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The Illusion of Linearity

From Analysis to Improvement

  • Book
  • © 2007

Overview

Authors:
  1. Dirk De Bock

    1. Centre for Instructional Psychology and Technology, K.U. Leuven,Belgium and EHSAL—European University College Brussels, Belgium

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  2. Wim Van Dooren

    1. Centre for Instructional Psychology and Technology, K.U. Leuven, Belgium

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  3. Dirk Janssens

    1. Department of Mathematics, K.U. Leuven, Belgium

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  4. Lieven Verschaffel

    1. Centre for Instructional Psychology and Technology, K.U. Leuven, Belgium

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  • 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
  • Includes supplementary material: sn.pub/extras

Part of the book series: Mathematics Education Library (MELI, volume 41)

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Table of contents (7 chapters)

  1. Front Matter

    Pages I-XIV
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  2. A Widespread Phenomenon

    • Dirk De Bock, Wim Van Dooren, Dirk Janssens, Lieven Verschaffel
    Pages 1-22

  3. In Search Of Empirical Evidence

    • Dirk De Bock, Wim Van Dooren, Dirk Janssens, Lieven Verschaffel
    Pages 23-38

  4. Searching For Explanations: A Series Of Follow-Up Studies

    • Dirk De Bock, Wim Van Dooren, Dirk Janssens, Lieven Verschaffel
    Pages 39-85

  5. An In-Depth Investigation

    • Dirk De Bock, Wim Van Dooren, Dirk Janssens, Lieven Verschaffel
    Pages 87-108

  6. A Teaching Experiment

    • Dirk De Bock, Wim Van Dooren, Dirk Janssens, Lieven Verschaffel
    Pages 109-125

  7. Stepping Outside The Classroom

    • Dirk De Bock, Wim Van Dooren, Dirk Janssens, Lieven Verschaffel
    Pages 127-141

  8. Psychological And Educational Analysis

    • Dirk De Bock, Wim Van Dooren, Dirk Janssens, Lieven Verschaffel
    Pages 143-164

  9. Back Matter

    Pages 165-184
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Keywords

About this book

Linear or proportional relationships are a major topic in mathematics education. However, recent research has shown that secondary school students strongly tend 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.

Authors and Affiliations

  • Centre for Instructional Psychology and Technology, K.U. Leuven,Belgium and EHSAL—European University College Brussels, Belgium

    Dirk De Bock

  • Centre for Instructional Psychology and Technology, K.U. Leuven, Belgium

    Wim Van Dooren, Lieven Verschaffel

  • Department of Mathematics, K.U. Leuven, Belgium

    Dirk Janssens

Bibliographic Information

  • Book Title: The Illusion of Linearity

  • Book Subtitle: From Analysis to Improvement

  • Authors: Dirk De Bock, Wim Van Dooren, Dirk Janssens, Lieven Verschaffel

  • Series Title: Mathematics Education Library

  • DOI: https://doi.org/10.1007/978-0-387-71164-5

  • Publisher: Springer New York, NY

  • eBook Packages: Humanities, Social Sciences and Law, Education (R0)

  • Copyright Information: Springer-Verlag US 2007

  • Hardcover ISBN: 978-0-387-71082-2Published: 13 September 2007

  • Softcover ISBN: 978-1-4419-4381-1Published: 19 November 2010

  • eBook ISBN: 978-0-387-71164-5Published: 30 September 2007

  • Series ISSN: 0924-4921

  • Series E-ISSN: 2214-983X

  • Edition Number: 1

  • Number of Pages: XIV, 184

  • Topics: Mathematics Education, Teaching and Teacher Education

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