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Full-Text Articles in Education
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, …
Advancing Pre-Service Teachers’ Mathematical Sophistication Via Mathematical Tasks, Kien H. Lim
Advancing Pre-Service Teachers’ Mathematical Sophistication Via Mathematical Tasks, Kien H. Lim
Kien H Lim
This article is based on the seminar that the author presented for the Hong Kong Association for Mathematics Education at the Hong Kong Baptist University on May 22, 2008. In this article, the author differentiates (a) between institutionalized mathematics and school mathematics, (b) between ways of understanding and ways of thinking as two complementary subsets of mathematics that students should develop, (c) between sophisticated learners and passive learners, and (d) between knowledge dissemination and knowledge engagement as two modes of instructions. Harel’s (2007) pedagogical principles are discussed in relation to the design of mathematical tasks and their use in classrooms. …
Mathematical Knowledge For Pre-Service Teachers, Kien H. Lim
Mathematical Knowledge For Pre-Service Teachers, Kien H. Lim
Kien H Lim
This presentation highlights Harel's notion of ways of thinking and its importance to learning mathematics. Examples of students' deficient ways of thinking are offered, categories of mathematical knowledge for teaching mathematics are presented, and relationships among ways of thinking, ways of understanding, and pedagogical content knowledge are discussed.
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 …
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, …