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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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2 
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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3 
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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4 
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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5 
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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6 
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. 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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). 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7 
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. 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