Learning and teaching number theory : research in cognition and instruction / edited by Stephen R. Campbell and Rina Zazkis.

ISBN:

9780313016035

9781280315466

Title:

Learning and teaching number theory : research in cognition and instruction / edited by Stephen R. Campbell and Rina Zazkis.

Author:

Campbell, Stephen R.

Publication Information:

Westport, Conn. : Ablex Pub., 2002.

Physical Description:

1 online resource (vi, 245 pages) : illustrations.

Series:

Mathematics, learning, and cognition. monograph series of the Journal of mathematical behavior ; v. 2

Contents:

Toward number theory as a conceptual field / Stephen R. Campbell and Rina Zazkis -- Coming to terms with division: Preservice teachers' understanding / Stephen R. Campbell -- Conceptions of divisibility: Success and understanding / Anne Brown, Karen Thomas, and George Tolias -- Language of number theory: Metaphor and rigor / Rina Zazkis -- Understanding elementary number theory at the undergraduate level: A semiotic approach / Pier Luigi Ferrari -- Integrating content and process in classroom mathematics / Anne R. Teppo -- Patterns of thought and prime factorization / Anne Brown -- What do students do with conjectures? Preservice teachers' generalizations on a number theory task / Laurie D. Edwards and Rina Zazkis -- Generic proofs in number theory / Tim Rowland -- The development of mathematical induction as a proff scheme: A model for DNR-based instruction / Guershon Harel -- Reflections on mathematics education research questions in elementary number theory / Annie Selden and John Selden.

Local Note:

eBooks on EBSCOhost

Subject Term:

Number theory -- Study and teaching.

Added Author:

Campbell, Stephen R.

Zazkis, Rina.

Format:

Electronic Resources

Electronic Access:

Click here to view

Publication Date:

2002

Publication Information:

Westport, Conn. : Ablex Pub., 2002.

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Shelf Number	Material Type	Copy	Shelf Location	Status
510 22	1:E-BOOK	1	1:ONLINE	Searching... Unknown

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Summary

Number theory has been a perennial topic of inspiration and importance throughout the history of philosophy and mathematics. Despite this fact, surprisingly little attention has been given to research in learning and teaching number theory per se. This volume is an attempt to redress this matter and to serve as a launch point for further research in this area. Drawing on work from an international group of researchers in mathematics education, this volume is a collection of clinical and classroom-based studies in cognition and instruction on learning and teaching number theory. Although there are differences in emphases in theory, method, and focus area, these studies are bound through similar constructivist orientations and qualitative approaches toward research into undergraduate students' and preservice teachers' subject content and pedagogical content knowledge.

Reviews (1)

Choice Review

This volume investigates the various ways of thinking and some of the problems related to learning and teaching number theory. The 11 chapters are self-contained and written by different authors. They can be read independently or, if preferred, collectively for a more expansive theoretical base. Every chapter represents the author's particular method for examining different cognitive and instructional dimensions of learning and teaching number theory. The first chapter provides an overview of the entire book and a brief discussion of number theory and its role in the curriculum. All of the studies concern themselves with various learners' approaches, such as problem solving, reasoning, and connecting, with topics on number theory and classroom implications. Additionally, most of the studies examine how number theory helps learners with their conceptual understanding of whole number arithmetic. The final three chapters investigate learners' abilities to generalize and conjecture about inductive and deductive proof strategies. Each chapter contains references and many contain concluding statements and relevant notes. Recommended for upper-division undergraduates, graduates, and professionals/practitioners. C. M. Bradley Northeastern Illinois University

1 Toward Number Theory as a Conceptual Field	p. 1
2 Coming to Terms with Division: Preservice Teachers' Understanding	p. 15
3 Conceptions of Divisibility: Success and Understanding	p. 41
4 Language of Number Theory: Metaphor and Rigor	p. 83
5 Understanding Elementary Number Theory at the Undergraduate Level: a Semiotic Approach	p. 97
6 Integrating Content and Process in Classroom Mathematics	p. 117
7 Patterns of Thought and Prime Factorization	p. 131
8 What Do Students Do with Conjectures? Preservice Teachers' Generalizations on a Number Theory Task	p. 139
9 Generic Proofs in Number Theory	p. 157
10	p. 185
11 Reflections on Mathematics Education Research Questions in Elementary Number Theory	p. 213
Author Index	p. 231
Subject Index	p. 235
About the Contributors	p. 243

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Table of Contents