S., Thompson, C.A. & Schneider, M. (2011). An integrated theory of whole number and fractions development. Cognitive Psychology, 62(4): 273–296. Siegler, R.S., Fazio, L.K., Bailey, D.H. & Zhou, X. (2013). Fractions: the new frontier for theories of numerical development, Trends in Cognitive Sciences, 17(1): 13–19. Small, M. (2009). Teaching to the Big Ideas K3, Mathfocus K3, Nelson. Smith, J. P. (2002). The development of students’ knowledge of fractions and ratios. In Litwiller, B. ve Bright, G. (Eds). Making Sense of Fractions, Ratios, and Proportions: Yearbook. P. 12. NCTM: Reston, VA. Steffe, L.P. & Olive, J. (2009). Children’s Fractional Knowledge. New York: Springer. Strang, T. (1990). The fractionconcept in comprehensive school at gradelevels 36 in Finland. In G. Booker, P. Cobb & T. N. Mendicuti (Eds.), Proceedings of the 14th PME International Conference, 3, 75–80. Tennyson, R. D. & Park, O. (1980). The teaching concept: A review of instructional design research literature. Review of Educational Research, 50(1): 55–70. Torbeyns, J., Schneider, M., Xin, Z. & Siegler, R.S. (2014). Bridging the gap: Fraction understanding is central to mathematics achievement in students from three different continents. Learning and Instruction, 37(1): 513. Vasilyev, N.S. & Gromyko, V.I. (2015). Propaedeutic Mathematical courses in the context of continuous learning, [Н.С. Васильев, В.И. Громыко, Пропедевтические курсы математики в условиях непрерывного образования. Гуманитарный вестник, МГТУ им. Н.Э. Баумана, 2(28):117]. Vygotsky, L.S. (1987). Thinking and Speech. In R.W. Rieber and A.S. Carton (Eds.), The collected works of L.S. Vygotsky (vol. 1, pp.39285). New York: Plenum Press. Watanabe, T. (2006). Teaching and learning of fractions: A Japanese perceptive, Teaching Children Mathematics, 12(7), 368–372. Watanabe, T. (2012). Thinking about learning and teaching sequences for the addition and subtraction of fractions. In C. Bruce (Chair), Think Tank on the Addition and Subtraction of Fractions. Think Tank conducted in Barrie, Ontario. Wittmann, G. (2013). The consistency of students’ error patterns in solving computationalproblems with fractions. In B. Ubuz, C. Haser & M. A. Mariotti (Eds.), Proceedings of the 8th Congress of the European Society for Research in mathematics Education, Antalya, 393–402. Zech, F. (1999). Grundkurs Mathematikdidaktik  Theoretische und praktische Anleitungen für das Lehren und Lernen von Mathematik, Beltz Verlag  Weinheim und Basel. 
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Development of Mathematics Achievement Test for Third Grade Students at Elementary School in IndonesiaViktor Pandra, Sugiman, Djemari Mardapi
pp. 769776  Article Number: iejme.2017.045
Abstract The aims of this research are: (1) to measure the difficulty level of grain test of mathematics achievement of third grade student at elementary school, (2) to know the differences of mathematics achievement test for third grade student of elementary school, (3) instrument reliability test of mathematics learning achievement of third grade students of elementary school. The research method used is research development, the data analysis to know the information about grains of mathematics test instrument using ITEMAN program. The results show: (1) the test which developed has difficulty level in the range 0,30 ≤ p ≤ 0,70 with accepted category, (2), the test which developed has differences level in range 0,30 ≤ B ≤ 0,39 and 0,40 ≤ B ≤ 1,00 with accepted category and satisfy, and (3) the test which developed has reliability coefficient of 0,783, show that mathematics test instrument give measuring result that stabile and consistent. Keywords: Development Test, Mathematics Achievement Test, Elementary School Mathematics References Allen, M. J. & Yen, W. M. (1979). Introduction to measurement theory. Belmont, CA: Wadsworth, MC. Brennan, R.L. (2006), Educational measurement. Iowa City: United State of America: American Council on Education and Praeger Publisher. Depdiknas. (2003). Undangundang RI Nomor 20 tahun 2003, tentang Sistem Pendidikan Nasional. Djemari Mardapi. (1999). Estimasi kesalahan pengukuran dalam bidang pendidikan dan implikasinya pada ujian nasional. Pidato Pengukuhan Guru Besar. Yogyakarta: Universitas Negeri Yogyakarta. Djemari Mardapi. (2012). Pengukuran, penilaian, dan evaluasi pendidikan. Yogyakarta: Nuha Litera. Ebel, R.L. & Frisbie, D.A. (1986). Essentials of educational measurement. Englewood Cliffs, NJ: PrenticeHall, Inc. Hambleton, R.K. & Swaminathan, H. (1985). Item response theory. Boston, MA: Kluwer Inc. Kumaidi. (2004). Sistem asesmen untuk menunjang kualitas pembelajaran. Jurnal pembelajaran, 27, 93106. Mehrens, W.A. & Lehmann, I.J. (1973). Measurement and evaluation in education and psychology. New York: Hold, Rinehart and Wiston, Inc. Nunnally, J.C. (1978). Educational measurement and evaluation. New york: MacGraw Hill Book Company. 
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Performance Assessment on High School Advanced AlgebraSanta Tejeda & Katherina Gallardo
pp. 777798  Article Number: iejme.2017.046
Abstract The lack of feedback in the studentteacher relationship creates an incomplete perspective about the learning process in Mathematics, as for example in Advanced Algebra. This research was conducted in Mexico using a theoretical framework for performance assessment, based on the competencies for Advanced Algebra learning at the high school level. The objective sought to explore students’ perceptions after a performance assessment process, using two groups of students who took Advanced Algebra for the second time because of low academic achievement. Mixed methods research was selected for understanding profoundly how performance assessment reports (PAR) could bring useful information to students for reaching expected performance levels. A performance rubric based on Marzano and Kendall’s New Taxonomy, as well as semistructured interviews, were used for data collection purposes. The findings confirm that changing the assessment method from traditional grading to performance assessing can be a clearer approach for understanding students’ strengths and weakness as Advanced Algebra learners. Keywords: Advanced Algebra, performance assessment, competencies, high school, feedback References Bahr, D. L. (2007). Creating Mathematics Performance Assessments that Address Multiple Student Levels. Australian Mathematics Teacher, 63(1), 3340. Retrieved from: https://eric.ed.gov/?id=EJ769974 Bayazit, I. (2010). The influence of teaching on student learning: The notion of piecewise function. International Electronic Journal of Mathematics Education, 5(3), 146–164. Bokhove, C., & Drijvers, P. (2012). Effects of feedback in an online algebra intervention. Technology, Knowledge and Learning, 17(1–2), 43–59. doi:https://doi.org/10.1007/s1075801291918 Carlson, M., Oehrtman, M., & Engelke, N. (2010). The precalculus concept assessment: A tool for assessing students’ reasoning abilities and understandings. Cognition and Instruction, 28(2), 113–145. http://dx.doi.org/10.1080/07370001003676587 Chi, M. T. H., Glasser, R., & Farr, M. J. (1988). The nature of expertise. Hillsdale, NJ.: Lawrence Erlbaum Associates, Inc., Publishers. Creswell, J. W., & Clark, V. L. P. (2007). Designing and conducting mixed methods research. Thousand Oaks, CA: SAGE Publications. Dupeyrat, C., Escribe, C., Huet, N., & Regner, I. (2011). Positive biases in selfassessment of mathematics competence, achievement goals, and mathematics performance. International Journal of Educational Research, 50(4), 241–250. Retrieved from http://0search.proquest.com.millenium.itesm.mx/docview/964175861?accountid=41938 Duval, R. (2006). A cognitive analysis of problems of comprehension in a learning of mathematics. Educational Studies in Mathematics, 61(1–2), 103–131. doi:https://doi.org/10.1007/s106490060400z Frey, B. B., Schmitt, V. L., & Allen, J. P. (2012). Defining authentic classroom assessment. Practical