Commentary on Theories of Mathematics Education

98 N. Presmeg
interview—a dramatic and startling phenomenon that pointed unequivocally to the
power of theoretical focus to influence what is observed. Thus data are not merely
collected; they are constructed according to the lens of a theoretical viewpoint.
It is no accident that in a field as complex as the teaching and learning of mathematics,
theories have proliferated, and have been drawn from many of the established
disciplines. Traditionally, psychology was considered to be a field of paramount
importance in the choice of theories. Cognition and affect, and even constructs
such as self-efficacy and self-actualization, were productive lenses for various
aspects. But the learning of mathematics typically originates in classrooms, and
hence the value of more recent approaches involving the sociological theories that
Lerman addresses. By using the meta-lens of Bernstein’s notions of hierarchy and
verticality, Lerman has provided a wider theoretical framework in which to situate
theories that are useful. In doing so, he has provided strong warrants for the claim
that plurality of theories is not a problem: in fact it is indispensable in addressing
the many complex issues that impinge on the teaching and learning of mathematics.