Gutiérrez, J. F. (2010). “I don’t know—I’m just genius!”: Distinguishing between the process and the product of student algebraic reasoning. 

In K. Gomez, L. Lyons, & J. Radinsky (Eds.), Learning in the Disciplines: Proceedings of (ICLS 2010) (Vol. 1 [Full Papers], pp. 905-912). University of Illinois at Chicago: International Society of the Learning Sciences: Chicago, IL.

This paper reports on a semiotic-cultural analysis of two high-school minority seniors’ participation in a mathematics instructional intervention conducted at a school for academically at-risk students. Focusing on the students’ speech acts, gestures, and artifact production during their successful collaborative engagement in an algebraic pattern-finding task, I adopt and adapt Radford’s (2003) framework to evaluate the quality of each student’s actual learning as implicated by their discursive contributions. By analyzing each student’s utterances as either “to” a semiotic mode (generalization) or just “in” the mode, and then overlaying these coded utterances, I show how one student’s participation, which appears to mark a developing algebraic command, in fact blinds the teachers to underlying discontinuity in the student’s meaning construction. The study illuminates critical tradeoffs in the design and facilitation of collaborative problem solving.

Gutierrez_JF_ICLS2010.pdf