Number Theory in Mathematics Education: Perspectives and Prospects

(Studies in Mathematical Thinking and Learning)

Rina Zazkis, Stephen R. Campbell

Lawrence Erlbaum Associates | 2006 | 304 páginas | pdf | 2,8 Mb

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This book offers multiple interconnected perspectives on the largely untapped potential of elementary number theory for mathematics education: its formal and cognitive nature, its relation to arithmetic and algebra, its accessibility, its utility and intrinsic merits, to name just a few. Its purpose is to promote explication and critical dialogue about these issues within the international mathematics education community. The studies comprise a variety of pedagogical and research orientations by an international group of researchers that, collectively, make a compelling case for the relevance and importance of number theory in mathematics education in both pre K-16 settings and mathematics teacher education. Topics variously engaged include: • understanding particular concepts related to numerical structure and number theory; • elaborating on the historical and psychological relevance of number theory in concept development; • attaining a smooth transition and extension from pattern recognition to formative principles; • appreciating the aesthetics of number structure; • exploring its suitability in terms of making connections leading to aha! insights and reaching toward the learner's affective domain; • reexamining previously constructed knowledge from a novel angle; • investigating connections between technique and theory; • utilizing computers and calculators as pedagogical tools; and • generally illuminating the role number theory concepts could play in developing mathematical knowledge and reasoning in students and teachers. Overall, the chapters of this book highlight number theory-related topics as a stepping-stone from arithmetic toward generalization and algebraic formalism, and as a means for providing intuitively grounded meanings of numbers, variables, functions, and proofs. Number Theory in Mathematics Education: Perspectives and Prospects is of interest to researchers, teacher educators, and students in the field of mathematics education, and is well suited as a text for upper-level mathematics education courses.

Contents
List of Contributors vii
Preface ix
1 Number Theory in Mathematics Education Research: Perspectives and Prospects
Rina Zazkis and Stephen R. Campbell
2 Understanding Elementary Number Theory in Relation to Arithmetic and Algebra
Stephen R. Campbell
3 What Makes an Example Exemplary: Pedagogical and Didactical Issues in Appreciating Multiplicative Structures
John Mason
4 For the Beauty of Number Theory 69
Nathalie Sinclair
5 On the Path to Number Theory: Repeating Patterns as a Gateway
Rina Zazkis and Peter Liljedahl
6 Learning by Teaching: The Case of Sieve of Eratosthenes and One Elementary School Teacher
Roza Leikin
7 Learning Elementary Number Theory Through a Chain of Discovery: Preservice Teachers’ Encounter with Pentominoes
Peter Liljedahl
8 The Number-Theoretic Experience of 12- to 15-Year-Olds in a Calculator Environment: The Intertwining Coemergence of Technique and Theory
Carolyn Kieran and José Guzmán
9 Learning Number Theory Concepts Via Geometrical Interactive Computerized Setting
Ilana Lavy
10 Overlooking Number Patterns in Algorithmic Problem Solving
David Ginat
11 Revisiting Algebra in a Number Theoretical Setting 249
Jennifer Christian Smith

Outros livros da mesma autora, disponíveis no blog:

- Campbell. S. R., & Zazkis, R. (Eds.) (2002). Learning and teaching number theory: Research in cognition and instruction. Westport, CT: Ablex Publishing 
- Leikin, R. & Zazkis, R. (Eds.) (2010). Learning through Teaching Mathematics:  Developing teachers’ knowledge and expertise in practice. Springer.

- Zazkis, R. (2011). Relearning mathematics: A challenge for prospective elementary school teachers. Information Age Publishing. Charlotte, NC.

Capítulos em livros, da mesma autora, disponíveis no blog:

- Zazkis, R. & Gadowsky, K. (2001). Attending to transparent features of opaque representations of natural numbers. In A. Cuoco (Ed.), NCTM 2001 Yearbook: The roles of representation in school mathematics (pp. 41-52). Reston, VA: NCTM. 
-  Zazkis, R. (2008). Divisibility and transparency of number representations. In M. P. Carlson & C. Rasmussen (Eds.), Making the Connection: Research and practice in undergraduate mathematics (pp. 81-92). MAA notes.