Number Theory in Mathematics Education (eBook, PDF)

Perspectives and Prospects
Redaktion: Zazkis, Rina; Campbell, Stephen R.

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Taylor & Francis eBooks
• Seitenzahl: 268
• Erscheinungstermin: 12. Oktober 2012
• Englisch
• ISBN-13: 9781136501364
• Artikelnr.: 38273027

Autorenporträt

Zazkis, Rina; Campbell, Stephen R.

Inhaltsangabe

Contents: Preface. R. Zazkis, S.R. Campbell, Number Theory in Mathematics
Education Research: Perspectives and Prospects. S.R. Campbell,
Understanding Elementary Number Theory in Relation to Arithmetic and
Algebra. J. Mason, What Makes an Example Exemplary: Pedagogical and
Didactical Issues in Appreciating Multiplicative Structures. N. Sinclair,
For the Beauty of Number Theory. R. Zazkis, P. Liljedahl, On the Path to
Number Theory: Repeating Patterns as a Gateway. R. Leikin, Learning by
Teaching: A Case of Sieve of Eratosthenes and One Elementary School
Teacher. P. Liljedahl, Learning Elementary Number Theory Through a Chain of
Discovery: Preservice Teachers' Encounter With Pentominoes. C. Kieran, J.
Guzman, The Number Theoretic Experience of 12-to 15 Year Olds in a
Calculator Environment: The Intertwining Co-Emergence of Technique and
Theory. I. Lavy, Learning Number Theory Concepts Via Geometrical
Interactive Computerized Setting. D. Ginat, Overlooking Number Patterns in
Algorithmic Problem Solving. J.C. Smith, Revisiting Algebra in a Number
Theoretical Setting.