References
- Andriessen, J. E. B., & Schwarz, B. B. (2009). Argumentative design. In N. Muller-Mirza & A. N. Perret-Clermont (Eds.), Argumentation and education – Theoretical foundations and practices (pp. 145–174). Heidelberg, Germany: Springer.
- Arcavi, A., Kessel, C., Meira, L., & Smith, J. P. (1998). Teaching mathematical problem solving: An analysis of an emergent classroom community. Research in Collegiate Mathematics Education III, 7, 1–70.
- Arzarello, F. (2006). Semiosis as a multimodal process. Relime, Numero Especial, 267–299.
- Arzarello, F., & Sabena, C. (2011). Semiotic and theoretic control in argumentation and proof activities. Educational Studies in Mathematics, 77(2–3) 189–206. doi:10.1007/s10649-010-9280-3
- Burkhardt, H. (1988). Teaching problem solving. In H. Burkhardt, S. Groves, A. Schoenfeld, & K. Stacey (Eds.), Problem solving--A world view (Proceedings of the problem solving theme group, ICME 5) (pp. 17–42). Nottingham: Shell Centre.
- Carlson, M. P., & Bloom, I. (2005). The cyclic nature of problem solving: An emergent multi-dimensional problem-solving framework. Educational Studies in Mathematics, 58(1), 45–75. doi:10.1007/s10649-005-0808-x
- Carpenter, T. P. (1989). Teaching as problem solving. In R. I. Charles & E. A. Silver (Eds.), The teaching and assessing of mathematical problem solving. (pp. 187–202). Reston, VA: National Council of Teachers of Mathematics.
- Carpenter, T. P., & Lewis, R. (1976). The development of the concept of a standard unit of measure in young students. Journal for Research in Mathematics Education, 7(1), 53–58. doi:10.2307/748765
- Cobb, P., & Bauersfeld, H. (Eds.) (1995). The emergence of mathematical meaning: Interaction in classroom culture. Hillsdale, NJ: LEA.
- Cobb, P., Wood, T., & Yackel, E. (1991). A constructivist approach to second grade mathematics. In E. von Glaserfield, (Ed.), Radical constructivism in mathematics education (pp. 157–176). Dordrecht, The Netherlands: Kluwer Academic.
- Doise, W., & Mugny, G. (1979). Individual and collective conflicts of centrations in cognitive development. European Journal of Social Psychology, 9(1), 105–108. doi:10.1002/ejsp.2420090110
- Duval, R. (2006). Les conditions cognitives de l'apprentissage de la géométrie: développement de la visualisation, différenciation des raisonnements et coordination de leur fonctionnement [Cognitive conditions of learning geometry: development of the visualization, differentiation of reasoning and coordination of their functioning], Annales de Didactique et de Sciences Cognitives [Annals of didactic and Cognitive Sciences], 10, 5–53.
- Hadas, N., Hershkowitz, R., & Schwarz, B. B. (2001). The role of surprise and uncertainty in promoting the need to prove in computerized environment. Educational Studies in Mathematics, 44(1–2), 127–150.
- Hershkowitz, R. (1990). Psychological aspects of geometry learning - Research and practice. In P. Nesher & J. Kilpatrick (Eds.), Mathematics and cognition (pp. 70–95). Cambridge: Cambridge University Press.
- Howe, C., Tolmie, A., Duchak-Tanner, V., & Rattray, C. (2000). Hypothesis-testing in science: Group consensus and the acquisition of conceptual and procedural knowledge. Learning and Instruction, 10(4), 361–391. doi:10.1016/S0959-4752(00)00004-9
- Leinhardt, G., & Schwarz, B. B. (1997). Seeing the problem: An explanation from Polya. Cognition and Instruction, 15(3), 395–434. doi:10.1207/s1532690xci1503_3
- Levav-Waynberg, A., & Leikin, R. (2009). Multiple solutions for a problem: A tool for evaluation of mathematical thinking in geometry. Proceedings of CERME 6, January 28th-February 1st, Lyon France.
- Limón, M. (2001). On the cognitive conflict as an instructional strategy for conceptual change: A critical appraisal. Learning & Instruction, 11(4–5), 357–380. doi:10.1016/S0959-4752(00)00037-2
- National Council of Teacher of Mathematics (NCTM). (2000). Principles and standards for school mathematics. Reston, VA: NCTM.
- Piaget, J., Inhelder, B., & Szeminska, A. (1981). The child's conception of geometry. New York, NY: Norton and Company.
- Polya, G. (1945/1957). How to solve it: A new aspect of mathematical method. Princeton Science Library. Princeton, NJ: Princeton University Press.
- Prusak, N., Hershkowitz, R., & Schwarz, B. B. (2012). From visual reasoning to logical necessity, through argumentative design. Educational Studies in Mathematics, 79(1), 19–40. doi:10.1007/s10649-011-9335-0
- Radford, L. (2002). The seen, the spoken and the written: A semiotic approach to the problem of objectification of mathematical knowledge. For the Learning of Mathematics, 22(2), 14–23.
- Radford, L. (2009). Why do gestures matter? Sensuous cognition and the palpability of mathematical meanings. Educational Studies in Mathematics, 70(2), 111–126. doi:10.1007/s10649-008-9127-3
- Rasmussen, C., & Stephan, M. (2008). A methodology for documenting collective activity. In A. E. Kelly, R. A. Lesh, & J. Y. Baek (Eds.), Handbook of design research methods in education (pp. 195–215). New York, NY and London: Routledge.
- Rogoff, B. (1990). Apprenticeship in thinking: Cognitive development in social context. New York, NY: Oxford University Press.
- Schoenfeld, A. H. (1985). Mathematical problem solving. New York, NY: Academic Press.
- Schoenfeld, A. H. (1994). Reflections on doing and teaching mathematics. In A. Schoenfeld (Ed.), Mathematical thinking and problem solving (pp. 53–69). Hillsdale, NJ: Lawrence Erlbaum Associates.
- Schwarz, B. B., & Hershkowitz, R. (1999). Prototypes: Brakes or levers in learning the function concept? The role of computer tools. Journal for Research in Mathematics Education, 30(4), 362–389. doi:10.2307/749706
- Schwarz, B. B., Hershkowitz, R., & Prusak, N. (2010). Argumentation and mathematics. In K. Littleton, & C. Howe (Eds.), Educational dialogues: Understanding and promoting productive interaction (pp. 103–127). London, UK: Taylor & Francis, Routledge.
- Stanic, G.M.A., & Kilpatrick, J. (1989). Historical perspectives on problem solving in the mathematics curriculum. In R. I. Charles & E. A. Silver (Eds.), Research agenda for mathematics education: Vol. 3. The teaching and assessing of mathematical problem solving (pp. 1–22). Hillsdale, NJ: Lawrence Erlbaum, & Reston, VA: National Council of Teachers of Mathematics.
- Sweller, J. (1990). Cognitive processes and instruction procedures. Australian Journal of Education, 34(2), 125–130.
- Tripathi, N. P. (2009). Problem solving in mathematics: a tool for cognitive development. Proceeding of epiSTEME-3 International Conference to Review Research in Science, Technology and Mathematics Education. Mumbai, India
- Wood, T. (1999). Creating a context for argumentation in mathematics class, Journal for Research in Mathematics Education, 30(2), 171–191. doi:10.2307/749609
- Yackel, E., & Cobb, P. (1996). Socio-mathematical norms, argumentation, and autonomy in Mathematics. Journal for Research in Mathematics Education, 27(4), 458–477.