Teaching and Learning Proof Across the Grades

Series Editor's Foreword: The Soul of Mathematics, Alan H. Schoenfeld Preface List of Contributors Introduction Section I: Theoretical Considerations on the Teaching and Learning of Proof 1. What I Would Like My Students to Already Know About Proof, Reuben Hersh 2. Exploring Relationships Between Disciplinary Knowledge and School Mathematics: Implications For Understanding the Place of Reasoning And Proof in School Mathematics, Daniel Chazan and H. Michael Lueke 3. Proving and Knowing In Public: The Nature of Proof in A Classroom, Patricio Herbst and Nicolas Balacheff Section II: Teaching and Learning of Proof in the Elementary Grades 4. Representation-based Proof in the Elementary Grades, Deborah Schifter 5. Representations that Enable Children To Engage in Deductive Argument, Anne K. Morris 6. Young Mathematicians At Work: The Role of Contexts And Models in the Emergence of Proof, Catherine Twomey Fosnot and Bill Jacob 7. Children's Reasoning: Discovering the Idea of Mathematical Proof, Carolyn A. Maher 8. Aspects of Teaching Proving In Upper Elementary School, David A. Reid and Vicki Zack Section III: Teaching and Learning of Proof in Middle Grades and High School 9. Middle School Students' Production of Mathematical Justifications, Eric J. Knuth, Jeffrey M. Choppin and Kristen N. Bieda 10. From Empirical to Structural Reasoning in Mathematics: Tracking Changes Over Time, Dietmar Kuchemann and Celia Hoyles 11. Developing Argumentation and Proof Competencies in the Mathematics Classroom, Aiso Heinze and Kristina Reiss 12. Formal Proof in High School Geometry: Student Perceptions of Structure, Validity And Purpose, Sharon M. Soucy McCrone and Tami S. Martin 13. When is an Argument Just An Argument? The Refinement of Mathematical Argumentation, Kay McClain 14. Reasoning-and-Proving in School Mathematics: The Case of Pattern Identification, Gabriel J. Stylianides and Edward A. Silver 15. Doing in Geometry Classrooms, Patricio Herbst, Chialing Chen, Michael Weiss, and Gloriana Gonzalez, with Talli Nachlieli, Maria Hamlin and Catherine Brach Section IV: Teaching and Learning of Proof in College 16. College Instructors' Views of Students Vis-a-Vis Proof, Guershon Harel and Larry Sowder 17. Understanding Instructional Scaffolding in Classroom Discourse on Proof, Maria L. Blanton, Despina A. Stylianou and M. Manuela David 18. Building a Community of Inquiry in a Problem-Based Undergraduate Number Theory Course: The Role of the Instructor, Jennifer Christian Smith, Stephanie Ryan Nichols, Sera Yoo and Kurt Oehler 19. Proof in Advanced Mathematics Classes: Semantic and Syntactic Reasoning in the Representation System of Proof, Keith Weber and Lara Alcock 20. Teaching Proving by Coordinating Aspects of Proofs with Students' Abilities, John Selden and Annie Selden 21. Current Contributions toward Comprehensive Perspectives on the Learning and Teaching of Proof, Guershon Harel & Evan Fuller References Index