![]() ![]() ![]() ![]() Providence, RI: American Mathematical Society. Dubinsky (Eds.), Research in collegiate mathematics (Vol. Student’s proof schemes: Results from exploratory studies. Harel (Eds.), Advances in Mathematics Education Research on Proof and Proving: an international perspective (pp. Types of epistemological justifications, with particular reference to complex numbers. Zandieh (Eds.), Challenges and strategies in teaching linear algebra (pp. The learning and teaching of linear algebra through the lenses of intellectual need and epistemological justification and their constituents. Leatham (Ed.), Vital direction for mathematics education research (pp. DNR perspective on mathematics curriculum and instruction, Part II, ZDM- The International Journal on Mathematics Education, 40, 893–907. ZDM-The International Journal on Mathematics Education, 40, 487–500. DNR perspective on mathematics curriculum and instruction: Focus on proving, Part I. Linear Algebra and its Applications, 302–303, 601–613. Students’ understanding of proofs: A historical analysis and implications for the teaching of geometry and linear algebra. Watkins (Eds.), Resources for teaching linear algebra, MAA Notes (Vol. Allan, (Eds.) Proceedings of the Joint Meeting of PME 38 and PME- NA 36 (Vol. Teaching linear algebra in the embodied, symbolic and formal worlds of mathematical thinking: Is there a preferred order? In S. VIII: Research in Collegiate Mathematics Education. Using geometry to teach and learn linear algebra (pp. Linear Algebra and its Applications, 275, 141–160. The role of formalism in the teaching of the theory of vector spaces. Wilhelm (Eds.), Teacher noticing: Bridging and broadening perspectives, contexts, and frameworks (pp. The FOCUS Framework: Characterising productive noticing during lesson planning, delivery and review. International Journal of Mathematical Education in Science and Technology, 40(7), 963–974.Ĭhoy, B. Linear algebra revisited: An attempt to understand students’ conceptual difficulties. Dordrecht: Kluwer.īritton, S., & Henderson, J. Tall (Ed.), Advanced Mathematical Thinking (pp. The results revealed that understanding a proof in order to gain personal conviction was a major concern of students.Īlibert, D., & Thomas, M. Although, these models are often applied to what students construct, we argue they can also be applied to how students perceive proofs. We employed Tall’s Three Worlds as well as Harel’s intellectual need to analyse the data. In particular, it addresses areas such as student views on understanding of proof, the purpose of a proof, and when and how proofs communicate to them. This paper opens the case for a pedagogy of proof in linear algebra and examines students’ reactions to, and voices on, proof in a first-year course in linear algebra. In this study, we examined responses to a set of interview questions on proof by a group of 16 first-year undergraduate students shortly after their final examination. Although research on proof in mathematics education is increasing, systematic studies on proof in linear algebra are still scarce. How do students view proof in linear algebra? Do they distinguish argumentation and proof, and if so how? are among many questions that are still unanswered. While an introduction to new concepts through definitions and theorems adds to the complexity of the course, proof remains the number one hurdle for many students. Proof has a prominent place in the linear algebra curriculum, teaching and learning but in first-year courses it continues to be challenging for both instructors and students. ![]()
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