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Learning Mathematics

Constructivist and Interactionist Theories of Mathematical Development

Editors: Cobb, Paul (Ed.)

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  • ISBN 978-94-017-2057-1
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About this book

The first five contributions to this Special Issue on Theories of Mathematical Learning take a cognitive perspective whereas the sixth, that by Voigt, takes an interactionist perspective. The common theme that links the six articles is the focus on students' inferred experiences as the starting point in the theory-building process. This emphasis on the meanings that objects and events have for students within their experiential realities can be contrasted with approaches in which the goal is to specify cognitive behaviors that yield an input-output match with observed behavior. It is important to note that the term 'experience' as it is used in these articles is not restricted to physical or sensory-motor experience. A perusal of the first five articles indicates that it includes reflective experiences that involve reviewing prior activity and anticipating the results of potential activity. In addition, by emphasizing interaction and communication, Voigt's contribution reminds us that personal experiences do not arise in a vacuum but instead have a social aspect. In taking a cognitive perspective, the first five contributions analyze the pro­ cesses by which students conceptually reorganize their experiential realities and thus construct increasingly sophisticated mathematical ways of knowing. The conceptual constructions addressed by these theorists, ranging as they do from fractions to the Fundamental Theorem of Calculus, indicate that experiential approaches to mathematical cognition are viable at all levels of mathematical development. Although the authors use different theoretical constructs, several additional commonalities can be discerned in their work.

Table of contents (6 chapters)

Table of contents (6 chapters)
  • Cognitive Play and Mathematical Learning in Computer Microworlds

    Pages 7-30

    Steffe, Leslie P. (et al.)

  • Exponential Functions, Rates of Change, and the Multiplicative Unit

    Pages 31-60

    Confrey, Jere (et al.)

  • Growth in Mathematical Understanding: How Can We Characterise It and How Can We Represent It?

    Pages 61-86

    Pirie, Susan (et al.)

  • The Gains and the Pitfalls of Reification — The Case of Algebra

    Pages 87-124

    Sfard, Anna (et al.)

  • Images of Rate and Operational Understanding of the Fundamental Theorem of Calculus

    Pages 125-170

    Thompson, Patrick W.

Buy this book

eBook $109.00
price for USA in USD
  • ISBN 978-94-017-2057-1
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $149.99
price for USA in USD
  • ISBN 978-0-7923-2823-0
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
Softcover $149.99
price for USA in USD
  • ISBN 978-90-481-4397-9
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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Bibliographic Information

Bibliographic Information
Book Title
Learning Mathematics
Book Subtitle
Constructivist and Interactionist Theories of Mathematical Development
Editors
  • Paul Cobb
Copyright
1994
Publisher
Springer Netherlands
Copyright Holder
Springer Science+Business Media Dordrecht
eBook ISBN
978-94-017-2057-1
DOI
10.1007/978-94-017-2057-1
Hardcover ISBN
978-0-7923-2823-0
Softcover ISBN
978-90-481-4397-9
Edition Number
1
Number of Pages
VI, 194
Topics