基本説明
Includes concrete examples to guide the development of a patterns approach in school mathematics curricula for the K-12 classroom.
Full Description
This book synthesizes research findings on patterns in the last twenty years or so in order to argue for a theory of graded representations in pattern generalization. While research results drawn from investigations conducted with different age-level groups have sufficiently demonstrated varying shifts in structural awareness and competence, which influence the eventual shape of an intended generalization, such shifts, however, are not necessarily permanent due to other pertinent factors such as the complexity of patterning tasks. The book proposes an alternative view of pattern generalization, that is, one that is not about shifts or transition phases but graded depending on individual experiences with target patterns. The theory of graded representations involving pattern generalization offers a much more robust understanding of differences in patterning competence since it is sensitive to varying levels of entry into generalization. Empirical evidence will be provided to demonstrate this alternative view, which is drawn from the author's longitudinal work with elementary and middle school children, including several investigations conducted with preservice elementary majors. Two chapters of the book will be devoted to extending pattern generalization activity to arithmetic and algebraic learning of concepts and processes. The concluding chapter addresses the pedagogical significance of pattern learning in the school mathematics curriculum.
Contents
-1 Introduction. -2 The Context of Generalization. -3 Types and Levels of Pattern Generalization. -4 The Theory of Graded Representations in Pattern Generalization. -5 Gestures, Words, and Incipient Generalizations. -6 Variables and Algebraic Generalizations. - 7 Patterns, Generalization, and Arithmetic Learning. -8 Patterns, Functional Thinking, and Algebraic Learning. -9 Pedagogical Issues and Implications. -10 Conclusions.
