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Using Design Research and History to Tackle a Fundamental Problem with School Algebra

  • Sinan Kanbir
  • M. A. (Ken) Clements
  • Nerida F. Ellerton

Part of the History of Mathematics Education book series (HME)

Table of contents

  1. Front Matter
    Pages i-xxiv
  2. Sinan Kanbir, M. A. (Ken) Clements, Nerida F. Ellerton
    Pages 1-10
  3. Sinan Kanbir, M. A. (Ken) Clements, Nerida F. Ellerton
    Pages 59-70
  4. Sinan Kanbir, M. A. (Ken) Clements, Nerida F. Ellerton
    Pages 71-86
  5. Sinan Kanbir, M. A. (Ken) Clements, Nerida F. Ellerton
    Pages 87-114
  6. Sinan Kanbir, M. A. (Ken) Clements, Nerida F. Ellerton
    Pages 115-140
  7. Sinan Kanbir, M. A. (Ken) Clements, Nerida F. Ellerton
    Pages 141-154
  8. Sinan Kanbir, M. A. (Ken) Clements, Nerida F. Ellerton
    Pages 155-192
  9. Sinan Kanbir, M. A. (Ken) Clements, Nerida F. Ellerton
    Pages 193-209
  10. Sinan Kanbir, M. A. (Ken) Clements, Nerida F. Ellerton
    Pages 211-221
  11. Back Matter
    Pages 223-327

About this book

Introduction

In this well-illustrated book the authors, Sinan Kanbir, Ken Clements, and Nerida
Ellerton, tackle a persistent, and universal, problem in school mathematics—why do
so many middle-school and secondary-school students find it difficult to learn algebra
well? What makes the book important are the unique features which comprise the
design-research approach that the authors adopted in seeking a solution to the problem. 

The first unique feature is that the authors offer an overview of the history of school
algebra. Despite the fact that algebra has been an important component of secondary-school
mathematics for more than three centuries, there has never been a comprehensive
historical analysis of factors influencing the teaching and learning of that component.
The authors identify, through historical analysis, six purposes of school algebra:
(a) algebra as a body of knowledge essential to higher mathematical and scientific
studies, (b) algebra as generalized arithmetic, (c) algebra as a prerequisite for entry to
higher studies, (d) algebra as offering a language and set of procedures for modeling
real-life problems, (e) algebra as an aid to describing structural properties in elementary
mathematics, and (f) algebra as a study of variables. They also raise the question
whether school algebra represents a unidimensional trait.

Kanbir, Clements and Ellerton offer an unusual hybrid theoretical framework for their
intervention study (by which seventh-grade students signifi cantly improved their
elementary algebra knowledge and skills). Their theoretical frame combined Charles
Sanders Peirce’s triadic signifier-interpretant-signified theory, which is in the realm of
semiotics, with Johann Friedrich Herbart’s theory of apperception, and Ken Clements’
and Gina Del Campo’s theory relating to the need to expand modes of communications
in mathematics classrooms so that students engage in receptive and expressive modes.
Practicing classroom teachers formed part of the research team.

This book appears in Springer’s series on the “History of Mathematics Education.”
Not only does it include an important analysis of the history of school algebra, but it
also adopts a theoretical frame which relies more on “theories from the past,” than on
contemporary theories in the field of mathematics education. The results of the well-designed
classroom intervention are sufficiently impressive that the study might have
created and illuminated a pathway for future researchers to take.

Keywords

History of education History of algebra education Design research in education Algebra education School algebra Algebra in middle and secondary school curricula

Authors and affiliations

  • Sinan Kanbir
    • 1
  • M. A. (Ken) Clements
    • 2
  • Nerida F. Ellerton
    • 3
  1. 1.Department of Mathematics SciencesUniversity of Wisconsin–Stevens PointStevens PointUSA
  2. 2.Department of MathematicsIllinois State UniversityNormalUSA
  3. 3.Department of MathematicsIllinois State UniversityNormalUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-59204-6
  • Copyright Information Springer International Publishing AG 2018
  • Publisher Name Springer, Cham
  • eBook Packages Education
  • Print ISBN 978-3-319-59203-9
  • Online ISBN 978-3-319-59204-6
  • Series Print ISSN 2509-9736
  • Series Online ISSN 2509-9744
  • Buy this book on publisher's site