Teaching and Learning Patterns in School Mathematics

Psychological and Pedagogical Considerations

Authors: Rivera, Ferdinand

  • The only book to advocate a patterns approach to mathematics education as a way of democratizing access to hard-to-reach concepts and processes
  • Provides a synthesis of twenty years of research on the use patterns in mathematics education
  • Includes concrete examples to guide the development of a patterns approach in school mathematics curricula for the K-12 classroom         ​
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eBook $119.00
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  • ISBN 978-94-007-2712-0
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Hardcover $159.00
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  • ISBN 978-94-007-2711-3
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  • Usually dispatched within 3 to 5 business days.
Softcover $159.00
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  • ISBN 978-94-007-9428-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

  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.     ​  

About the authors

Dr. Rivera is interested in issues involving visualization and algebraic thinking, in particular, generalization. His overall research program at San Jose State University falls under the category of psychology of mathematics education, which involves studying learning and teaching conditions that influence curriculum and instruction. He recently concluded a three-year longitudinal study on pattern generalization at the middle school level. Results of his findings are reported in various peer-reviewed journals, book chapters, and conference proceedings. He has recently published a book, Toward a Visually-Oriented School Mathematics Curriculum, that is a volume in the Springer Mathematics Education Library series. This year, Dr. Rivera will be completing a one-year longitudinal research study in a Grade 2 class. He intends to follow the same kids through Grade 3 during the next school year. Dr. Rivera's research is supported by a Career grant from the National Science Foundation.

Table of contents (7 chapters)

  • Introduction

    Rivera, Ferdinand

    Pages 1-24

  • Contexts of Generalization in School Mathematics

    Rivera, Ferdinand

    Pages 25-54

  • Types and Levels of Pattern Generalization

    Rivera, Ferdinand

    Pages 55-91

  • A Theory of Graded Representations in Pattern Generalization

    Rivera, Ferdinand

    Pages 93-110

  • Graded Pattern Generalization Processing of Elementary Students (Ages 6 Through 10 Years)

    Rivera, Ferdinand

    Pages 111-150

Buy this book

eBook $119.00
price for USA (gross)
  • ISBN 978-94-007-2712-0
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $159.00
price for USA
  • ISBN 978-94-007-2711-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $159.00
price for USA
  • ISBN 978-94-007-9428-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Teaching and Learning Patterns in School Mathematics
Book Subtitle
Psychological and Pedagogical Considerations
Authors
Copyright
2013
Publisher
Springer Netherlands
Copyright Holder
Springer Science+Business Media Dordrecht
eBook ISBN
978-94-007-2712-0
DOI
10.1007/978-94-007-2712-0
Hardcover ISBN
978-94-007-2711-3
Softcover ISBN
978-94-007-9428-3
Edition Number
1
Number of Pages
IX, 216
Topics