Assessment, Research & Evaluation, 17(2). Available online: http://pareonline.net/getvn.asp?v=17&n=2 Gray, E., Pinto, M., Pitta, D., & Tall, D. (1999). Knowledge construction and diverging thinking in elementary & advanced mathematics. In D. Tirosh (Ed.), Forms of mathematical knowledge: Learning and teaching with understanding (pp. 111–133). Dordrecht, Netherlands: Springer Netherlands. Godino, J. D., Castro, W. F., Aké, L. P., & Wilhelmi, M. R. (2012). Naturaleza del razonamiento algebraico elemental (The nature of elemetary algebraic reasoning). Boletim de Educação Matemática, 26(42B), 483–511.http://dx.doi.org/10.1590/S0103636X2012000200005 Hancock, D. (2007). Effects of performance assessment on the achievement and motivation of graduate students. Active Learning in Higher Education, 8(3), 219231. Retrieve from: http://alh.sagepub.com/content/8/3/219.short Iannone, P., & Simpson, A. (2015). Students’ views of oral performance assessment in mathematics: straddling the ‘assessment of and assessment for learning divide. Assessment & Evaluation in Higher Education, 40(7), 971987. Jupri, A., Drijvers, P., & van den HeuvelPanhuizen, M. (2014). Student difficulties in solving equations from an operational and a structural perspective. Mathematics Education, 9(1), 39–55. Kartal, O., Dunya, B. A., DiefesDux, H. A., & Zawojewski, J. S. (2016). The relationship between students' performance on conventional standardized mathematics assessments and complex mathematical modeling problems. International Journal of Research in Education and Science, 2(1), 239–252. Retrieved from http://0search.proquest.com.millenium.itesm.mx/docview/1826538713?accountid=41938 KleinCollins, R. (2013). Sharpening our focus on learning: The rise of competencybased approaches to degree completion. Occasional Paper, 20. Retrieved from: https://pdfs.semanticscholar.org/818d/803c2cac48a729a578f4497543d9eb7aad6d.pdf Kop, P. M. G. M., Janssen, F. J. J. M., Drijvers, P. H. M., Veenman, M. V. J., & van Driel, J. H. (2015). Identifying a framework for graphing formulas from expert strategies. The Journal of Mathematical Behavior, 39, 121–134. https://doi.org/10.1016/j.jmathb.2015.06.002 Lesh, R., & Doerr, H. M. (2003). Foundations of a model and modeling perspective on mathematics teaching, learning, and problem solving. In R. A. Lesh & H. M. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching, (pp. 3–34). Mahwah, NJ: Lawrence Erlbaum Associates, Inc., Publishers. Logan, T. (2015). The influence of test mode and visuospatial ability on mathematics assessment performance. Mathematics Education Research Journal, 27(4), 423–441. Retrieved from http://0search.proquest.com.millenium.itesm.mx/docview/1773219202?accountid=41938 Marzano, R. J., & Kendall, J. S. (2007). The new taxonomy of educational objectives (2nd ed.). Thousand Oaks, CA: Corwin Press. Mayfield, K. H., & Glenn, I. M. (2008). An evaluation of interventions to facilitate algebra problem solving. Journal of Behavioral Education, 17(3), 278–302. doi:https://doi.org/10.1007/s108640089068z Oehrtman, M., Carlson, M., & Thompson, P. W. (2008). Foundational reasoning abilities that promote coherence in students’ function understanding. In M. P. Carlson & C, Rasmussen (Eds.), Making the connection: Research and teaching in undergraduate mathematics education, (pp. 27–42). Washington, DC: Mathematical Association of America, Oehrtman, M., Carlson, M., & Thompson, P. W. (2008). Foundational reasoning abilities that promote coherence in students’ function understanding. Making the connection: Research and teaching in undergraduate mathematics education, 27, 42. OCDE (2016). PISA 2015 Mathematics Framwork. Retrieve from: http://edu.hioa.no/pdf/9816021ec005.pdf Palm, T. (2008). Performance assessment and authentic assessment: A conceptual analysis of the literature. Practical assessment, research & evaluation, 13(4), 111. Retrieve from: http://pareonline.net/getvn.asp?v=13&n=4 Polya, G. (1957). How to solve it: A new aspect of mathematical method (2nd ed.). Princeton, NJ: Princeton University Press. Sadler, D. R. (1989). Formative assessment and the design of instructional systems. Instructional Science, 18(2), 119–144. doi:https://doi.org/10.1007/BF00117714 Schoenfeld, A. H. (2007). What is mathematical proficiency and how can it be assessed? In A. H. Schoenfeld (Ed.), Assessing mathematical proficiency (pp. 59–73).Cambridge, UK: Cambridge University Press. Secretaría de Educación Pública (SEP). (2008, March 21). Acuerdo número 444 por el que se establecen las competencias que constituyen el marco curricular común del sistema nacional de bachillerato. Retrieved from: https://www.sep.gob.mx/work/models/sep1/Resource/7aa2c3ffaab8479fad93db49d0a1108a/a444.pdf Star, J. R., & RittleJohnson, B. (2009). Making algebra work: Instructional strategies that deepen student understanding, within and between representations. ERS Spectrum, 27(2), 11–18. https://nrs.harvard.edu/urn3:HUL.InstRepos:4889486 VegaCastro, D., Molina, M., & Castro, E. (2012). Sentido estructural de estudiantes de bachillerato en tareas de simplificación de fracciones algebraicas que involucran igualdades notables (High school students’ structural sense in the context of simplification of algebraic fractions that involve notable equations). Revista latinoamericana de investigación en matemática educativa, 15(2), 233–258. Vinner, S. (1983). Concept definition, concept image and the notion of function. International Journal of Mathematical Education in Science and Technology, 14(3), 293–305. http://dx.doi.org/10.1080/0020739830140305 Vollrath, H. J. (1984). Methodik des Begriffslehrens im Mathematikunterricht. Stuttgart, Germany: Klett, Weigand, H. G. (2004). Sequences—Basic elements for discrete mathematics. ZDM, 36(3), 91–97. doi:https://doi.org/10.1007/BF02652776 Williams, L. M. (2000). Academic maturity: Qualifications to teach the nurse professionals of the future. Collegian, 7(4), 19–23. doi:https://doi.org/10.1016/S13227696(08)603868 Wiggins, G. (1998). Educative assessment. Designing assessments to inform and improve student performance. San Francisco, CA: JosseyBass Publishers, Yachina, N. P., Gorev, P. M., & Nurgaliyeva, A. K. (2015). Open type tasks in mathematics as a tool for students’ metasubject results assessment. Mathematics Education, 10(3), 211–220. doi: 10.12973/mathedu.2015.116a 
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Secondary Students’ Implicit Conceptual Knowledge of Algebraic Symbolism. An Exploratory Study through Problem PosingElena FernándezMillán, Marta Molina
pp. 799826  Article Number: iejme.2017.047
Abstract Through the task of problem posing, we inquire into students’ conceptual knowledge of algebraic symbolism developed in compulsory secondary education. We focus on identifying the characteristics of equations and systems of equations that made the problem posing task difficult for the students and analyzing the meanings that they gave to the operations contained in the expressions. To collect the data we used two questionnaires in which students were asked to pose problems that could be solved by using given equations or system of equations. In the second questionnaire a specific meaning for the unknowns in the given expression was suggested. The results complement those of a previous study. Students evidence a good conceptual knowledge of algebraic symbolism when meanings for the unknowns are suggested. Decimal numbers and an equation including parenthesis and multiplication of unknowns are the main elements that made some weaknesses in students’ knowledge to surface. The results are more promising. They suggest the potential for compulsory algebra instruction to develop students’ conceptual knowledge, although greater attention should be paid to the semantic aspects of algebra if students are to access such knowledge unaided. Keywords: Algebraic symbolism; conceptual knowledge; equations; Problem posing; unknown References Álvarez, I. & GómezChacón, I. M. (2015). Understanding