Lee, R. G., Hung, M., Negrete, A. G., & Abrahamson, D. (2013). Rationale for a ratio-based conceptualization of slope: Results from a design-oriented embodied-cognition domain analysis. 

Paper presented at the annual meeting of the American Educational Research Association (Special Interest Group on Research in Mathematics Education), San Francisco, April 27 – May 1.

We report encouraging results from the Planning Phase of a co-participatory design-based research project that brings together researchers and teachers interested in incorporating educational technology into high school mathematics classrooms. The following two ideas, which were pivotal to aligning our perspectives, co-emerged in our discourse following curricular reviews and cognitive domain analyses that specifically investigated the potential role of proportional reasoning in learning algebra content: (a) product-based conceptualization of proportional equivalence is pedagogically advantageous over process-based conceptualization; and (b) ratio-based conceptualization of slope is pedagogically advantageous over rate-based conceptualization. We detail findings from our collaborative reflection process and outline principles for the Design Phase, during which our embodied-interaction systems will be further developed to incorporate a product-based conceptualization of slope.