Teaching and Learning Patterns in School Mathematics

Psychological and Pedagogical Considerations

  • Ferdinand Rivera

Table of contents

  1. Front Matter
    Pages i-ix
  2. Ferdinand Rivera
    Pages 1-24
  3. Ferdinand Rivera
    Pages 55-91
  4. Ferdinand Rivera
    Pages 183-197
  5. Back Matter
    Pages 199-216

About this book

Introduction

This book draws on research findings on patterns in the last twenty years or so in order to argue for a theory of graded representations in pattern generalization. Pattern generalization encompasses the construction and justification of structures that give meanings to sequences of numerical and figural objects. While empirical studies 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 but parallel and graded, adaptive, and fundamentally distributed among a variety of cognitive and noncognitive sources that mutually influence each other. Thus, the emergence and complexity of the pattern generalization process cannot be reduced to a simple narrative of cognitive shifts from the arithmetic to the algebraic, from the recursive to the functional, from discerning details to perceiving properties, and so on and so forth. In this book, we pursue an alternative view of pattern generalization processing, that is, one that is not about permanent shifts or transition phases but graded and multimodal depending on individual learners’ experiences with patterns and, especially, the manner in which they perceive, think about, and act on them.  

 

A nonlinear graded perspective offers a much more robust and dynamic understanding of the similarities and differences in patterning competence since it is sensitive to, and acknowledges, the varying learning conditions and opportunities that shape generalization processing and representational conversion. Empirical evidence from a variety of sources will be provided to demonstrate this emergent perspective. Further, instructional implications commingle with research knowledge throughout the book, providing researchers and teachers with usable information that will help them cope with issues they may encounter when they use patterns to engage learners in generalization activity, which involves various aspects of abstract, quantitative, model-driven, structural, and regularity thinking.

 

Keywords

Algebraic thinking and patterns Mathematical cognition and patterns Pattern generalization Patterning activity in mathematics education Psychology in Mathematics Education Use of patterns for mathematical thinking and learning

Authors and affiliations

  • Ferdinand Rivera
    • 1
  1. 1.Dept. MathematicsSan Jose State UniversitySan JoseUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-007-2712-0
  • Copyright Information Springer Science+Business Media Dordrecht 2013
  • Publisher Name Springer, Dordrecht
  • eBook Packages Humanities, Social Sciences and Law
  • Print ISBN 978-94-007-2711-3
  • Online ISBN 978-94-007-2712-0
  • About this book