the algebraic variable: Comparative Study of Mexican and Spanish students. Eurasia Journal of Mathematics, Science & Technology Education, 11(6), 15071529 Arcavi, A. (1994). Symbol sense: informal sensemaking in formal mathematics. For the Learning of Mathematics, 1(3), 2435. Arcavi, A. (2005). Developing and using symbol sense in mathematics. For the learning of mathematics, 25(2), 4247. Arnau, D. & Puig, L. (2013). Actuaciones de alumnos instruidos en la resolución algebraica de problemas en la hoja de cálculo y su relación con la competencia en el método cartesiano. Enseñanza de las Ciencias, 31(3), 4966. DOI: https://doi.org/10.5565/rev/ec/v31n3.967 Bills, L. (2001). Shifts in the Meanings of Literal Symbols. In M. Van den HeuvelPanhuizen (Ed.), Proceedings of the Twentyfifth PME International Conference (pp. 2161, 2168). Utrecht, The Neatherlands: PME. Booth, L.R. (1984). Algebra: Children’s strategies and errors. Windsor, UK: NFERNelson. Capraro, M. & Joffrion, H. (2006). Algebraic Equations: Can MiddleSchool Students Meaningfully Translate from Words to Mathematical Symbols? Reading Psychology, 27(23), 147164. Carpenter, T. & Moser, J. (1982). The development of addition and subtraction problem solving skills. In T. Carpenter, J. Moser & T. Romberg (Eds.), Addition and subtraction: Developmental perspective (pp. 924). Hillsdale, N. Jersey: Lawrence Erlbaum Associates. Castro, E. (2001). Multiplicación y división. In E. Castro (Ed.), Didáctica de la matemática en educación primaria. Madrid, España: Síntesis, pp. 203230. Castro, E. & Castro, E. (1997). Representaciones y modelización. In L. Rico (Ed.), La educación matemática en la enseñanza secundaria (pp. 95124). Barcelona, España: Horsori. Castro, A., Prat, M. & Gorgorió, N. (2016). Conocimiento conceptual y procedimental en matemáticas: su evolución tras décadas de investigación. Revista de Educación, 374, 4368 Cedillo, T. E. (2001). Toward an algebra acquisition support system: A study based on using graphic calculators in the classroom. Mathematical Thinking and Learning, 3, 221–259. Cerdán, F. (2010). Las igualdades incorrectas producidas en el proceso de traducción algebraico: un catálogo de errores. PNA, 4(3), 99110. Chalouh, L. & Herscovics, N. (1988). Teaching algebraic expressions in a meaningful way. In A.F. Coxford & A.P. Shulte (Eds.), The ideas of algebra K12 (pp. 3342). Reston, Virginia: NCTM. Chappell, M. F. (2001). Creating connections: Promoting algebraic thinking with concrete models. Mathematics Teaching in the Middle School, 7, 20–25. Crooks, N. & Alibali, M. (2014). Defining and measuring conceptual knowledge in mathematics. Developmental Review, 34(4), 344377 FernándezMillán E. y Molina, M. (2016). Indagación en el conocimiento conceptual del simbolismo algebraico de estudiantes de secundaria mediante la invención de problemas. Enseñanza de las Ciencias, 34(1), 5371. DOI: http://dx.doi.org/10.5565/rev/ensciencias.1455 Ferrucci, B. J., Kaur, B., Carter, J. A. & Yeap, B. (2008). Using a model approach to enhance algebraic thinking in the elementary school mathematics classroom. In C. E. Greenes & R. Rubenstein (Eds.), Algebra and algebraic thinking in school mathematics: 2008 Yearbook (pp. 195–209). Reston, VA: National Council of Teachers of Mathematics. Filloy, E. & Rojano, T. (1989). Solving equations: The transition from arithmetic to algebra. For the learning of Mathematics, 9(2), 1925. Filloy, E., Rojano T. & Puig, L. (2008). Educational algebra. A theoretical and empirical approach. New York, NY: Springer. Fujii, T. & Stephens, M. (2008). Using number sentences to introduce the idea of variable. In C. E. Greenes & R. Rubenstein (Eds.), Algebra and algebraic thinking in school mathematics: 2008 Yearbook (pp. 127–140). Reston, VA: National Council of Teachers of Mathematics. Furinghetti, F. & Paola, D. (1994). Parameters, unknowns and variables: a little difference? In J.P. da Ponte & J.F. Matos (Eds.), Proceedings of the XVIII International Conference for the Psychology of Mathematics (vol. 2, pp. 368375). Lisboa, Portugal: Universidad de Lisboa. Gómez, P. (2007). Desarrollo del conocimiento didáctico en un plan de formación inicial de profesores de matemáticas de secundaria. PhD Thesis. Granada: Universidad de Granada. GonzálezCalero, J. A., Arnau, D. & Puig, L. (2013). Dificultades en la construcción de nombres de cantidades durante la resolución algebraica de problemas verbales por estudiantes de primaria. In A. Berciano, G. Gutiérrez, A. Estepa, & N. Climent (Eds.), Investigación en Educación Matemática XVII (pp. 301310). Bilbao, Spain: Sociedad Española de Investigación en Educación Matemática. Herscovics, N. & Kieran, C. (1980). Constructing meaning for the concept of equation. Mathematics Teacher, 73(8), pp. 572580. Hiebert, J. & Lefevre, P. (1986). Conceptual and Procedural Knowledge in Mathematics: An Introductory Analysis. In J. Hiebert (Ed.), Conceptual and Procedural Knowledge: The Case of Mathematics (pp. 127). Hillsdale, NJ: Lawrence Erlbaum Associates. Hoch, M. & Dreyfus, T. (2005). Students’ difficulties with applying a familiar formula in an unfamiliar context. In H. L. Chick & J. L. Vincent (Eds.), Proceedings of the 29th conference of the international group for the psychology of mathematics education (Vol. 3, pp. 145–152). Melbourne, Australia: University of Melbourne. Kaput, J. (1989). Linking representations in the symbolic systems of algebra. In S. Wagner & C. Kieran (Eds.), Research agenda for mathematics education: Research issues in the learning and teaching of algebra (pp. 167194). Reston, VA: NCTM. Küchemann, D.E. (1981). Algebra. In K.M. Hart, M.L. Brown, D.E. Kuchemann, D. Kerslake, G. Ruddock & M. McCartney (Eds.), Children’s understanding of mathematics: 1116 (pp. 102119). London, Reino Unido: John Murray, Lin, P. J. (2004). Supporting teachers on designing problemposing tasks as a tool of assessment to understand students' mathematical learning. In M. Hoines y A. Fuglestad (Eds.), Proceedings of the 28th annual meeting of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 257264). Bergen, Noruega: Bergen University College. Mestre J. P. (2002). Probing adults' conceptual understanding and transfer of learning via problem posing. Journal of Applied Developmental Psychology, 23(1), 950. Mitchell, J. M. (2001). Interactions between natural language and mathematical structures: the case of “wordwalking”. Mathematical Thinking and Learning, 3(1), 2952. Molina, M. (2014). Traducción del simbolismo algebraico al lenguaje verbal: indagando en la comprensión de estudiantes de diferentes niveles educativos. La Gaceta de la RSME, 17(3), 559579. Molina, M., RodríguezDomingo, S., Cañadas, M.C. & Castro, E. (2016). Secondary School Student’s Errors in the Translation of Algebraic Statements. International Journal of Science and Mathematics Education, 13(3), 120. Ng, S. F. & Lee, K. (2009). The model method: Singapore children’s tool for representing and solving algebraic word problems. Journal for Research in Mathematics Education, 40(3), 282–313. Orrantia, J., González, L.B. & Vicente, S. (2005). Un análisis de los problemas aritméticos en los libros de texto de Educación Primaria. Infancia y Aprendizaje, 28, 420451. http://dx.doi.org/10.1174/021037005774518929 Resnick, L.B., CauzinilleMarmeche, E. & Mathieu, J. (1987). Understanding algebra. In J.A. Sloboda & D. Rogers (Eds.), Cognitive process in mathematics (pp. 169203). Oxford, Reino Unido: Clarendon Press. RittleJohnson, B. & Schneider, M. (2015). Developing Conceptual and Procedural Knowledge of Mathematics. In R.C. Kadosh & A. Dowker (Eds.), Oxford Handbook of Numerical Cognition (pp. 11181134). Oxford, UK: Oxford University Press RittleJohnson, B. & Star, J. R. (2007). Does comparing solution methods facilitate conceptual and procedural knowledge? An experimental study on learning to solve equations. Journal of Educational Psychology, 99, 561–574. doi: 10.1037/0022–0663.99.3.561. RodríguezDomingo, S. (2015). Traducción