This is the summary of a presentation given at the Joint Mathematics
Meetings, January 10-13, 1996, Orlando, Florida.
Constructivism in mathematics education---what does it mean?
The most influential and widely accepted philosophical
perspective in mathematics education today is constructivism.
This view, which holds that individuals construct their own
knowledge, can be traced back to Piaget and beyond. While
it takes many forms, at its simplest, it sees the learner as an
active participant, not as a blank slate upon which we write or
as an empty vessel which we fill. In this view, cognition is
considered adaptive, in the sense that it tends to organize
experiences so they "fit" with a person's previously constructed
knowledge. As a consequence, both researchers and teachers
ask, "What is going on in students' minds when . . . ?", rather than
speaking of behavioral outcomes and asking, "Which stimulus
will elicit a desired response?"
The term "constructivism" often designates this view of how
people learn, and constructivist teaching often simply means
taking students' views and background into account so as to
engender active, meaningful learning. However, constructivism
comes in a variety of "flavors." There is a "moderate" version,
compatible with the way most mathematicians see mathematics,
and a social constructivist version, inspired by the work of
Vygotsky, which takes into account sociocultural perspectives.
There is the radical constructivism of von Glasersfeld, and beyond
that, the sociology of scientific knowledge (SSK), which replaces
the idea of truth with that of utility. We will describe these views
and place them along a (increasingly radical) continuum from the
above "plain vanilla" version, which almost everyone in mathematics
education today accepts and tries to act on, through the radical
view, to the very relativistic SSK.
Adopting the "plain vanilla" view that students construct
(or reconstruct) knowledge for themselves does not prescribe
a single "constructivist way of teaching." It does, however,
suggest that lecturing is likely to be less effective, than more
active approaches such as cooperative group learning, and as a
result, students are likely to make weak constructions. Ways
of teaching that require students, not only to be more active,
but to reflect on their work, are likely to encourage them to
make strong constructions that result in increased conceptual
knowledge and more connections. We will indicate some
general principles this constructivist view entails.
John Selden, MERC, Box 2781, Cookeville, TN 38502
Annie Selden, Tennessee Technological University, Cookeville, TN 38505
As a supplement to this presentation, see also "Kinds of Constructivism: An Annotated Bibliography."