Engendering multiplicative reasoning in students with learning disabilities in mathematics: Sam's computer-assisted transition to anticipatory unit differentiation-and-selection
We examined how a student with learning disabilities (SLD) in mathematics constructed a scheme for differentiating, selecting, and properly operating on/with units that constitute a multiplicative situation, namely, singletons (‘1s’) and composite units (abbreviated UDS). Conducted as part of a larger teaching experiment in a learning environment that synergizes human and computer-assisted teaching, this study included 12 videotaped teaching episodes with a 5th grader (pseudonym-Sam), analyzed qualitatively. Our data provide a window onto the conceptual transformation involved in advancing from absence, through a participatory, to an anticipatory stage of a UDS scheme—a cognitive root for the distributive property. We postulate this scheme as a fundamental step in SLDs’ learning to reason multiplicatively, and highlight the transfer-empowering nature of constructing it at the anticipatory stage.
McClintock, E., Tzur, R., Xin, Y. P., & Si, L. (2011). Engendering multiplicative reasoning in students with learning disabilities in mathematics: Sam's computer-assisted transition to anticipatory unit differentiation-and-selection. In L. R. Wiest & T. D. Lamberg (Eds.), Proceedings of the 33rd annual meeting of the North American chapter of the International Group for the Psychology of Mathematics Education (pp. 164-172). Reno, NV: University of Nevada, Reno.