entre los sistemas de representación simbólico y verbal: un estudio con alumnado que inicia su formación algebraica en secundaria. PhD thesis. Granada: Universidad de Granada. Ross, A. & Willson, V. (2012). The Effects of Representations, Constructivist Approaches, and Engagement on Middle School Students’ Algebraic Procedure and Conceptual Understanding. School, Science and Mathematics, 112(2), 117128. Sheikhzade, M. (2008, July). Promoting skills of problemposing and problem solving in making a creative social studies classroom. Presented at 4th Global Conference, Oxford. Available at http://www.interdisciplinary.net/ati/education/cp/ce4/Sheikhzade%20paper.pdf. Stoyanova, E. & Ellerton, N. F. (1996). A framework for research into students' problem posing in school mathematics. In P. C. Clarkson (Ed.), Technology in mathematics education (Proceedings of the 19th annual conference of the Mathematics Education Research Group of Australasia) (pp. 518–525). Melbourne: Mathematics Education Research Group of Australasia. Usiskin Z. (1988). Conceptions of School Algebra and Uses of Variables. In Coxford A.F. & Shulte A. P. (Eds.), The Ideas of Algebra K12 (pp. 819). VA: National Council of Teachers of Mathematics. VegaCastro, D., Molina, M. & Castro, E. (2012). Sentido estructural de estudiantes de bachillerato en tareas de simplificación de fracciones algebraicas que involucran igualdades notables. Relime, 15(2), 233–258. Wagner, S. (1981). An analytical framework for mathematical variables. In Equipe de Recherche Pedagogique (Eds.), Proceedings of the 5th International PME Conference (pp.165170). Grenoble, France: PME. 
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Effect of Tutoring on Passing Remedial Mathematics CoursesYanhong Wu, Björg Jóhannsdóttir, Viji Sundar
pp. 827835  Article Number: iejme.2017.048
Abstract The goal of this study was to investigate the effect of tutoring on students passing rate in remedial mathematics algebra courses, and to probe students’ own reasons for failing an introductory mathematics course. Two experiments were conducted, one to study the impact of individual tutoring for students taking a remedial course for the second time, and the second to study the impact of an inclass tutoring for a whole group. In both experiments, statistical analysis indicated that tutoring significantly improved passing rate in the remedial courses and increased the mean scores for the first time takers. Keywords: Remedial Mathematics; Logistic model; Repeated measurement model; Passing rate References Cherif, A.H., Adams, G.E., Movahedzadeh, F., Martyn, M.A, & Dunning, J. (2014). Why do students fail? Faculty perspective. http://cop.hlcommision.org/LearningEnvironments/ Cholewa, B. & Ramaswam, S. (2015). The effect of counseling on the retention and academic performance of underprepared freshmen. J. College Student Retention, 17, 204225. Cooper, E. (2010). Tutoring center effectiveness: The effect of dropin tutoring. Journal of College reading and Learning, 40(2), 2134. Diggle, P.J., Heagerty, P.J., Liang,KY., & Zeger, S.L. (2002). Analysis of Longitudinal Data. 2nd Eds., Oxford University Press. Hendriksen, S.I., Yang, L., Love, B., & Hall, M. C. (2005). Assessing academic support: The effects of tutoring on student learning outcomes. Journal of College Reading and Learning, 35(2), 5665. Hock, M., Deshler, D., & Schumaker, J. (1999). Tutoring programs for academically underprepared college students: A review of the literature. Journal of College Reading and Learning, 29(2), 101122. Hodges, R. (2001). Encouraging highrisk student participation in tutoring and supplemental instruction. Journal of Developmental Education, 24(3), 27. Long, J.D. (2012). Longitudinal Data Analysis for the Behavioral Sciences Using R. SAGE Publications, Inc. Lotkowski, V., Robbins, S., & Noeth, R. (2004). The role of academic and nonacademic factors in improving college retention. ACT Policy Report. NavarraMadsena, J. & Ingram, P. (2010). Mathematics tutoring and student success, Procedia Social and Behavioral Sciences, 8, 207212 Reinheimer, D. & McKenzie, K. (2011). The impact of tutoring on the academic success of undeclared students. Journal of College Reading and Learning, 41(2), 2236. Russ, V.A. (2015). The Relationship between Final Grades and Tutoring of Methods of Atrisk College Freshmen. Walden Dissertations and Doctoral Studies. Tinto, V. (1975). Dropouts from higher education: A theoretical synthesis of recent research. Review of Educational Research, 45, 89125. Tinto, V. (1993). Leaving college: Rethinking the causes and cures of student attrition (2nd Ed.). Chicago: University of Chicago Press. Tinto, V. (2006). Research and practice of student retention: What next? J. College Student Retention, 8, 119. Xu, Y., Hartman, S., & Mencke, R. (2001). The effects of peer tutoring on undergraduate students’ final examination scores in mathematics. Journal of College Reading and Learning, 32(1), 2231. 
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The Application of Scientific Plus Learning to Improve Mathematics Learning Achievement of Junior High School Students Grade VIILa Ode Ahmad Jazuli, Mustamin Anggo, Utu Rahim, Latief Sahidin, Salim
pp. 837844  Article Number: iejme.2017.049
Abstract Learning will be meaningful if it links the students' reallife experiences with mathematical ideas or concepts in learning process through contextual issues. One of the meaningful mathematics and mathematical oriented learning in daily life experiences is scientific plus learning. The purpose of this research was to describe the students’ spiritual attitude and social competence, learning skills, and the improvement of students’ Mathematics achievement on the material “Numbers” in class VII.B of Junior High School of Satria Kendari through a scientific plus approach. This research was classroom action research and the subject of this research consisted of 34 students of class VII.B of Junior High School of Satria Kendari. The results showed that the students’ spiritual attitude were in the good category, social attitudes were in the good category, learning skills was predicated B+, Mathematics achievement was completed in the cycle IV with the average score was 79.96 and the percentage of completeness was 81.81% predicated A, and the learning management that was applied through a scientific plus approach by the teacher achieved 86% in the fourth cycle. Keywords: Scientific plus, Mathematics, learning outcomes References Ahiri, Jafar. (2008). Faktor Faktor yang Mempengaruhi Hasil Belajar. Kendari: Unhalu Press. Beckmann, A Et Al. (2009). The Science Math Project. Germany: The Science MathGroup Budiyanto, Moch. Agus Krisno.,Waluyo, Lud., Mokhtar, Ali. (2016). Implementasi Pendekatan Saintifik dalam Pembelajarandi Pendidikan Dasar di Malang. Proceeding Biology Education Conference,13(1),4651. Idris, Invany, &Silalahi, Desri Kristina. (2016). Penerapan Pendekatan Pendidikan Matematika Realistik Indonesia(PMRI) untuk Meningkatkan Kemampuan Penyelesaian Soal Cerita padaKelas VII A SMP UTY. Jurnal EduMatSains, 1 (1), 7382. Jazuli, L.A. (2007). Pembelajaran Matematika Realistik untuk Subtopik Luas Permukaan Kubus, Balok, Prisma, dan Limas Di Kelas VIII SMP Negeri 5 Kendari. Surabaya: Universitas Negeri Surabaya. Jazuli, L.A., dkk.( 2010). Workshop Penelitian Tindakan Kelas (PTK) bagi GuruGuru Sekolah Dasar Kabupaten Wakatobi. Kendari: Universitas Halu OLeo. Kemendikbud. (2013). Peraturan menteri pendidikan dan kebudayaan Nomor 65. Jakarta: Kementerian Pendidikan dan Kebudayaan Republik Indonesia. Machin, A. (2014). Implementasi Pendekatan Saintifik, Penanaman Karakter Dan Konservasi Pada Pembelajaran MateriPertumbuhan. Jurnal Pendidikan IPA Indonesia, 3 (1), 2835. Sardiman A. M. (2007). Interaksi dan Motivasi Belajar Mengajar. Jakarta: Raja Grafindo Persada. Varelas, M and Ford M. (2009). The scientific method and scientific inquiry: Tensions in teachingand learning. USA: Wiley InterScience. 
