Learning and Teaching Number Theory

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.