Teaching and Learning Proof Across the Grades

Despina A. Stylianou is an Associate Professor of Mathematics Education at the City College of the City University of New York.Maria L. Blanton is a Senior Executive Research Associate at the James J. Kaput Center for Research and Innovation in Mathematics Education and an Associate Professor of Mathematics Education at the University of Massachusetts, Dartmouth.Eric J. Knuth is an Associate Professor of Mathematics Education at the University of Wisconsin-Madison.

• Series Editor's Foreword: The Soul of Mathematics, Alan H. SchoenfeldPreface List of ContributorsIntroductionSection I: Theoretical Considerations on the Teaching and Learning of Proof1. What I Would Like My Students to Already Know About Proof, Reuben Hersh2. 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 Lueke3. Proving and Knowing In Public: The Nature of Proof in A Classroom, Patricio Herbst and Nicolas BalacheffSection II: Teaching and Learning of Proof in the Elementary Grades4. Representation-based Proof in the Elementary Grades, Deborah Schifter5. Representations that Enable Children To Engage in Deductive Argument, Anne K. Morris6. Young Mathematicians At Work: The Role of Contexts And Models in the Emergence of Proof, Catherine Twomey Fosnot and Bill Jacob7. Children’s Reasoning: Discovering the Idea of Mathematical Proof, Carolyn A. Maher8. Aspects of Teaching Proving In Upper Elementary School, David A. Reid and Vicki ZackSection III: Teaching and Learning of Proof in Middle Grades and High School9. Middle School Students’ Production of Mathematical Justifications, Eric J. Knuth, Jeffrey M. Choppin and Kristen N. Bieda10. From Empirical to Structural Reasoning in Mathematics: Tracking Changes Over Time, Dietmar Küchemann and Celia Hoyles11. Developing Argumentation and Proof Competencies in the Mathematics Classroom, Aiso Heinze and Kristina Reiss12. Formal Proof in High School Geometry: Student Perceptions of Structure, Validity And Purpose, Sharon M. Soucy McCrone and Tami S. Martin13. When is an Argument Just An Argument? The Refinement of Mathematical Argumentation, Kay McClain14. Reasoning-and-Proving in School Mathematics: The Case of Pattern Identification, Gabriel J. Stylianides and Edward A. Silver15. "Doing Proofs" in Geometry Classrooms, Patricio Herbst, Chialing Chen, Michael Weiss, and Gloriana González, with Talli Nachlieli, Maria Hamlin and Catherine BrachSection IV: Teaching and Learning of Proof in College16. College Instructors’ Views of Students Vis-á-Vis Proof, Guershon Harel and Larry Sowder17. Understanding Instructional Scaffolding in Classroom Discourse on Proof, Maria L. Blanton, Despina A. Stylianou and M. Manuela David18. 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 Oehler19. Proof in Advanced Mathematics Classes: Semantic and Syntactic Reasoning in the Representation System of Proof, Keith Weber and Lara Alcock20. Teaching Proving by Coordinating Aspects of Proofs with Students’ Abilities, John Selden and Annie Selden21. Current Contributions toward Comprehensive Perspectives on the Learning and Teaching of Proof, Guershon Harel & Evan FullerReferencesIndex

Select Guide Rating