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An Exploration of Learners’ Attitudes towards Mobile Learning TechnologyBased Instruction Module and its Use in Mathematics EducationMuthandwa Chinamhora Sincuba, Merlin John
pp. 845858  Article Number: iejme.2017.050
Abstract The study explored learners’ experiences with the mobile learning technologybased instruction module (MLTBIM) in learning Functions and related concepts. A sample of thirtynine participants was purposefully drawn from the Grade 10 Mathematics classes in a selected historically disadvantaged rural senior secondary school. Adopting a case study research design, an attitude test was used in the collection of data. Microsoft Excel was used in presenting and analysing the data. The first finding of the study was that most respondents viewed the Mobile Learning TechnologyBased application as very useful in the teaching and learning of Functions and related concepts. Secondly, most respondents upheld the view that Mobile Learning TechnologyBased Instruction (MLTBI) was an effective method to learn Mathematics. Lastly, most of the respondents advocated that the application used in MLTBI enhanced their conceptual understanding of linear, quadratic and exponential functions. To conclude, the participants were convinced that cell phone devices and the Math4Mobile software were very useful and effective in the teaching and learning of Functions and related concepts regardless of the fact that there were some shortcomings involved. Keywords: attitudes, mathematics education, functions, Mobile Learning TechnologyBased Instruction References Archer, S. (2006). Ideas for teaching science. New York: Continuum International Publishing Group. Attewell, J. (2005). Mobile technologies and learning: A technology update and mlearning project summary. Learning and Skills Development Agency: United Kingdom. http://www.mlearning.org/. Babie, E.R. (2008). The Basics of Social Research. 4th ed. United States of America: Thomas Wadsworth publications. Benta, K.I., Cremene, M. & Padurean, R. (2004). Multimedia mlearning using mobile phones. In Proceedings of MLEARN 2004: Mobile Learning anytime everywhere, 56 July 2004, pp. 2728, Rome, Italy; London: Learning and Skills Development Agency. Bernstein, A. (2011). Centre for Development and Enterprise Challenges the public education sector to form a social movement to improve education in South Africa. Mail & Guardian, 21 September, 25p. Botha, A. (2007). Mobile education. Mail & Guardian Online. Retrieved from http://www.mg.co.za/article/20070801mobileeducation. Broadbooks, W.J., Elmore, P.B., Pedersen, K. & Bleyer, D.R. (1981). A Construct validation study of the Fennema Sherman mathematics attitudes scale. Educational and Psychological Measurement, 41, 551557. Brodie K. (2004). Rethinking teachers’ mathematical knowledge: A focus on thinking practice. Perspectives in Education, 22(1), 6580. Burstein, L. (1992). The analysis of multilevel data in educational research and evaluation. Review of Research in Education. 8, 158223. Butgereit, L. (2009). Using text adventure games to entice learners to practice arithmetic skills over Mxit. In J. H. Meyer & A. Van Biljon (Eds.), Proceedings of the 15th Annual Congress of the Association of Mathematics Education of South Africa (Vol. 2, pp. 310). Bloemfontein: AMESA. Available at http://www.amesa.org.za/amesa2009/Proceedings.htm. Chu, Y. & Liu, T. (2007). Handheld computer supported contextaware learning with 2D barcodes. In Proceedings of the Seventh IEEE International Conference on Advanced Learning Technologies, (ICALT 2007), 1820 July 2007, 485486, Niigata, Japan. ConwaySmith, E. (2010). Teaching with cell phones. GlobalPost.http://www.globalpost.com/dispatch/education/100720/southafricateachingcellphones? Cook, J., Bradley, C., Lance, J., Smith, C. & Haynes, R. (2007). Generating learning contexts with mobile devices. Mobile learning: Towards a research agenda. WLE Centre Occasional Papers in WorkBased Learning, ed. Norbert Pachler, 5574, London:WLE Centre. http://www.wlecentre.ac.uk/cms/files/occasionalpapers/mobilelearning_pachler2007.pdf Department of Basic Education (2012). National Strategy for Mathematics, Science and Technology Education in General and Further Education and Training. Pretoria: Government Printers. Department of Basic Education (2013). National Senior Certificate: Technical Report. Pretoria: Government Printers. Eastern Cape Department of Basic Education (2014). National Senior Certificate: Technical Report. Pretoria: Government Printers. www.ecdoe.gov.za Faux, F., Mcfarlane, A., Roche, N. & Facer, K. (2006). Learning with handheld technologies: A handbook from Futurelab. Bristol, UK: Futurelab. http://www.futurelab.org.uk/research. Federal Republic of Nigeria. (2004). National Policy on Education (Revised) NERC. Glennie, J., Harley, K., Butcher, N. & Van Wyk, T. ( 2012). Open Educational Resources and change in Higher Education: Reflections from practice. British Colombia: Vancouver. HartnellYoung, E. & Heym, N. (2008). How mobile phones help learning in secondary schools? BECTA.http://research.becta.org.uk/index.php?catcode=_re_rp_02&rid=15482§ion=rh, [17 November 2013]. Howie, S. J. (2003). Language and other background factors affecting secondary pupils’ performance in Mathematics in South Africa. African Journal of research in Mathematics, Science and Technology Education, 7, 120. http://www.scit.wlv.ac.uk/brendan/mLearn2008.pdf,[30 November 2013]. Johnson, B. & Christensen, L. (2012). Educational Research. Quantitative, qualitative, and mixed approaches, 4th ed. Thousand Oaks, CA: Sage Publications. Kadirire, J. (2007). Instant messaging for creating interactive and collaboration mLearning environments. International Review of Research in Open and Distance Learning, 2(8),114. Kahn, M. J. (1994). Science and Mathematics education in the formal system: Science and technology education and training for economic development. Johannesburg: Centre for Education Policy Development. Kalloo, V. & Mohan, P. (2012). MobileMath: an innovative solution to the problem of poor Mathematics performance in the Caribbean. Caribbean Teaching Scholar, 2(1), 518. Khuzwayo, B., (2005). A history of Mathematics education research in South Africa: The apartheid years. Researching Mathematics education in South Africa: Perspectives, practices and possibilities, 234, 286p. Kinsley, J. (2002). A four stage model of mathematical learning. The Mathematics Educator Journal, 12 (1), 1116. Koller, O., Baumert, J. & Schnabel, K. (2001). Does Interest Matter? The Relationship Between Academic Interest and Achievement in Mathematics. Journal for Research in Mathematics Education, 32 (5), 448470. Kriek, J. & Grayson, D. (2009). A Holistic Professional Development model for South African Physical Science teachers. South African Journal of Education, 29, 185203. Kumar, A., Tewari, A., Shroff, G., Chittamuru, D., Kam, M. & Canny, J. (2010). An Exploratory Study of Unsupervised Mobile Learning in Rural India. In CHI 2010, 10–15 April 2010, Atlanta, Georgia, USA. Liebenberg, J. & ConwaySmith. (2008). Mobile Mathematics–lessons learned. In Proceedings of the mLearn 2008 Conference, The Bridge From Text To Context, 710 October 2008, 346p.UK.Ironbridge Gorge: Shropshire. Lubega, J., McCrindle, R., Williams, S., Armitage, U. & Clements, I. (2004). Uses of mobile phones in higher education. In Cantoni and McLaughlin (eds) Proceedings of EDMEDIA 2004. Switzerland: Lugano. Makgato M. & Mji, A. (2006). Factors associated with high school learners’ performance: A spotlight on mathematics and physical science. South African Journal of Education, 26(2), 253266. Manoucherhri, A. (1999). Computers and school mathematics reform: Implications for mathematics teacher education. Journal of Computers in Mathematics and Science Teaching, 18(1), 3148. Maree, K., (2007). First steps in Research. 