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. Upon seeing a problem, students commonly rush into action without analyzing the problem situation. As teachers, we witness some students ’ inappropriate use of procedures, what Fischbein and Barash (1993) call improper application of algorithmic models. On the other hand, we also witness engagement in exploration and analysis of the problem situation among certain students. This research seeks to characterize the differences in the manner students solve problems involving algebraic inequalities and equations