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Mathematical Habits Of Mind, Kien H. Lim, Annie Selden
Mathematical Habits Of Mind, Kien H. Lim, Annie Selden
Kien H Lim
The idea of “mathematical habits of mind” has been introduced to emphasize the need to help students think about mathematics “the way mathematicians do.” There seems to be considerable interest among mathematics educators and mathematicians in helping students develop mathematical habits of mind. The objectives of this working group are: (a) to discuss various views and aspects of mathematical habits of mind, (b) to explore avenues for research, (c) to encourage research collaborations, and (d) to interest doctoral students in this topic. To facilitate the discussion during the working group meetings, we provide an overview of mathematical habits of mind, …
Improving Students’ Algebraic Thinking: The Case Of Talia, Kien H. Lim
Improving Students’ Algebraic Thinking: The Case Of Talia, Kien H. Lim
Kien H Lim
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.
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 …