1st ed. Pretoria: Van Schaik publishers. McMillan, J.H. & Schumacher, S. (2010). Research in education: Evidencebased inquiry. 7th ed. New York: Pearson. MoMath, (2010). Mobile learning for Mathematics: Nokia project in South Africa Symbian tweet, http://www.symbiantweet.com/mobilelearningforMathematics in South Africa, [20 February 2014] Mulhern, F. & Rae, G. (1998). Development of shortened form of the FennemaSherman mathematics attitude scales. Educational and Psychological Measurement, 41, 551557. Nagaki, T., Kobayashi, Y. & Nakagawa, H. (2004). Attitude survey for pupils about using cellular phones in Classrooms. In Cantoni and McLaughlin (eds.) Proceedings of EDMEDIA 2004, Switzerland: Lugano. Naismith, L. & Corlett, D. (2006). Reflections on success: A retrospective of the mLearn conference series 20022005. Paper presented at mLearn 2006  Across generations and cultures. Canada. Banff. http://hal.archivesouvertes.fr/docs/00/19/73/66/PDF/NaismithCorlett2006.pdf. Ndafenongo, G. (2011). An investigation into how cell phones can be used in the teaching of Mathematics using Vitalmaths video clips: a case study of 2 schools in Grahamstown, South Africa. Thesis, Degree of Master of Education, Rhodes University (Faculty of Education), Grahamstown, South Africa. Ornstein, A.C. (1990). Strategies for effective teaching. New York: McGrawHill Inc. Peker, M. (2005).The relationship between learning styles and Mathematics achievement students’ acquiring primary Mathematics teacher education. Eurasian Journal of Educational Research, 5 (21), 200210. Project KNect. (2008). http://www.projectknect.org/Project%20KNect/Home.html http://www.cxc.org/examinations/examresultsreports. [30 May 2014]. Retrieved from http://mlearningafrica.net/category/projects/ Saha, S. (2007). A study of Gender Attitude to Mathematics. Cognitive Style and Achievement in Mathematics. Experiments in Education 35(6). Sharples, M. (2003). Disruptive devices: mobile technology for conversational learning. International Journal of Continuing Engineering Education and Lifelong Learning, 1(5& 6), 504520. Stead, G. (2005). Moving mobile into the mainstream. In Proceedings of mLearn: Mobile technology: The future of learning in your hands, 2528 October 2005, South Africa, Cape Town, London: WLE Centre. Sweeting, K. (2011). Early Years Teachers’ Attitudes in Mathematics. M.Ed Thesis. Queensland University of Technology. University of Haifa. http://construct.haifa.ac.il. Vahey, P. & Crawford, V. (2003). Learning with handhelds: Findings from classroom research. http://makingsens.stanford.edu/pubs/LearningFromHandhelds.pdf. [15 May 2014]. Vosloo, S. & Botha, A. (2009). Mobile learning: South African examples. Paper presented at the Mobile Learning Institute Summit. Lusaka, Zambia. Retrieved from http://www.slideshare.net/stevevosloo/mobilelearningsouthafricanexamples. Vosloo, S. (2007). MOBITM. Vosloo, S. (2008). M4Girls. Retrieved from http://mlearningafrica.net/category/projects/ Vosloo, S. (2009). ImfundoYami/ImfundoYethu: Mobile learning for Mathematics. Retrieved from http://mlearningafrica.net/category/projects/ Wilson, P. (2008). Promoting positive attitudes. Retrieved November 10, 2015 from Electronic Resources Information Centre (ERIC) database (ERIC Document No EJ815090). Xia, X., Lu, C. & Wang, B. (2008). Research on Mathematics Instruction Experiment Based Problem Posing, Journal of Mathematics Education, 1(1),153163. Yerushalmy, M. & Weizman, A. (2007). Math4Mobile mobile environments. The University of Haifa. http://www.math4mobile.com/[12 February 2014]. Yerushalmy, M. (2007). Math4Mobile mobile environments. The University of Haifa. http://www.math4mobile.com/ [12 February 2014] 
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44 
Analysis of Mathematics Students Ability ın Learning Metacognitive Strategy Type Ideal (Identify, Define, Explore, Act, Look)Hasbullah & Basuki Wibawa
pp. 859872  Article Number: iejme.2017.051
Abstract This study aims to analyze the problem solving skills of grade VII students in learning metacognitive strategy type IDEAL. The method used is qualitative research with descriptive approach to analyze the result of mathematics problem solving test with indicator 1) understand and represent problem, 2) choose or plan the solution, 3) solve the problem according to plan, and 4) recheck the result. This research was conducted in Madrasah Tsanawiyah Wanasaba subdistrict. The time of the research was conducted in the even semester of the 2015/2016 school year, starting from February 2016 until March 2016. The results showed that 6.41% of students were able to plan the solution, 11.54% of the students were able to solve the problem as planned and 82.05 % of students were able to reexamine the results obtained. Based on these results, IDEAL type metacognitive learning strategy can improve students' math problem solving skills. Keywords: Problem Solving Abilities, Mathematics, Metacognitive Learning Strategy, IDEAL References Anderson, Rin W. and David R. K. (2001). A Taxonomy for Learning, teaching and Assessing: A revision of Bloom's Taxonomy of Education Objectives. New York: Addison Wesley Lonman Inc. Beetlestone, F. (1998). Creative Children, Imaginative Teaching. Philadelphia: Marston Book Services Limites. Chidsey, Rachel B. & Rebekah B. (2016). Practical Handbook of MultiTiered Systems of Support: Building Academic and Behavior Success in Schools. Ney York: The Guilford Press. Franklin, J. (2014). An Aristotelian Realist Philosophy of Mathematics: Mathematics as Science of Quantity and Structure. New York: Palgrave Macmillan. Graham, S. & Denise S. (2015). Strategies for Secondary Listening: Current Scenarios and Improved Pedagogy. Chennai: Palgrave Macmilan. Gredler, Margaret E. (2009). Learning and Instruction: Theory into Practice Sixth Edition. London, Pearson. Hardy, Colin A. & Mick M. (2003). Learning and Teaching in Physical Education. London: Falmer Press. Hartas, D. (2010). Educatinal Research and Inquiry: Qualitative and Quatitative Approaches. London: Continum International Publishing Group. Henningsen, M. & M. K. Stein. (1997). "Mathematical tasks and student cognition: Classroombased factors that support and inhibit highlevel mathematical thinking and reasoning," Journal for Research in Mathematics Education, Vol. 28 (5), h. 524. Huisman, J. & Malcolm T. (2015). Theory and Methods in Higher Education Research. Bingley: Emerald Group Publishing Limited. Idris, N. (2006). Teaching and Learning of Mathematics: Making Sense and Developing Cognitive Abilities. Kuala Lumpur: Maziza. Juan, Ester U. & Alicia Martinez F. (2006). Current Trend in The Delopment and Teaching of the Four Language Skills. New York: ANSI. Kesumawai, N. (2014). "Improving Mathematical Problem Solving Ability of Junior High School Students Mellaui Approach of Indonesian Realistic Mathematics Education (PMRI)," Jurnal Pendidikan Matematika, Vol. 8 (2), h. 2. Kleden, Maria Agustina, Yaya S. Kusumah, and Utari S. (2015). "The Analysis of Enhancement of Mathematical Education Competency through Metacognitive Learning," International Journal of Education and Research, Vol. 3 (9). NCTM. (2000). Principles and Standard