Session Information
24 SES 09, Int. Contexts in Mathematics Education
Paper Session
Contribution
Method
Expected Outcomes
References
Battista, M.T. (2007). The development of geometric and spatial thinking. In F. Lester (Ed.) Second Handbook of Research on Mathematics Teaching and Learning. Charlotte, NC: NCTM/Information Age Publishing, 843-908. Burger, W.F. & Shaughnessy, J.M. (1986). Characterising the Van Hiele levels of development in geometry. Journal for Research in Mathematics Education, 17(1), 31-48. Erez, M. & Yerushalmy, M. (2006). “If you can turn a rectangle into a square, you can turn a square into a rectangle”: young students’ experience the dragging tool, International Journal of Computers for Mathematical Learning, 11(3), 271-299. Fujita, T. and Jones, K. (2007), Learners’ understanding of the definitions and hierarchical classification of quadrilaterals: towards a theoretical framing, Research in Mathematics Education, 9(1&2), 3-20. Govender, R. & de Villiers, M. (2002). Constructive evaluation of definitions in a sketchpad context. Paper represented at AMESA, 1-5 July 2002, Univ. Natal, Dirban, South Africa, http://www.sun.ac.za/mathed/AMESA/. Heinze, A. (2002). …because a square is not a rectangle – Students’ knowledge of simple geometrical concepts when starting to learn proof. In A. D. Cockburn & E. Nardi (Eds.), Proceedings of the annual conference of the 26th International Group for the Psychology of Mathematics Education, Vol. 3. Hiroshima: PME, 81-88 Inhelder, B. & Piaget, J. (1964). The early growth of logic in the child. London: Routledge & Kegan Paul. Keiser, J. M. (2000). The role of definition. Mathematics Teaching in the Middle School, 5(8), 506-511. Leikin, R. & Winicki-Landman, G. (2000). On equivalent and non-equivalent definitions: part 1. For the Learning of Mathematics 20 (1), 17-21. Linchesvsky, L., Vinner, S. & Karsenty, R. (1992). To be or not to be minimal? Student teachers' views about definitions in geometry. In W. Geeslin,W., & K. Graham (Eds.), Proc. of the 16th Conf. of the Int. Group for the Psychology of Mathematics Education, Vol. 2. Durham,USA: PME, 48-55. Mariotti, M.A. & Fischbein, E. (1997). Defining in classroom activities. Educational Studies in Mathematics, 34(3), 219-248. Matsuo, N. (2000). States of understanding relations among concepts of geometric figures: Considered from the aspect of concept image and concept definition. In T. Nakahara & M. Koyama (Eds.), Proc. 24th Conf. of the Int. Group for the Psychology of Mathematics Education Vol. 3. Hiroshima, Japan: PME, 271-278 Matsuo, N. (2004). The effect of understanding definitions of geometric figures on concept formation of them: Analysis of the sixth- and eighth- grade students’ understanding. In Japanese. Proc. of the 37th Presentation of Theses on Mathematical Education. Okayama, Japan: Japan Society of Mathematical Education, 307-312. Matsuo, N. (2006). The significance of teaching definitions of geometric figures: Focus on efficiency of teaching definitions of parallelograms. In Japanese, including an English summary. Bulletin of the Faculty of Education, Chiba University, 54, 175-183. Monaghan, F. (2000). What difference does it make? Children views of the difference between some quadrilaterals. Educational Studies in Mathematics, 42(2), 179-196. Morgan, C. (2005). Words, Definitions and Concepts in Discourses of Mathematics, Teaching and Learning. Language and Education, 19(2), 103-117. Niehuhr, V.N. & Molfese, V.J. (1978). Two Operations in Class Inclusion; Quantification of Inclusion and Hierarchical Classification. Child Development, 49(3), 892-89. Ouvrier-Buffet, C. (2006a) Classification Activities and Definition Construction at the Elementary Level. In J. Novotná, H. Moraová, M .Krátká, N. Stehliková (Eds.) Proc. of the 30th Conf. of the Int. Group for the Psychology of Mathematics Education (Vol 4, pp. 297-304). Charles University, Prague. The Czech Republic: PME. Ouvrier-Buffet, C. (2006b) Exploring Mathematical Definition Construction Processes. Educational Studies in Mathematics, 63(3), 259-282. Pasnak, R., Chooke, W.D. & Hendricks, C. (2006). Enhancing Academic Performance by Strengthening Class-Inclusion Reasoning. The Journal of Psychology 140(6), 603-613. Pickreign, J. (2007). Rectangle and rhombi: how well do pre-service teachers know them? Issues in the Undergraduate Mathematics Preparation of School Teachers, 1, Content Knowledge. Available online at: http://www.k-12prep.math.ttu.edu/journal/content knowledge/¬pickreign01/article.pdf. Rosch, E. (1978). Principles of Categorisation. In E. Rosch & B. Lloyd (Eds.), Cognition and categorisation. Hillsdale: Lawrence Erlbaum Associates, 251-270. Senk, S. L. (1989) Van Hiele levels and achievement in writing geometry proofs. Journal for Research in Mathematics Education, 20(3), 309-321. Serow P. (2007). Utilising the Rasch Model to Gain Insight into Students’ Understandings of Class Inclusion Concepts in Geometry. In J. Watson & K. Beswick (Eds.) Mathematics: Essential Research, Essential Practice. Proceedings of the 30th annual conference of the Mathematics Education Research Group of Australasia, Vol. 2. Adelaide: MERGA, 651-660. Silfverberg, H. (1999). Peruskoulun oppilaan geometrinen käsitetieto. [The conceptual geometric knowledge of pupils in the upper level of the comprehensive school.] Acta Universitatis Tamperensis; 710, Tampere, Finland: University of Tampere (In Finnish, including an English summary). Silfverberg, H. (2000). Study of the development process of pupils' conceptual geometric knowledge. NOMAD, Nordic Studies in Mathematics Education, 8(1), 72-75. Silfverberg, H. & Matsuo, N. 2007. About the Context-Dependency of Understanding the Class Inclusion of Geometric Figures. In J.-H. Woo, H.C. Lew, K.-S. Park & D.Y. Seo (Eds.) Proceedings of the 31st Conference of the International Group for the Psychology of Mathematics Education, Seoul Korea: PME, 284. van Hiele, P.M. (1984). A child's thought and geometry. In D. Geddes, D. Fuys, & R. Tischler (Eds.), English translation of selected writings of Dina van Hiele-Geldof and P. M. van Hiele. Washington, D.C.: NSF, 243-252. Vinner, S. (1991). The role of definitions in teaching and learning of mathematics. In D. Tall (Ed.), Advanced mathematical thinking (pp.). Dordrecht: Kluwer, 6581. Zaslavsky, O. & Shir, K. (2005). Students’ conceptions of a mathematical definition. Journal for Research in Mathematics Education, 36(4), 317-346.
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