Commentary on Theories of Mathematics Education

Complexity Theories and Theories of Learning:
Literature Reviews and Syntheses
Andy Hurford
Prelude Systems approaches that try to understand experience by looking at patterns
of activity or interest and the relationships between them are becoming increasingly
prevalent and important in widely disparate disciplines. The purpose of this chapter
is to undertake a discussion of the use of dynamic systems-theoretical approaches
for making sense of (human) learning. The chapter begins with a review of the development
of systems-theoretical perspectives and explores three of these in detail.
Those sections are followed by discussion of apparent congruencies between interdisciplinary
complex systems models and cognitive models of learning. The chapter
concludes with brief remarks about projected directions for research into modeling
learning as a complex system.
General Systems Approaches
The use of systems-theoretical approaches for trying to understand experience is
not new (van Gelder and Port 1995, p. 4), and as has been pointed out by Chen and
Stroup (1993), Aristotle’s “whole is greater than the sum of the parts” is perhaps
the oldest recorded axiom of systems theoretical perspectives. It seems reasonable
to believe that thinking about “aggregates” (e.g., flocks, herds, armies) of “agents”
(geese or cattle or people) creating global patterns (Vs or stampedes or battles)
predates even Aristotle. From the ancient, to the modern, to the present the development
and utilization of systemic perspectives have been recurrent events. What
is relatively new however is a concerted and multidisciplinary effort toward developing
mathematized formalizations of systems-theoretical ideas, phraseology, and
methods into something approaching what John Casti (1994) refers to as a “science
of surprise” (p. 15).
For the past several hundred years the bulk of scientific and mathematical thinking
has been predominantly about dividing experience and phenomena into smaller
and smaller parts in efforts to understand our world. However for the last century
or so, when human enterprise has turned to describing, explaining, or predicting
dynamical activities various strains of (holistic) systems-mathematical approaches
have occasionally been invoked. Chen and Stroup (1993, p. 449) credit
A. Hurford ()
Department of Teaching and Learning, University of Utah, Salt Lake City, USA
e-mail: hurfor@me.com
B. Sriraman, L. English (eds.), Theories of Mathematics Education,
Advances in Mathematics Education,
DOI 10.1007/978-3-642-00742-2_54, © Springer-Verlag Berlin Heidelberg 2010
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