## ABSTRACT

**A Co-Publication of Routledge for the National Council of Teachers of Mathematics (NCTM)**

In recent years there has been increased interest in the nature and role of proof in mathematics education; with many mathematics educators advocating that proof should be a central part of the mathematics education of students at all grade levels. This important new collection provides that much-needed forum for mathematics educators to articulate a connected K-16 "story" of proof. Such a story includes understanding how the forms of proof, including the nature of argumentation and justification as well as what counts as proof, evolve chronologically and cognitively and how curricula and instruction can support the development of students’ understanding of proof. Collectively 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. By building and extending on existing research and by allowing a variety of voices from the field to be heard, *Teaching and Learning Proof Across the Grades* not only highlights the main ideas that have recently emerged on proof research, but also defines an agenda for future study.

## TABLE OF CONTENTS

part I|51 pages

Theoretical Considerations on the Teaching and Learning of Proof

chapter 2|19 pages

#### Exploring Relationships Between Disciplinary Knowledge and School Mathematics

part II|82 pages

Teaching and Learning of Proof in the Elementary Grades

chapter 6|18 pages

#### Young Mathematicians at Work

part III|122 pages

Teaching and Learning of Proof in Middle Grades and High School

chapter 12|18 pages

#### Formal Proof in High School Geometry

chapter 13|13 pages

#### When is an Argument Just an Argument?

part VI|102 pages

Teaching and Learning of Proof in College