(Page 2 of 8) - Enculturation: The Neglected Learning Metaphor in Mathematics Education authored by Kirshner, David.

This dialectic orientation for enculturation-oriented theories can be contrasted with the

unifocal character of behaviorism, cognitive psychology, and (psychological) constructivism that
study the individual constitution of learning. For instance, Greeno (1997) describes the
Afactoring ## email not listed ## of cognitive science: Awe can analyze properties of cognitive processes
and structures [independently] and treat the properties of other systems [e.g., social systems] as
contexts in which those processes and structures ## email not listed ## (p. 6)Ba characterization Anderson,
Reder, & Simon (1997) readily accept. Similarly, constructivism, in its Piagetian origins and its
initial radical variation in mathematics education, examined conceptual structures from a
unifocal individualist perspective:

Von Glasersfeld acknowledges a significant debt to Piaget, which may explain why he
focuses on the individual knower, and pays scant attention to the social processes in
knowledge construction. (Von Glasersfeld=s ... educational concerns of course lead him
to address the role of the teacher. But he faces severe problems of consistency here: It is
clear that in much of his writing von Glasersfeld problematizes the notion of a ## email not listed ##
external to the cognitive apparatus of the individual knower/learner. But as a result, it is
difficult to see how he can consistently allow that social influences exist....) (Phillips,
1995, p. 8)

Within the rich mix of psychological theories that ground our pedagogical discourse, my

concern is that the multifocal theorizations of enculturation index the second class status of this
learning metaphor in teaching. Consider, for example, the behaviorist, cognitive, and situative
rubrics offered by Greeno, Collins, and Resnick (1996) in their overview of learning theory and
education. Whereas the first two are unifocal in their pedagogical orientation, the situative
approach to education is integrative: ASequences of learning activities can be organized with
attention to students= progress in a variety of practices of learning, reasoning, cooperation, and
communication, as well as to the subject matter contents that should be ## email not listed ## (p. 28).
Enculturating students toward modes of engagement (e.g., Apractices of learning, reasoning,
cooperation, and ## email not listed ##) is never addressed educationally as a bona fide pedagogical
focus in its own right; only in conjunction with the (predominating) interests in developing
students= skills and concepts.

This concern needs to be couched within the crossdisciplinary perspective (Kirshner, 2000,

2002) that frames the current analysis. Crossdisciplinarity offers a broad critique of the
integrative tendency of our pedagogical discourse in which Agood ## email not listed ## functions as a
unitary construct. The basis for this concern is the simple observation that psychological theory
has not yet succeeded in establishing a paradigmatic consensus about learning. Rather, in its
current preparadgimatic state (Kuhn, 1970), multiple notions of learning compete with one
another for paradigmatic hegemony. Because Agood ## email not listed ## is teaching that supports
learning, until a consensus about learning is achieved we need to be suspicious of any
formulation of good teaching that claims to generality. For although integrative theorizations are
offered in the situated cognition, sociocultural, and social constructivist camps, none has yet
succeeded in establishing more than a toehold in the broader theoretical spectrum, and each pays
a heavy price in clarity and accessibility for taking on the dialectic challenge of bridging across
independently sensible metaphors for learning (e.g., Kirshner & Whitson, 1998; Lerman, 1996).

The crossdisciplinary alternative is to articulate discrete, theory based models of good

teaching for the discrete learning metaphors. This process requires that each of the three
metaphors be independently interrogated as to its implications for teaching, leaving to teachers
the values decisions as to which notion(s) of learning to pursue with their students, as well as the
tactical problems of coordination and balance in case more than a single metaphor is aspired to.