Characteristics of Pre-Service Primary School Teachers’ Configural Reasoning

REFERENCES

• Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389–407.
   Web of Science ®Google Scholar
• Barrantes, M. & Blanco, L. (2006). A study of prospective primary teachers’ conceptions of teaching and learning school geometry. Journal of Mathematics Teacher Education, 9(5), 411–436.
   Google Scholar
• Battista, M. T. (2007). The development of geometric and spatial thinking. In F. Lester ( Ed.), Second Handbook of Research on Mathematics Teaching and Learning (pp. 843–908). Charlotte, NC: NCTM/Information Age Publishing.
   Google Scholar
• Chinnappan, M. (1998). Schemas and mental models in geometry problem solving. Educational Studies in Mathematics, 36, 201–217.
   Google Scholar
• Chinnappan, M. & Lawson, M. (2005). A framework for analysis of teachers’ geometric content knowledge and geometric knowledge for teaching. Journal of Mathematics Teacher Education, 8, 197–221.
   Google Scholar
• Clement, J. (2000). Analysis of clinical interviews: Foundations and model viability. In A. E. Kelly & R. A. Lesh ( Eds.), Handbook of Research Design in Mathematics and Science Education (pp. 547–589). Mahwah: NJ: Lawrence Erlbaum.
   Google Scholar
• Cooney, T. J. & Wiegel, H. G. (2003). Examining the mathematics in mathematics teacher education. In A. J. Bishop, M. A. Clements, C. Keitel-Kreidt, J. Kilpatrick, and F. K.-S. Leung ( Eds.), Second International Handbook of Mathematics Education (pp. 795–828). Dordrecht, The Netherlands: Kluwer.
   Google Scholar
• Davis, B. & Simmt, E. (2006) Mathematics-for-teaching: An ongoing investigation of the mathematics that teachers (need to) know. Educational Studies in Mathematics, 61, 293–319.
   Google Scholar
• Duval, R. (1995). Geometrical pictures: Kinds of representation and specific processes. In R. Sutherland & J. Mason ( Eds.), Exploiting Mental Imagery with Computers in Mathematical Education (pp. 142–157). Berlin, Germany: Springer.
   Google Scholar
• Duval, R. (1998). Geometry from a cognitive point of view. In C. Mammana & V. Villani ( Eds.), Perspectives on the Teaching of Geometry for the 21st Century. An International Commission on Mathematical Instruction (ICMI) Study [Chapter 2.2] (pp. 37–52). Dordrecht, The Netherlands: Kluwer.
   Google Scholar
• Duval, R. (1999). Representation, vision and visualization: Cognitive functions in mathematical thinking. Basis issues for learning. In F. Hitt & M. Santos ( Eds.), Proceedings of the 21st Annual Meeting North American Chapter of the International Group of PME (pp. 3–26). Cuernavaca, México. Columbus, OH: ERIC/CSMEE Publications—The Ohio State University.
   Google Scholar
• Duval, R. (2007). Cognitive functioning and the understanding of mathematical processes of proof. In P. Boero ( Ed.), Theorems in School. From History, Epistemology and Cognition to Classroom Practice (pp. 137–162). Rotterdam, The Netherlands: Sense Publishers.
   Google Scholar
• Fischbein, E. (1993). The theory of figural concepts. Educational Studies in Mathematics, 24, 139–162.
   Google Scholar
• Fujita, T. (2011). Learners’ level of understanding of the inclusion of quadrilaterals and prototype phenomenon. Journal of Mathematical Behavior, 31, 60–72.
   Google Scholar
• Gómez-Chacón, I. M. & Kuzniak, A. (2013). Spaces for geometric work. Figural, instrumental, and discursive geneses of reasoning in a technological environment. International Journal of Science and Mathematics Education [Online]. doi:10.1007/s10763-013-9462-4.
   Google Scholar
• Gutierrez, A. & Jaime, A. (1999). Pre-service primary teachers’ understanding of the concept of altitude of a triangle. Journal of Mathematics Teacher Education, 2(3), 253–275.
   Google Scholar
• Hershkowitz, R. (1990). Psychological aspects of learning geometry. In P. Nesher & J. Kilpatrick ( Eds.), Mathematics and Cognition. A Research Synthesis by the International Group for the Psychology of Mathematics Education (pp. 70–95). Cambridge, MA: Cambridge University Press.
