Teaching and Learning Proof Across the Grades: A K-16 Perspective

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

  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

  1. Representation-based Proof in the Elementary Grades
    Deborah Schifter
  2. Representations that Enable Children to Engage in Deductive Argument
    Anne K. Morris
  3. Young Mathematicians at Work: The Role of Contexts and Models in the Emergence of Proof
    Catherine Twomey Fosnot and Bill Jacob
  4. Children's Reasoning: Discovering the Idea of Mathematical Proof
    Carolyn A. Maher
  5. 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

  1. Middle School Students' Production of Mathematical Justifications
    Eric J. Knuth, Jeffrey M. Choppin, and Kristen N. Bieda
  2. From Empirical to Structural Reasoning in Mathematics Tracking Changes Over Time
    Dietmar Küchemann and Celia Hoyles
  3. Developing Argumentation and Proof Competencies in the Mathematics Classroom
    Aiso Heinze and Kristina Reiss
  4. Formal Proof in High School Geometry: Student Perceptions of Structure, Validity and Purpose
    Sharon A. Soucy McCrone and Tami S. Martin
  5. When is an Argument Just an Argument? The Refinement of Mathematical Argumentation
    Kay McClain
  6. Reasoning-and-Powering in School Mathematics: The Case of Pattern Indentification
    Gabriel J. Stylianides and Edward A. Silver
  7. "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

  1. College Instructors' Views of Students Vis-à-Vis Proof
    Guershon Harel and Larry Sowder
  2. Understanding Instructional Scaffolding in Classroom Discourse on Proof
    Maria L. Blanton, Despina A. Stylianou, and M. Manuela David
  3. 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
  4. Proof in Advanced Mathematics Classes: Semantic and Syntactic Reasoning in the Representation System of Proof
    Keith Weber and Lara Alcock
  5. Teaching Proving by Coordinating Aspects of Proofs with Students' Abilities
    John Selden and Annie Selden
  6. Current Contributions Toward Comprehensive Perspectives on the Learning and Teaching of Proof
    Guershon Harel and Evan Fuller

References
Index

 

Purchase this book through Routledge, Taylor Francis Group.