Copyright (c) 2009 All rights reserved. http://works.bepress.com/kien_lim Recent documents in Kien H Lim en-us Sun, 08 Nov 2009 22:05:46 PST 3600 http://works.bepress.com/kien_lim/14 http://works.bepress.com/kien_lim/14 Mon, 21 Sep 2009 13:59:46 PDT This paper reports an ongoing study that is aimed at developing an instrument for measuring two particular problem-solving dispositions: (a) impulsive disposition refers to students' proclivity to spontaneously proceed with an action that comes to mind, and (b) analytic disposition refers to the tendency to analyze the problem situation. The instrument is under development and consists of likelihood-to-act items in which participants indicate on a scale of 1 to 5 how likely they are to take a particular action in a given situation. The instrument was administered to 318 college students, mainly pre-service teachers. Statistical analysis indicates that likelihood-to-act items are reliable and that the current version of the instrument has room for further improvement. Kien H. Lim http://works.bepress.com/kien_lim/13 http://works.bepress.com/kien_lim/13 Thu, 04 Jun 2009 09:09:24 PDT 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, including concepts that are closely related to habits of mind--ways of thinking, mathematical practices, knowing-to act in the moment, cognitive disposition, and behavioral schemas. We invite mathematics educators who are interested in habits of mind, and especially those who have conducted research related to habits of mind, to share their work during the first working group meeting. If you would like to give a 10-minute presentation, please contact Kien Lim or Annie Selden in advance. Kien H. Lim Mathematics Education http://works.bepress.com/kien_lim/12 http://works.bepress.com/kien_lim/12 Tue, 24 Mar 2009 18:20:04 PDT According to Harel's Necessity Principle (1998) "students are most likely to learn when they see a need for what we intend to teach them, where by need is meant intellectual need, not social or economic need" (p. 501). Intellectual need for a particular mathematical concept is an internal drive experienced by a learner to solve a problem. In this paper, I discuss how tasks can be designed to provoke the intellectual need for two mathematical ideas, prime factorization and lowest common multiple. Kien H. Lim Mathematics Education http://works.bepress.com/kien_lim/11 http://works.bepress.com/kien_lim/11 Tue, 24 Mar 2009 17:59:52 PDT In learning proportions students must understand what makes a situation proportional. If all the missing-value problems encountered by middle-school students involve proportional situations, then there is no need for students to check the equivalence of the two ratios in the proportion they set up. The use of non-proportional situations presents a need for students to analyze the problem situation, determine the manner in which quantities co-vary, and identify the relationship that is invariant. Kien H. Lim Mathematics Education http://works.bepress.com/kien_lim/9 http://works.bepress.com/kien_lim/9 Fri, 09 Jan 2009 00:52:15 PST Cuoco, Goldenberg, and Mark advocate habits of mind as an organizing principle for a mathematics curriculum where students learn to be "pattern sniffers, experimenters, describers, tinkerers, inventors, visualizers, conjecturers, and guessers." Harel regards habits of mind as interiorized ways of thinking--conceptual tools that are necessary for constructing mathematical objects. Presenters for this session offer various perspectives and strategies for helping students develop mathematical habits of mind, including examples from different content areas and at different levels. Kien H. Lim Series of Presentations on Mathematical Habits of Mind http://works.bepress.com/kien_lim/8 http://works.bepress.com/kien_lim/8 Fri, 02 Jan 2009 16:25:41 PST 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. Examples are presented to illustrate how mathematical tasks can be designed to accomplish certain learning and teaching objectives, such as provoking the need for students to learn a particular concept, promoting desirable ways of thinking, deterring undesirable ways of thinking, and assessing students' conceptual understanding. Kien H. Lim Mathematics Education http://works.bepress.com/kien_lim/7 http://works.bepress.com/kien_lim/7 Thu, 15 May 2008 00:46:51 PDT This presentation highlights Harel's notion of ways of thinking and its importance to learning mathematics. Kien H. Lim Mathematics Education http://works.bepress.com/kien_lim/5 http://works.bepress.com/kien_lim/5 Thu, 20 Mar 2008 11:06:32 PDT A Project NeXT panel on "Helping Students Develop Mathematical Habits of Mind without Compromising Key Concepts from the Syllabus" was held at the San Diego Joint Mathematics Meetings 2008. This article summarizes the main points presented by four panelists: Al Cuoco, Harel Guershon, Hyman Bass, and Annie Selden. Selden Annie Mathematics Education http://works.bepress.com/kien_lim/4 http://works.bepress.com/kien_lim/4 Tue, 23 Oct 2007 16:09:07 PDT The role of prediction in the teaching and learning of mathematics has not received much attention in the field of mathematics education. In this paper three reasons for conducting research related to use of prediction in mathematics classrooms are discussed: students' prediction can reveal their conception, prediction plays an important role in reasoning, and prediction facilitates mathematical learning. Three perspectives on prediction are offered as an initial framework for research on prediction: prediction as a mathematical task, prediction as a mental act, and prediction as a social practice. A discussion group is formed to provide an avenue for researchers who are interested in the role of prediction in teaching and learning mathematics to exchange perspectives, discuss theoretical and methodological issues, identify potential areas of research, and consequently form collaborative teams. Kien H. Lim Mathematics Education http://works.bepress.com/kien_lim/3 http://works.bepress.com/kien_lim/3 Tue, 23 Oct 2007 16:09:06 PDT 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.http://www.pmena.org/2006/cd/ALGEBRAIC%20THINKING/ALGEBRAIC%20THINKING-0002.pdf Kien H. Lim Mathematics Education