How to Study as a Mathematics Major

Description

These essays inform educators and researchers at different grade levels about the teaching and learning of proof at each level and, thus, help advance the design of further empirical and theoretical work in this area. --from publisher description. What I would like my students to already know about proof / Reuben Hersh -- Exploring relationships between disciplinary knowledge and school mathematics: implications for understanding the place of reasoning and proof in school mathematics / Daniel Chazan, H. Michael Leuke -- Proving and knowing in public: the nature of proof in a classroom / Patricio Herbst, Nicolas Balacheff -- Representation-based proof in the elementary grades / Deborah Schifter -- Representations that enable children to engage in deductive argument / Anne K. Morris -- Young mathematicians at work: the role of contexts and models in the emergence of proof / Catherine Twomey Fosnot, Bill Jacob -- Children's reasoning: discovering the idea of mathematical proof / Carolyn A. Maher -- Aspects of teaching proving in upper elementary school / David A. Reid, Vicki Zack -- Middle school students' production of mathematical justifications / Eric J. Knuth, Jeffrey M. Choppin, Kristen N. Bieda -- From empirical to structural reasoning in mathematics: tracking changes over time / Dietmar Küchemann, Celia Hoyles -- Developing argumentation and proof competencies in the mathematics classroom / Aiso Heinze, Kristina Reiss -- Formal proof in high school geometry: student perceptions of structure, validity, and purpose / Sharon M. Soucy McCrone, Tami S. Martin. When is an argument just an argument? the refinement of mathematical argumentation / Kay McClain -- Reasoning-and-proving in school mathematics: the case of pattern identification / Gabriel J. Stylianides, Edward A. Silver -- "Doing proofs" in geometry classrooms / Patricio Herbst [and others] -- College instructors' views of students vis-à-vis proof / Guershon Harel, Larry Sowder -- Understanding instructional scaffolding in classroom discourse on proof / Maria L. Blanton, Despina A. Stylianou, M. Manuela David -- Building a community of inquiry in a problem-based undergraduate number theory course: the role of the instructor / Jennifer Christian Smith [and others] -- Proof in advanced mathematics classes: semantic and syntactic reasoning in the representation system of proof / Keith Weber, Lara Alcock -- Teaching proving by coordinating aspects of proofs with students' abilities / John Selden, Annie Selden -- Current contributions toward comprehensive perspectives on the learning and teaching of proof / Guershon Harel, Evan Fuller.