![]() Educational Studies in Mathematics, 44, 151–161. Dynamic geometry environments as a source of rich learning contexts for the complex activity of proving. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. Educational Studies in Mathematics, 44, 55–85. Providing a foundation for deductive reasoning: Students’ interpretations when using dynamic geometry software and their evolving mathematical explanations. ![]() Villani (Eds.), Perspectives on the teaching of geometry for the 21st century. For the Learning of Mathematics, 17(1), 7–16. The curricular shaping of students’ approaches to proof. International Journal of Computers for Mathematical Learning, 6, 63–86. Using dynamic geometry software to add contrast to geometric situations-A case study. International Journal of Computers for Mathematical Learning, 6, 235–256. ![]() Software tools for geometric problem solving: Potentials and pitfalls. Educational Studies in Mathematics, 44, 5–23. Proof, explanation and exploration: An overview. Educational Studies in Mathematics, 44, 127–150. He role of contradiction and uncertainty in promoting the need to prove in dynamic geometry environments. Hadas, N., Hershkowitz, R., & Schwarz, B. Chazan (Eds.), Designing learning environments for developing understanding of geometry and space. International Journal of Mathematical Education in Science and Technology, 32(3), 319–335. Students approaching proof through conjectures: Snapshots in a classroom. Albany: State University of New York Press.įuringhetti, F., Olivero, F., & Paola, D. Social constructivism as a philosophy of mathematics. International Journal of Computers for Mathematical Learning, 2, 187–215.Įrnest, P. Exploring the territory before proof: Students’ generalizations in a computer microworld for transformation geometry. Cambridge, Massachusetts: MIT.Įdwards, L. Changing minds: Computers, learning, and literacy. Emeryville, CA: Key Curriculum.ĭi Sessa, A. Rethinking proof with the Geometer’s Sketchpad. An alternative approach to proof in dynamic geometry. Washington, DC: The Mathematical Association of America.ĭe Villiers, M. Schattschneider (Eds.), Geometry turned on: Dynamic software in learning, teaching, and research. The role of proof in investigative, computer-based geometry: Some personal reflections. New York: Houghton Mifflin.ĭe Villiers, M. British Educational Research Journal, 20(1), 41–53.ĭavis, P. Proof practices and constructs of advanced mathematics students. Hillsdale, NJ: Erlbaum.Ĭoe, R., & Ruthven, K. Wilson (Eds.), The geometric supposer: What is it a case of?. Instructional implications of students’ understanding of the differences between empirical verification and mathematical proof. Educational Studies in Mathematics, 24, 359–387.Ĭhazan, D. ![]() High school geometry students’ justification for their views of empirical evidence and mathematical proof. International Newsletter on the Teaching and Learning of Mathematical Proof, 7(8). Argumentation and mathematical proof: A complex, productive, unavoidable relationship in mathematics and mathematics education. The Netherlands: University of Maastricht.īoero, P. Hakkarainen (Eds.), The proceedings of the first European conference on computer-supported collaborative learning (pp. Designing social infrastructure: The challenge of building computer-supported learning communities. A program for raising the level of student achievement in secondary level mathematics. Furthermore, I suggest software modifications that will better support learners’ participation in authentic proof tasks.Īllen, F. I argue that knowledge building is a suitable pedagogical approach for the proof model presented in this paper. This leads me to an examination of a certain CSCL tool whose design is guided by knowledge-building pedagogy. Tracing the move from absolutism to fallibilism in the philosophy of mathematics, I highlight the vital role of community in the production of mathematical knowledge. I argue that two major forces have given rise to this conception of proving: a particular learning perspective promoted in reform documents and a genre of computer tools, namely dynamic geometry software, which affords this perspective of learning within the context of mathematical proof. I introduce a model of proof in school mathematics that incorporates both empirical and deductive ways of knowing. In this paper, I review both mathematics education and CSCL literature and discuss how we can better take advantage of CSCL tools for developing mathematical proof skills.
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