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

by Stylianou; Despina A.

• ISBN13: 9780415989848
• ISBN10: 0415989841
• Edition: 1st
• Format: Hardcover
• Copyright: 2009-03-05
• Publisher: Routledge

Summary

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 Gradesnot only highlights the main ideas that have recently emerged on proof research, but also defines an agenda for future study.

Table of Contents

Series Editor Introduction

List of Contributors

Preface

Introduction

What I Would Like My Students to Already Know About Proof

Exploring Relationships Between Disciplinary Knowledge and School Mathematics: Implications For Understanding the Place of Reasoning And Proof in School Mathematics

Proving and Knowing In Public: The Nature of Proof in A Classroom

Representation-Based Proof in the Elementary Grades

Representations that Enable Children To Engage in Deductive Argument

Young Mathematicians At Work: The Role of Contexts And Models in the Emergence of Proof

Children's Reasoning: Discovering the Idea of Mathematical Proof

Aspects of Teaching Proving In Upper Elementary School

Middle School Students' Production of Mathematical Justifications

From Empirical to Structural Reasoning in Mathematics: Tracking Changes Over Time

Developing Argumentation and Proof Competencies in the Mathematics Classroom

Formal Proof in High School Geometry: Student Perceptions of Structure, Validity And Purpose

When is an Argument Just An Argument? The Refinement of Mathematical Argumentation

Reasoning-and-Proving in School Mathematics: The Case of Pattern Identification

"Doing Proofs" in Geometry Classrooms

College Instructors' Views of Students Vis a Vis Proof

Understanding Instructional Scaffolding in Classroom Discourse on Proof

Building a Community of Inquiry in a Problem-Based Undergraduate Number Theory Course: The Role of the Instructor

Proof in Advanced Mathematics Classes: Semantic and Syntactic Reasoning in the Representation System of Proof

Teaching Proving by Coordinating Aspects of Proofs with Students' Abilities

Current Contributions toward Comprehensive Perspectives on the Learning and Teaching of Proof

References

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