for School Mathematics. United States of America: NCTM. Ozsoy, G. (2009). "The Effects of Metacognitive Strategy Training on Mathematical Problem Solving Achievement". International Electronic Journal of Elementary Education, Vol.1 (2). h. 3. Peirce, Charles S. (2010). Philosophy of Mathematics: Selescted Writings. Indiana: Indiana University Press, . Petroselli, Calvin L. (2010). Science Education Issues and Developments. New York: Nova Science Publishers, Inc. Phillipson, Shane N. & Bickhar L. (2011). Learning Teaching in the Chinese Classroom: Responding to Individual Needs. Hong Kong: Hongkong University Press. Purnomo, Eko A. & Venissa D. (2014). "Improving ProblemSolving Ability through Ideal Problem Solving Learning Model Based on Project Based Learning", JKPM, VOL. 1 (1). Rahayu, R. & Kartono. The Effect of Mathematical Disposition to Problem Solving Ability Based On IDEAL Problem Solver. International Journal of Science and Research (IJSR). VOL. 3 (10), h. 1315 Rani, T. S. (2008). Teaching of Mathematics Delhi: Navin Shahdara. Selvan, A. (2010). Human Rights Education: Moderan Approaches and Strategies. New Delhi: Concept. Surya, M. (2015). Cognitive Strategies in Learning Process. Bandung: Alfabeta. Wehmeyer, Michael L. (2007). Promoting Selfdetermination in Students with Developmental Disabilities. New York: The Guilford Press. Weiner, Irving B. (2003). Hanbook of Psychology: Educational Psychology Volume 7, New Jersew: John Wiley and Sons, Inc. Wena, M. (2009). Contemporary Innovative Learning Strategy: An Operational Conceptual Review. Jakarta: Earth Script. Woolfolk, A. (2007). Educational Psychology Tenth Edition. Boston: Pearson. Facer, K. (2006). Learning with handheld technologies: A handbook from Futurelab. Bristol, UK: Futurelab. http://www.futurelab.org.uk/research. Federal Republic of Nigeria. (2004). National Policy on Education (Revised) NERC. Glennie, J., Harley, K., Butcher, N. & Van Wyk, T. ( 2012). Open Educational Resources and change in Higher Education: Reflections from practice. British Colombia: Vancouver. HartnellYoung, E. & Heym, N. (2008). How mobile phones help learning in secondary schools? BECTA.http://research.becta.org.uk/index.php?catcode=_re_rp_02&rid=15482§ion=rh, [17 November 2013]. Howie, S. J. (2003). Language and other background factors affecting secondary pupils’ performance in Mathematics in South Africa. African Journal of research in Mathematics, Science and Technology Education, 7, 120. http://www.scit.wlv.ac.uk/brendan/mLearn2008.pdf,[30 November 2013]. Johnson, B. & Christensen, L. (2012). Educational Research. Quantitative, qualitative, and mixed approaches, 4th ed. Thousand Oaks, CA: Sage Publications. Kadirire, J. (2007). Instant messaging for creating interactive and collaboration mLearning environments. International Review of Research in Open and Distance Learning, 2(8),114. Kahn, M. J. (1994). Science and Mathematics education in the formal system: Science and technology education and training for economic development. Johannesburg: Centre for Education Policy Development. Kalloo, V. & Mohan, P. (2012). MobileMath: an innovative solution to the problem of poor Mathematics performance in the Caribbean. Caribbean Teaching Scholar, 2(1), 518. Khuzwayo, B., (2005). A history of Mathematics education research in South Africa: The apartheid years. Researching Mathematics education in South Africa: Perspectives, practices and possibilities, 234, 286p. Kinsley, J. (2002). A four stage model of mathematical learning. The Mathematics Educator Journal, 12 (1), 1116. Koller, O., Baumert, J. & Schnabel, K. (2001). Does Interest Matter? The Relationship Between Academic Interest and Achievement in Mathematics. Journal for Research in Mathematics Education, 32 (5), 448470. Kriek, J. & Grayson, D. (2009). A Holistic Professional Development model for South African Physical Science teachers. South African Journal of Education, 29, 185203. Kumar, A., Tewari, A., Shroff, G., Chittamuru, D., Kam, M. & Canny, J. (2010). An Exploratory Study of Unsupervised Mobile Learning in Rural India. In CHI 2010, 10–15 April 2010, Atlanta, Georgia, USA. Liebenberg, J. & ConwaySmith. (2008). Mobile Mathematics–lessons learned. In Proceedings of the mLearn 2008 Conference, The Bridge From Text To Context, 710 October 2008, 346p.UK.Ironbridge Gorge: Shropshire. Lubega, J., McCrindle, R., Williams, S., Armitage, U. & Clements, I. (2004). Uses of mobile phones in higher education. In Cantoni and McLaughlin (eds) Proceedings of EDMEDIA 2004. Switzerland: Lugano. Makgato M. & Mji, A. (2006). Factors associated with high school learners’ performance: A spotlight on mathematics and physical science. South African Journal of Education, 26(2), 253266. Manoucherhri, A. (1999). Computers and school mathematics reform: Implications for mathematics teacher education. Journal of Computers in Mathematics and Science Teaching, 18(1), 3148. Maree, K., (2007). First steps in Research. 1st ed. Pretoria: Van Schaik publishers. McMillan, J.H. & Schumacher, S. (2010). Research in education: Evidencebased inquiry. 7th ed. New York: Pearson. MoMath, (2010). Mobile learning for Mathematics: Nokia project in South Africa Symbian tweet, http://www.symbiantweet.com/mobilelearningforMathematics in South Africa, [20 February 2014] Mulhern, F. & Rae, G. (1998). Development of shortened form of the FennemaSherman mathematics attitude scales. Educational and Psychological Measurement, 41, 551557. Nagaki, T., Kobayashi, Y. & Nakagawa, H. (2004). Attitude survey for pupils about using cellular phones in Classrooms. In Cantoni and McLaughlin (eds.) Proceedings of EDMEDIA 2004, Switzerland: Lugano. Naismith, L. & Corlett, D. (2006). Reflections on success: A retrospective of the mLearn conference series 20022005. Paper presented at mLearn 2006  Across generations and cultures. Canada. Banff. http://hal.archivesouvertes.fr/docs/00/19/73/66/PDF/NaismithCorlett2006.pdf. Ndafenongo, G. (2011). An investigation into how cell phones can be used in the teaching of Mathematics using Vitalmaths video clips: a case study of 2 schools in Grahamstown, South Africa. Thesis, Degree of Master of Education, Rhodes University (Faculty of Education), Grahamstown, South Africa. Ornstein, A.C. (1990). Strategies for effective teaching. New York: McGrawHill Inc. Peker, M. (2005).The relationship between learning styles and Mathematics achievement students’ acquiring primary Mathematics teacher education. Eurasian Journal of Educational Research, 5 (21), 200210. Project KNect. (2008). http://www.projectknect.org/Project%20KNect/Home.html http://www.cxc.org/examinations/examresultsreports. [30 May 2014]. Retrieved from http://mlearningafrica.net/category/projects/ Saha, S. (2007). A study of Gender Attitude to Mathematics. Cognitive Style and Achievement in Mathematics. Experiments in Education 35(6). Sharples, M. (2003). Disruptive devices: mobile technology for conversational learning. International Journal of Continuing Engineering Education and Lifelong Learning, 1(5& 6), 504520. Stead, G. (2005). Moving mobile into the mainstream. In Proceedings of mLearn: Mobile technology: The future of learning in your hands, 2528 October 2005, South Africa, Cape Town, London: WLE Centre. Sweeting, K. (2011). Early Years Teachers’ Attitudes in Mathematics. M.Ed Thesis. Queensland University of Technology. University of Haifa. http://construct.haifa.ac.il. Vahey, P. & Crawford, V. (2003). Learning with handhelds: Findings from classroom research. http://makingsens.stanford.edu/pubs/LearningFromHandhelds.pdf. [15 May 2014]. Vosloo, S. & Botha, A. (2009). Mobile learning: South African examples. Paper presented at the Mobile Learning Institute Summit. Lusaka, Zambia. Retrieved from http://www.slideshare.net/stevevosloo/mobilelearningsouthafricanexamples. Vosloo, S. (2007). MOBITM. Vosloo, S. (2008). M4Girls. Retrieved from http://mlearningafrica.net/category/projects/ Vosloo, S. (2009). ImfundoYami/ImfundoYethu: Mobile learning for Mathematics. Retrieved from http://mlearningafrica.net/category/projects/ Wilson, P. (2008). Promoting positive attitudes. Retrieved November 10, 2015 from Electronic Resources Information Centre (ERIC) database (ERIC Document No EJ815090). Xia, X., Lu, C. & Wang, B. (2008). Research on Mathematics Instruction Experiment Based Problem Posing, Journal of Mathematics Education, 1(1),153163. Yerushalmy, M. & Weizman, A. (2007). Math4Mobile mobile environments. The University of Haifa. http://www.math4mobile.com/[12 February 2014]. Yerushalmy, M. (2007). Math4Mobile mobile environments. The University of Haifa. http://www.math4mobile.com/ [12 February 2014] 
