In P. A. Kirschner, F. Prins, V. Jonker & G. Kanselaar (Eds.), Proceedings of the Eighth International Conference of the Learning Sciences—International Perspectives in the Learning Sciences: Cre8ing a Learning World (ICLS2008) (Vol. 1, pp. 27-34). Utrecht, The Netherlands: ISLS.
Reflecting on analyses of data from our respective design-based research studies of mathematical cognition and learning, we propose the utility of the instrumental genesis model (Vérillon & Rabadel, 1995) for examining students’ engagement with designed learning artifacts. The model has helped each of us to account for gaps between intended and enacted sequences in relation to these artifacts. In particular, instrumental genesis provides a mechanism for differentiating between the designer’s arc of intentionality and the student’s learning trajectory, two vectors that may be tacitly aligned for historically evolved learning materials but at variance for recently created materials. Characteristic of our case studies—a networked-classroom design for functions and a mixed-media design for probability—are breakdowns in which students’ behavior deviated either from the designer’s intention or from classic models of constructivist design. In both cases, the breakdowns were valuable in that they occasioned refinement of our theories and designs.