Authors:
- 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)
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Front Matter
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Back Matter
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
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Centre for Instructional Psychology and Technology, K.U. Leuven,Belgium and EHSAL—European University College Brussels, Belgium
Dirk De Bock
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Centre for Instructional Psychology and Technology, K.U. Leuven, Belgium
Wim Van Dooren, Lieven Verschaffel
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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