Improving students’ algebraic thinking: The case of Talia
This paper presents the case of an 11th grader, Talia, who demonstrated improvement in her algebraic thinking after five one-hour sessions of solving problems involving inequalities and equations. She improved from association-based to coordination-based predictions, from impulsive to analytic anticipations, and from inequality-as-a-signal-for-a-procedure to inequality-as-a-comparison-of-functions conceptions. In the one-on-one teaching intervention, she progressed from the sub-context of manipulating symbols, to working with specific numbers, to reasoning with “general” numbers, and eventually to reasoning with symbols. Three features were identified to account for her improvement: (a) attention to meaning, (b) opportunity to repeat similar reasoning, and (c) opportunity to explore.
Kien H. Lim. "Improving students’ algebraic thinking: The case of Talia" Proceedings of the Thirty-first Conference of the International Group for the Psychology of Mathematics Education. Seoul, Korea. Jul. 2007.
Available at: http://works.bepress.com/kien_lim/2