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

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

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

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.

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

- 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