Stylianou, D. A., Blanton, M. L., & Knuth, E. J. (Eds.) (2009). Teaching and Learning Proof Across the Grades: A K-16 Perspective. New York/Washington, DC: Routledge/National Council of Teachers of Mathematics.

**Table of Contents**

*Series Editor’s Foreward: The Soul of Mathematics, by Alan H. Schoefeld
Preface
Acknowledgements
List of Contributors
Introduction
*

Section I:Theorectical Considerations on the Teaching and learning of Proof

- 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 and H. Michael Lueke* - 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

- 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 and 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 and Vicki Zack*

Section III: Teaching and Learning Proof in Middle Grades and High School

- Middle School Students’ Production of Mathematical Justifications

*Eric J. Knuth, Jeffrey M. Choppin, and Kristen N. Bieda* - From Empirical to Structural Reasoning in Mathematics Tracking Changes Over Time

*Dietmar Küchemann and Celia Hoyles* - Developing Argumentation and Proof Competencies in the Mathematics Classroom

*Aiso Heinze and Kristina Reiss* - Formal Proof in High School Geometry: Student Perceptions of Structure, Validity and Purpose

*Sharon A. Soucy McCrone and Tami S. Martin* - When is an Argument Just an Argument? The Refinement of Mathematical Argumentation

*Kay McClain* - Reasoning-and-Powering in School Mathematics: The Case of Pattern Indentification

*Gabriel J. Stylianides and Edward A. Silver* - “Doing Proofs” in Geometry Classrooms

*Patricio Herbst, Chialing Chen, Michael Weiss, and Gloriana González, with Talli Nachlieli, Maria Hamlin, and Catherine Brach*

Section IV: Teaching and Learning Proof in College

- College Instructors’ Views of Students Vis-à-Vis Proof

*Guershon Harel and Larry Sowder* - Understanding Instructional Scaffolding in Classroom Discourse on Proof

*Maria L. Blanton, Despina A. Stylianou, and M. Manuela David* - 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 Too, and Kury Oehler* - Proof in Advanced Mathematics Classes: Semantic and Syntactic Reasoning in the Representation System of Proof

*Keith Weber and Lara Alcock* - Teaching Proving by Coordinating Aspects of Proofs with Students’ Abilities

*John Selden and Annie Selden* - Current Contributions Toward Comprehensive Perspectives on the Learning and Teaching of Proof

*Guershon Harel and Evan Fuller*

*References
Index
*

* *

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