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45 
Articulators for Thinking Modes of the Derivative from a Local PerspectiveIrma Ercira PintoRojas & Marcela Parraguez
pp. 873898  Article Number: iejme.2017.052
Abstract The purpose of this paper is to show and validate a design for a deep understanding of the derivative from its local perspective. Based on a historical and epistemological study of the derivative, we performed an extension of the Sierpinska theoretical framework – Thinking Modes– of the domain of the derivative from its local perspective, and therefore identified three ways of thinking about the derivative, described as the SyntheticGeometricConvergent (SGC), AnalyticOperational (AO) and AnalyticStructural (AE, for its name in Spanish), as the components that, along with its articulators comprise a design for deep understanding of its local aspect. Methodologically, hypothetically proposed articulators are compared to data obtained in case studies with two groups of university students, in addition to a semistructured interview to mathematicians, researchers and scholars, through which the proposed articulators elements were validated and clarified. The result is a design for the understanding of the derivative from its local aspect as a viable tool to cause the rupture from a purely algebraic thinking about this topic, and that benefits its deep understanding, being this, the ability of a student to articulate these thinking modes. Keywords: Derivative, thinking modes, understanding, articulators, local perspective References Artigue, M. (1995). La enseñanza de los principios del cálculo: problemas epistemológicos, cognitivos y didácticos. In P. Gómez (Ed.), Ingeniería Didáctica en Educación Matemática (pp.97140). México: Grupo Editorial Iberoamericano. Bachelard, G. (2000). La formación del espíritu científico. México DF: Siglo XXI. Badillo, E., Azcárate, C. y Font, V. (2011). Analysis of comprehension levels of objects f’(a) and f’(x) in Mathematics teachers. Enseñanza de las Ciencias, 29(2), 191206. Boyer, C. (1959). The History of the Calculus and its Conceptual Development. New York: Dover Publications. D’Amore, B. and Godino, J. (2007) El enfoque Ontosemiótico como un desarrollo de la teoría Antropológica en Didáctica de la matemática. Revista Latinoamericana de Investigación en Matemática Educativa, 10(002), 191218. FerriniMundy, J. & Graham, K. (1994). Research in calculus learning: Understanding of limits, derivatives and integrals. In J. Kaput & E. Dubinsky (Eds.), Research issues in undergraduate mathematics learning (pp. 3145). Washington: MAA Notes. Grabiner, J. (1983). The changing concept of change: The derivative from Fermat to Weierstrass. Mathematics Magazine, 56(4), 195206. Jaafar, R. and Lin, Y. (2017). Assessment for Learning in the Calculus Classroom: A Proactive Aproach to Engange Students in Active Learning. IEJMEMathematics Education 12(5), 503520. Kinley, M. (2016). Grade Twelve Students Establishing the Relationship Between Differentiation and Integration in Calculus Using graphs. IEJMEMathematics Education, 11(9), 33713385. Lang, S. (1972). Introduction to Differential Manifold. Yale: Springer. Mena, A., Mena, J., Montoya, E, Morales, A. y Parraguez, M., (2015). El obstáculo epistemológico del infinito actual. The epistemological obstacle of the current infinite. Revista Latinoamericana de Investigación en Matemática Educativa, 18(3), 329358. Montoya Delgadillo, E. & Vivier, L. (2015). ETM de la noción de tangente en un ámbito gráfico  Cambios de dominios y de puntos de vista, Proceedings of CIAEM XIV, (pp.57), Chiapas: Tuxtla Gutiérrez. Park, J. (2015) Is the derivative a function? If so, how do we teach it? Educational Studies in Mathematics, 89(2), 233250. Parraguez, M. (2012). Teoría los modos de pensamiento. Didáctica de la Matemática. Valparaíso: Ediciones Instituto de Matemática de la Pontificia Universidad Católica de Valparaíso. PinoFan, L., Godino, J. y Font, V. (2011). Faceta epistémica del conocimiento DidácticoMatemático sobre la Derivada. Educação Matemática Pesquisa, 13(1), 141178. Poole, D. (2014). Linear Algebra: A Modern Introduction. New York: Brooks/Cole. Redon, S. y Angulo, J. (2017). Investigación Cualitativa en Educación. Argentina: Miño y Dávila. SánchezMatamoros, García, G., García Blanco, M., and Llinares Ciscar, S. (2008). El desarrollo del esquema de derivada. Enseñanza de las ciencias. Revista de investigación y experiencias didácticas, 24(1), 8598. Sfard, A. (1991). On the Dual Nature of Mathematical Conceptions: Reflections on Processes and Objects as Different Sides of the Same Coin. Educational Studies in Mathematics, 22(1), 136. Sierpinska, A. (1985). Obstacles épistémologiques relatifs à la notion de limite. Recherches en Didactique des Mathématiques, 6(1), 567. Sierpinska, A. (2000). On some Aspects of Student´s thinking in Linear Algebra. In J. Dorier.(Ed.), The Teaching of Linear Algebra in Question (pp. 209246). Netherlands: Kluwer Academic Publishers. Sierpinska, A. (2005) On Practical and Theoretical Thinking and Other False Dichotomies in Mathematics Education. In M.H. Hoffmann, J. Lenhard, F. Seeger. (Ed) Activity and Sign (pp.117135). Boston: Springer. Sierpinska, A., Nnadozie, A. y Oktaç, A. (2002) A Study of relationships between theoretical thinking and high achievement in linear algebra. Concordia University: Montreal. Stake, R. (2010). Investigación con estudio de casos. Madrid: Morata. Steward, I. (2007). Historia de las matemáticas en los últimos 10.000 años. España: Drakontos. Tallman, M., Carlson, M. P., Bressoud, D., & Pearson, M. (2016). A characterization of calculus I final exams in U.S. colleges and universities. International Journal of Research in Undergraduate Mathematics Education, 2(1), 105133. Vandebrouck, F. (2011). Perspectives et domaines de travail pour l’étude des fonctions. Annales de Didactique et de Sciences Cognitives, 16(1), 149185. Zandieh, M. (2000). A theoretical framework for analyzing student understanding of the concept of derivative. In E. Dubinsky, A. Schoenfeld, J. Kaput, (Ed.), Research in collegiate mathematics education. IV. Issues in mathematics education (pp. 103127). Providence, RI: American Mathematical Society. Zimmermann, W. y Cunningham, S. (1991). Visualisation in Teaching and Learning Mathematics. Washington DC, USA: Mathematical Association of America. 
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