The Paradox of Conceptual Change

In re-reading through my stack of mathematics education journal articles for a paper I’m writing, I came across this quote in the wonderful chapter by Philipp (2007):

“How do mathematics educators change teachers’ beliefs by providing practice-based evidence if teachers cannot see what they do not already believe?” (p. 309)

That is THE paradox of conceptual change, and it’s why I am so fascinated by the initial, unconscious coding of stimuli (along the lines of Gladwell’s Blink) that marks a phenomenon as worthy of attention. Such initial coding is often marked by a general affective valence of positive/negative. Not surprisingly, we tend to pay greater attention to that which is first perceived as negative, but then all kinds of defense mechanisms arise to cope with the dissonant information being received. Thus, the key, in my opinion, is either global paradigmatic change that redefines what is considered negative and what is positive (such as a religious transformation, for example), or on a more domain-specific level, some kind of conceptual tool introduced into the situation, either via self-regulation through self-talk for instance, or through the scaffolding of others (think of a psychologist helping a snake-phobic patient redefine the experience of touching the snake’s cold skin). A la Vygotsky, what happens on the social plane eventually becomes internalized, so the therapist is no longer needed after a time as the patient talks herself through the next experience with a snake.

Implications for teaching? Coaching/mentoring, for one. Very specific, focused coaching that allows the more experienced teacher to identify those “knots,” discrepancies “between ‘what is’ and ‘what must be” (Wagner, as cited in Engstrom, 1998), and works to provide alternative interpretations and new ways of behaving in difficult situations.

References
Engeström, Y. (1998). Reorganizing the motivational sphere of classroom culture: An activity-theoretical analysis of planning in a teacher team. In F. Seeger, J. Voigt & U. Waschesio (Eds.), The culture of the mathematics classroom (pp. 76–103). Cambridge, UK: Cambridge University Press.

Philipp, R. A. (2007). Mathematics teachers’ beliefs and affect. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning: A project of the National Council of Teachers of Mathematics. (pp. 257–315). Charlotte, NC: Information Age Pub.