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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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2 
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. THe Elementary School Journal, 90, 449466. Barwell, R. (2004). What is Numeracy? For the Learning of Mathematics, 24(1), 2022. Blais, K. & Bath, J. (1992). Drug calculation errors of baccalaureate nursing students. Nurse Educator, 17(1), 1215. Bone, A. A., Carr, J. A, Daniele, V.A., Fisher, R., Fones, N .B., Innes, J. I., Maher, H. P., Osborn, H.G. & Rockwell, D.L. (1984). Promoting a clear path to technical education. Washington DC: Model Secondary School for the Deaf. Booth, J.L. & Newton, K.J. (2012). Fractions: Could they really be the gatekeeper’s doorman? Contemporary Educational Psychology, 37(4), 247253. Booth, J.L., Newton, K.J. & TwissGarrity, L.K. (2014). The impact of fraction magnitude knowledge on algebra performance and learning. Journal of Experimental Child Psychology, 118, 110118. Bowie, L. (2014). Report on mathematics courses for intermediate phase student teachers at five universities. Johannesburg: JET Education Services. 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. Torbeyns, J., Schneider, M., Xin, Z. & Siegler R.S. (2015). Bridging the gap: Fraction understanding is central to mathematics achievement in students from three different continents. Learning and Instruction, 37, 513. Watts, T.W., Duncan, G.J., Siegler, R.S. & DavisKean, P.E. (2014). What's Past Is Prologue: Relations Between Early Mathematics Knowledge and High School Achievement. Educational Researcher, 43(7), 352360. Wilson, T.M. & MacGillivray, H.L. (2007). Counting on the basics: mathematical skills among tertiary entrants. International Journal of Mathematical Education in Science and Technology, 38(1), 1941. Wu, H. (2001). How to prepare students for Algebra. American Educator, 25(2), 1017 
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3 
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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4 
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. DOI : 10.5897/ ERR2013.1578. ISSN 19903839 © 2013 Academic Journals. http://www.academicjournals.org/ERR Schneider, W. &Lockl, K. (2002).The Development of Metacognitive Knowledge in Children and Adolescents. In Perfect, T. and Schwartz, B. (Eds.), Applied Metacognition. Cambridge, UK: Cambridge University Press. Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition, and sensemaking in mathematics.In D. Grouws (Ed.), Handbook for Research on Mathematics Teaching and Learning (pp. 334370).New York: MacMillan. Tersedia: http://hplengr.engr.wisc.edu/Math_Schoenfeld.pdf Schraw, G. & Dennison, R.S. (1994). Assessing metacognitive awareness. Contemporary Educational Psychology, 19, 460475. Schraw, G. & Moshman D. (1995).Metacognitive Theories.Published InEducational Psychology Revie, 7:4, 351–371. Schunk, Dale H. (2012). Learning Theories: as Education Perspective (Teoriteori Pembelajaran: Perspektif Pendidikan) Edisi keenam. Yogyakarta: Pustaka Pelajar Shrawder, Jack H. (2006). Planning a Successful Lesson Publisher/Editor, Teaching For Success South Lake Tahoe, CA jack@teachingforsuccess.com) Steffe, L. P., Cobb, P., & Glasersfeld, E. v. (1988). Construction of arithmetic meanings and strategies. New York : SpringerVerlag. Steffe, L. P., Glasersfeld, E. v., Richards, J., & Cobb, P. (1983). Children’s counting types: Philosophy, theory, and application. New York: Praeger Scientific TEAL (Teaching Excellence in Adult Literacy). (2012). Just Write! Guide. Washington DC: American Institute for Research (AIR). Toit, Stephan du. (2009). The Use of Metacognitive Strategies in The Teaching and Learning of Mathematics. Proceedings of the 15th Annual Congress of the Association for Mathematics Education of South Africa (AMESA), 1, 921. Toit, Stephan du; Gawie du Toit. (2013). The Journal for Transdisciplinary Research in Southern Africa, 9(3), Special edition, December 2013, pp. 505530 Uno, H.B. (2009). Model Pembelajaran Menciptakan Proses Belajar Mengajar yang Kreatif dan Efektif. Jakarta: PT Bumi Aksara. Veenman, M.V.J., Wilhelm, P., Beishuizen, J.J. (2004).The Relation between Intellectual and Metacognitive Skills from a Developmental Perspective.Learning and Instruction (Elsevier), 14, 89 – 109. Voskoglou, Michael Gr. (2008). Problem Solving in Mathematics Education: Recent Trends and Development. Quaderni di Ricerca in Didattica (Scienze Matematiche), 18, 22 – 28, G.R.I.M. (Department of Mathematics, University of Palermo). Yevdokimov, Oleksiy and Tim Passmore.( 2008). Problem Solving Activities in a Constructivist Framework : Exploring how Students Approach Difficult Problems. Proceedings of the 31st Annual Conference of the Mathematics Education Research Group of Australasia M. Goos, R. Brown, & K. Makar (Eds.), © MERGA Inc. 2008 
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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. 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10 
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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11 
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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