Learning and Teaching Number Theory: Research in Cognition and Instruction (Mathematics, Learning, and Cognition: Monograph Series of the Journal of Mathematical Behavior)

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.Collectively, these studies draw on a variety of cognitive, linguistic, and pedagogical frameworks that focus on various approaches to problem solving, communicating, representing, connecting, and reasoning with topics of elementary number theory, and these in turn have practical implications for the classroom. Learning styles and teaching strategies investigated involve number theoretical vocabulary, concepts, procedures, and proof strategies ranging from divisors, multiples, and divisibility rules, to various theorems involving division, factorization, partitions, and mathematical induction. Since the beginning of the ancient Greek Pythagorean tradition over two and a half millennia ago, striving for a conceptual understanding of numbers and their properties, patterns, structures, and forms has constituted the heart, if not the soul, of mathematics and mathematical thinking. Annotation Essential to developing deeper understandings of mathematics, number theory has received scant attention in mathematics education research. This volume redresses this matter and serves as a launch point for further research in this important area This work aims to cover research in learning and teaching number theory. It is a collection of clinical and classroom-based studies in cognition and instruction on learning and teaching number theory. Edited By Stephen R. Campbell And Rina Zazkis. Includes Bibliographical References And Indexes. Mode Of Access: World Wide Web.