Characterizing students’ thinking: Algebraic inequalities and equations
This paper presents the findings of a study that explores the viability of using students’ act of anticipating as a means to characterize the way students think while solving problems in algebra. Two types of anticipating acts were identified: predicting a result and foreseeing an action. These acts were characterized using Harel’s framework, which involves the concepts of mental act, way of understanding, and way of thinking. Categories for characterizing acts of predicting and foreseeing were identified and developed based on thirteen 11th graders’ responses to problems involving algebraic inequalities and equations. The quality of students’ acts of predicting and foreseeing was found to be related to the quality of their interpretations of inequalities and equations.
Kien H. Lim. "Characterizing students’ thinking: Algebraic inequalities and equations" Proceedings of the Twenty-eight Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Merida, Mexico. Nov. 2006.
Available at: http://works.bepress.com/kien_lim/3