Commentary on Theories of Mathematics Education

Preface to Part IX
Jinfa Cai
As the title shows, this chapter is aimed at providing a future direction of problemsolving
research. To do so, they first did a retrospective survey of the reviews of
problem-solving research in the past two decades. Even though problem solving is
still a hot topic in the field of mathematics education, the field literally made very
little progress about problem solving research in the past two decades according to
the authors. Moreover, while problem solving has received an increased attention as
an integral part of school mathematics curriculum world wide, yet research in this
area decreased dramatically in recent years.
Why are there these paradoxical phenomena? The authors of this chapter identified
five factors contributing to the decline of problem-solving research and then
provided explanations for the paradoxical phenomena. Their discussion of the five
factors is both diagnostic and prescriptive. However, these contributing factors are
rooted so deeply in the current practices of mathematics education research and
classroom instruction, it might be unrealistic to expect a quick fix within a short
period of time.
The major section of the chapter is about the advancement of the fields of problem
solving research and curriculum development. This section not only gives us
hope, but also sends out a loud and clear message. That is, mathematical modeling
is an option to advance problem-solving research and curriculum development. The
authors take a strong position that mathematical modeling should not just be privileged
to secondary and college students. Instead, mathematical modeling should
also be an integral part of elementary school curriculum. Their principal argument
for this alternative to advance problem solving research is the following assumption:
The more we can integrate genuinely real-world problems into school mathematics,
the better our chances of enhancing students’ motivation and competencies
in mathematical problem solving. They contend that the alternative perspective on
problem solving should challenge and transform current school curricula and national
standards and should draw upon a wider range of research across disciplines.
Unfortunately, the authors did not use enough space to show what a “mathematical
modeling” curriculum would look like. In the process of reading this chapter, readers
might be reminded of the Realistic Mathematics in Netherlands (Freudenthal 1991;
de Lange 1996) and Standards-based mathematics curricula in the United States
(Senk and Thompson 2003) because of the extensive modeling activities in these
J. Cai ()
Department of Mathematical Sciences, University of Delaware, Newark, USA
e-mail: jcai@math.udel.edu
B. Sriraman, L. English (eds.), Theories of Mathematics Education,
Advances in Mathematics Education,
DOI 10.1007/978-3-642-00742-2_26, © Springer-Verlag Berlin Heidelberg 2010
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