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Didactics of Mathematics as a Scientific Discipline, 103-116.
© 1994 Dordrecht: Kluwer Academic Publishers. Printed in the Netherlands.
1. INTRODUCTION
In this chapter, I will raise the issue of what it means to be scientific in the
context of conducting research on teaching and teacher education. I will ar-
gue that our notion of being scientific is related to how we see change
evolving in the teaching and learning of mathematics. The concepts of au-
thority and adaptation will be considered as they are related to teacher edu-
cation.

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the latest educational fad is even worse. (Brophy, 1975, p. 15)
While the debate raged in the 1970s over the applicability of science to the
art of teaching, what was obscured was the question of what constitutes sci-
ence. A review of published research in the United States during this period
suggests a view of science as an exercise in yielding statistical generaliza-
tions. Most of this research involved the process/product paradigm in which
teacher behaviors were correlated with achievement – usually defined in
terms of basic skills (see, e.g., Rosenshine & Furst, 1973). In the main, this
research had little impact on the field of mathematics education.
By the late 1970s, the field was beginning to turn its head. Researchers, at
least in the United States, began to study teachers' decision-making pro-
cesses, thereby giving the impression that the questions were more cogni-
tively oriented, yet holding tightly to the notion of "traditional" science. A
study by Peterson and Clark (1978) is illustrative, as they traced the nature
and types of decisions teachers made using correlational analyses. But there
were other voices being heard, some inside and some outside the field of
mathematics education, that raised more fundamental issues. From a
methodological perspective, Mitroff and Kilmann (1978) concluded that
"science is in serious need of methodological and epistemological reform"
(p. 30). The authors maintained that "Even if there were no 'crises of belief '
in science, there would still be good reasons for considering reform at this
time, given the new cultural forces and streams of thought being articulated"
(p. 3). Mitroff and Kilmann's (1978) analysis led them to identify four types
of scientist. One type, the analytic scientist, believes in the value-free nature
of science, that is, knowledge is separable from values. In contrast, the au-
thors identified two other types, the conceptual humanist and the particular
humanist, who focus on descriptions of human activity, raising the question
of whether stories are an appropriate mechanism for communicating re-
search findings.
Perhaps the most serious attack on the notion of "traditional science"
came from Feyerabend (1988) who maintained that "the events, procedures,
and results that constitute the sciences have no common structure" (p. 1).
Feyerabend's (1988) orientation toward science supports an eclectic view of
the way science should be conducted. According to Feyerabend, science, as
defined by an allegiance to regimented procedures, runs the risk of under-
mining the value gained from human ingenuity, insight, and compassion.
Similarly, Mitroff and Kilmann (1978) observed that, "The greatest scien-
tists seem not only to combine the attributes of opposing types but to delight
in doing so" (p. 12).
At one level, we can say that research on teaching has moved from what
teachers were (i.e., their characteristics) in the 1950s and 1960s, to what
teachers did in the 1970s, to what teachers decided in the early 1980s, to the
more recent focus on what teachers believe (see Brown, Cooney, & Jones,
1990; Thompson, 1992). Such an analysis would miss, however, what was
104
SCIENCE AND TEACHER EDUCATION

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happening conceptually and methodologically in mathematics education.
With the emerging prominence of the constructivist epistemology (in its
many forms), a premium has been placed on meaning and context. This em-
phasis challenges us to reconsider what we mean by being scientific, includ-
ing the notion of being objective. Von Glasersfeld addresses the issue of ob-
jectivity in the following way:
In order to observe anything, in order to "collect data," one must have some no-
tion – no matter how primitive and preliminary – of the particular experiences
one intends to relate to one another. It is, obviously, these experiences that one
will be looking for. In order to find them, one necessarily assimilates and
disregards all sorts of differences in individual observations. The longer this goes
on successfully and the more often the model one has constructed proves useful,
the stronger becomes the belief that one has discovered a real connection, if not a