   Google Scholar
• Hilbert, T., Renkl, A., Kessler, S., & Reiss, K. (2008). Learning to prove in geometry: Learning from heuristic examples and how it can be supported. Learning and Instruction, 18, 54–65.
   Web of Science ®Google Scholar
• Lin, F. & Yang, K. (2007). The reading comprehension of geometric proofs: The contribution of knowledge and reasoning. International Journal of Science and Mathematics Education, 5(4), 729–754.
   Google Scholar
• Lin, F., Yang, K., Lo, J., Tsamir, P., Tirosh, D., & Stylianides, G. (2012). Teachers’ professional learning of teaching proof and proving. In G. Hanna & M. de Villiers ( Eds.), Proof and Proving in Mathematics Education. The 19^th ICMI Study (pp. 327–346). New York, NY: Springer.
   Google Scholar
• Ma, L. (1999). Knowing and Teaching Elementary Mathematics: Teacher’s Understanding of Fundamental Mathematics in China and the United States. Mahwah, NJ: Lawrence Erlbaum Associates
   Google Scholar
• Mesquita, A. L. (1998). On conceptual obstacles linked with external representation in geometry. Journal of Mathematical Behavior, 17(2), 183–195.
   Google Scholar
• Nason, R., Chalmers, Ch., & Yeh, A. (2012). Facilitating growth in prospective teachers’ knowledge: Teaching geometry in primary schools. Journal of Mathematics Teacher Education, 15, 227–249.
   Google Scholar
• Presmeg, N. (2006). Research on visualization in learning and teaching mathematics. In A. Gutierrez & P. Boero ( Eds.), Handbook of Research on the Psychology of Mathematics Education. Past, Present and Future (pp. 205–235). Rotterdam, The Netherlands: Sense Publishers.
   Google Scholar
• Prior, J. & Torregrosa, G. (2013). Razonamiento configural y procedimientos de verificación en contexto geométrico. [Configural reasoning and verification procedures in geometric context]. RELIME. Revista Latinoamericana de Investigación en Matemática Educativa, 16(3), 339–368.
   Google Scholar
• Sinclair, N. & Robutti, O. (2013). Technology and the role of proof: The case of dynamic geometry. In M. A. (Ken) Clements, A. J. Bishop, Ch. Keitel, J. Kilpatrick, & F. K. S. Leung ( Eds.), Third International Handbook of Mathematics Education (pp. 571–596). New York, NY: Springer.
   Google Scholar
• Stylianides, A. J. & Ball, D. (2008). Understanding and describing mathematical knowledge for teaching: Knowledge about proof for engaging students in the activity of proving. Journal of Mathematics Teacher Education, 11, 307–332.
   Google Scholar
• Stylianides, G., Stylianides, A., & Shilling-Traina, L. N. (2013). Prospective teachers’ challenges in teaching reasoning-and-proving. International Journal of Science and Mathematics Education, 11(6), 1463–1490. doi:10.1007/s10763-013-9409-9.
   Google Scholar
• Stylianou, D. A., Blanton, M. L., & Knuth, E. J. (2011). Teaching and Learning Proof Across the Grades. A K–16 Perspective. New York, NY: Routledge-Taylor & Francis Group.
   Google Scholar
• Tall, D. & Vinner, S. (1981). Concept image and concept definition in mathematics with particular reference to limits and continuity. Educational Studies in Mathematics, 12, 151–169.
   Google Scholar
• Torregrosa, G. & Quesada, H. (2007). Coordinación de procesos cognitivos en Geometría [Coordination of cognitive processes in geometry]. RELIME. Revista Latinoamericana de Investigación en Matemática Educativa, 10(2), 275–300.
   Google Scholar
• Torregrosa, G., Quesada, H., & Penalva, M.C. (2010). Razonamiento configural como coordinación de procesos de visualización [Configural reasoning as coordination of visualisation process]. Enseñanza de las Ciencias, 28(3), 327–340.
   Google Scholar
• Yang, K. & Lin, F. (2008). A model of reading comprehension of geometry proof. Educational Studies in Mathematics, 67(1), 59–76.
   Google Scholar