Studio mathematics: The epistemology and practice of design pedagogy as a model for mathematics learning

Shaffer, D. W. (2005). Studio mathematics: The epistemology and practice of design pedagogy as a model for mathematics learning (WCER Working Paper No. 2005-3). Madison: University of Wisconsin-Madison, Wisconsin Center for Education Research. http://www.wcer.wisc.edu/publications/workingPapers/Working_Paper_No_2005_3.pdf

Abstract:

This paper is part of a small but growing literature on how professional practices and professional training can inform the creation of learning environments for younger students (Cossentino, 2002; Cossentino & Shaffer, 1999; Erickson & Lehrer, 1998; Hmelo, Holton, & Kolodner, 2000; Jacobson & Lehrer, 2000; Kafai, 1996; Kolodner, Crismond, Gray, Holbrook, & Puntambekar, 1998; Penner, Schauble, & Lehrer, 1998; Resnick & Ocko, 1991; Schon, 1985; Shaffer, 1997c, 2002a, 2002b, 2003, 2004b; Stevens, 2000). The paper describes one particular project in this genre, Escher’s World, as an occasion to explore one of the theories that underlies such work, the theory of pedagogical praxis (Shaffer, 2004a). Pedagogical praxis suggests that new technologies make it possible to take pedagogies developed in the context of professional training–pedagogies that typically emphasize participation in meaningful projects in epistemologically rich contexts and adapt them for younger students. That is, pedagogical praxis suggests that the practices through which professionals are trained can provide constructive models for helping students learn from participation in personally relevant projects using computational microworlds. In the discussion that follows, my goal is to use Escher’s World as an occasion to examine some of the mechanisms that underlie learning through pedagogical praxis. My intent is not to prove that Escher’s World was a ‘successful intervention.’ It would hardly come as a surprise that students would learn some mathematics after participating in 56 hours of design activity in a mathematical microworld, and previous work (Shaffer, 1997b, 1997c, 2002b) has already shown that students can and do learn mathematics through microworld-based design activities similar to those in Escher’s World. Rather, my aim here is to uncover some of the processes through which middle school students developed mathematical understanding in a computational microworld while engaging in activities based on the practices through which designers are trained. I focus particularly on the interactions among three precursors to the development of mathematical understanding in Escher’s World: (a) enactment of specific participant frameworks from the design studio, (b) the autoexpressive properties of the computational tool being used, and (c) the articulation and transformation of students’ own interests through their design work.