Mathematics Education Library

The Illusion of Linearity

From Analysis to Improvement

Authors: de Bock, D., van Dooren, W., Janssens, D., Verschaffel, L.

  • State-of-the-art research on the illusion of linearity
  • Addresses a related set of flaws in mathematics education and proposes remedies
  • Integrates and organizes existing literature on mathematics education
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eBook $149.00
price for USA (gross)
  • ISBN 978-0-387-71164-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $199.00
price for USA
  • ISBN 978-0-387-71082-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $199.00
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  • ISBN 978-1-4419-4381-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

Linear or proportional relationships are a major topic in mathematics education. However, recent research has shown that secondary school students have a strong tendency to apply the linear model also in situations wherein it is not applicable. This overgeneralization of linearity is sometimes referred to as the "illusion of linearity" and has a strong negative impact on students’ reasoning and problem solving skills.

"The Illusion of Linearity: From Analysis to Improvement" presents the reader with a comprehensive overview of the major findings of the recent research on the illusion of linearity. Although the empirical study of students’ improper linear reasoning clearly constitutes a new line of research, it owes a great deal to prior work in mathematics education research community such as the work of the scholars of the Freudenthal Institute on realistic mathematics education.

Based on both quantitative and qualitative research, "The Illusion of Linearity: From Analysis to Improvement" discusses the following issues: (1) how the illusion of linearity appears in diverse domains of mathematics and science and how it is conceptually related to other more general misconceptions identified in the research literature, (2) what are the crucial psychological, mathematical, and educational factors being responsible for the occurrence and persistence of the phenomenon, and (3) how the illusion of linearity can be remedied by appropriate instruction.

"The Illusion of Linearity: From Analysis to Improvement" is essential to those working in mathematics education, particularly teacher educators and curriculum research and development.

Table of contents (7 chapters)

  • A Widespread Phenomenon

    Bock, Dirk De (et al.)

    Pages 1-22

  • In Search Of Empirical Evidence

    Bock, Dirk De (et al.)

    Pages 23-38

  • Searching For Explanations: A Series Of Follow-Up Studies

    Bock, Dirk De (et al.)

    Pages 39-85

  • An In-Depth Investigation

    Bock, Dirk De (et al.)

    Pages 87-108

  • A Teaching Experiment

    Bock, Dirk De (et al.)

    Pages 109-125

Buy this book

eBook $149.00
price for USA (gross)
  • ISBN 978-0-387-71164-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $199.00
price for USA
  • ISBN 978-0-387-71082-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $199.00
price for USA
  • ISBN 978-1-4419-4381-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
The Illusion of Linearity
Book Subtitle
From Analysis to Improvement
Authors
Series Title
Mathematics Education Library
Series Volume
41
Copyright
2007
Publisher
Springer US
Copyright Holder
Springer-Verlag US
eBook ISBN
978-0-387-71164-5
DOI
10.1007/978-0-387-71164-5
Hardcover ISBN
978-0-387-71082-2
Softcover ISBN
978-1-4419-4381-1
Series ISSN
0924-4921
Edition Number
1
Number of Pages
XIV, 184
Topics