The Illusion Of Linearity

From Analysis to Improvement

  • Dirk De Bock
  • Wim Van Dooren
  • Dirk Janssens
  • Lieven Verschaffel

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

Table of contents

  1. Front Matter
    Pages I-XIV
  2. Dirk De Bock, Wim Van Dooren, Dirk Janssens, Lieven Verschaffel
    Pages 1-22
  3. Dirk De Bock, Wim Van Dooren, Dirk Janssens, Lieven Verschaffel
    Pages 23-38
  4. Dirk De Bock, Wim Van Dooren, Dirk Janssens, Lieven Verschaffel
    Pages 39-85
  5. Dirk De Bock, Wim Van Dooren, Dirk Janssens, Lieven Verschaffel
    Pages 87-108
  6. Dirk De Bock, Wim Van Dooren, Dirk Janssens, Lieven Verschaffel
    Pages 109-125
  7. Dirk De Bock, Wim Van Dooren, Dirk Janssens, Lieven Verschaffel
    Pages 127-141
  8. Dirk De Bock, Wim Van Dooren, Dirk Janssens, Lieven Verschaffel
    Pages 143-164
  9. Back Matter
    Pages 165-184

About this book

Introduction

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.

Keywords

Freud calculus curriculum development education educational research experiment mathematics problem solving qualitative research research research & development (R&D) school science teaching

Authors and affiliations

  • Dirk De Bock
    • 1
  • Wim Van Dooren
    • 2
  • Dirk Janssens
    • 3
  • Lieven Verschaffel
    • 2
  1. 1.Centre for Instructional Psychology and TechnologyK.U. Leuven,Belgium and EHSAL—European University College BrusselsBelgium
  2. 2.Centre for Instructional Psychology and TechnologyK.U. LeuvenBelgium
  3. 3.Department of MathematicsK.U. LeuvenBelgium

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-387-71164-5
  • Copyright Information Springer Science+Business Media, LLC 2007
  • Publisher Name Springer, Boston, MA
  • eBook Packages Humanities, Social Sciences and Law
  • Print ISBN 978-0-387-71082-2
  • Online ISBN 978-0-387-71164-5
  • About this book