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
significantly 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
havecreated and illuminated a pathway for future researchers to take.
