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Characterizing Students’ Thinking: Algebraic Inequalities And Equations, Kien H. Lim
Characterizing Students’ Thinking: Algebraic Inequalities And Equations, Kien H. Lim
Kien H Lim
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 …
Students’ Mental Acts Of Anticipating In Solving Problems Involving Algebraic Inequalities And Equations, Kien Hwa Lim
Students’ Mental Acts Of Anticipating In Solving Problems Involving Algebraic Inequalities And Equations, Kien Hwa Lim
Kien H Lim
Anticipating is the mental act of conceiving a certain expectation without performing a sequence of detailed operations to arrive at the expectation. This dissertation seeks to characterize students’ problem-solving in terms of two types of anticipating acts: (a) foreseeing an action, which refers to the act of conceiving an expectation that leads to an action, prior to performing the operations associated with the action, and (b) predicting a result, which refers to the act of conceiving an expectation for the result of an event without actually performing the operations associated with the event. Harel’s (in press) triad of determinants—mental act, …