Kien H Lim Copyright (c) 2011 All rights reserved. http://works.bepress.com/kien_lim Recent documents in Kien H Lim en-us Sun, 04 Sep 2011 01:47:23 PDT 3600 Planting the seeds of computational thinking: An introduction to programminsuitable for inclusion in STEM curriculag http://works.bepress.com/kien_lim/24 http://works.bepress.com/kien_lim/24 Fri, 02 Sep 2011 15:13:18 PDT Inadequate math preparation discourages many capable students – especially those from traditionally underrepresented groups – from pursuing or succeeding in STEM academic programs. iMPaCT is a family of―"Media Propelled" courses and course enrichment activities that introduce students to―"Computational Thinking." iMPaCT integrates exploration of math and programmed computation by engaging students in the design and modification of tiny programs that render raster graphics and simulate familiar kinematics. Through these exercises, students gain experience and confidence with foundational math concepts necessary for success in STEM studies, and an understanding of programmed computation.

This paper presents early results from our formal evaluation of semester-length iMPaCT courses indicating improved academic success in concurrently and subsequently attended math courses. They also indicate changes to the nature of student engagement with problem solving using mathematics.

This paper also describes iMPaCT-STEM, a nascent effort of computer science and mathematics faculty to distill iMPaCT’s pedagogy into sequences of short learning activities designed to teach and reinforce a variety of mathematical and kinematic concepts that can be directly integrated into math and science courses.

]]> Eric A. Freudenthal et al. Impulsive-Analytic Disposition: Instrument Pilot Testing http://works.bepress.com/kien_lim/23 http://works.bepress.com/kien_lim/23 Sat, 14 May 2011 20:51:34 PDT The likelihood-to-act (LtA) survey measures impulsive and analytic dispositions in solving mathematics problems. The current version has 16 impulsive and 16 analytic items. Its validity was assessed using a sample of 27 in-service and 92 pre-service teachers. Both the impulsive and analytic subscales were found to have internal consistency reliability, but they were not correlated with one another. The impulsive subscale was predictive of correctness in classifying the LtA items. The analytic subscale was predictive of how well a participant would perform in Part 2 of a math test after taking Part 1 and being warned that some items could be tricky.

]]> Kien H. Lim et al. Mathematics Education Continuing Discussion of Mathematical Habits of Mind http://works.bepress.com/kien_lim/22 http://works.bepress.com/kien_lim/22 Mon, 29 Nov 2010 20:57:09 PST 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 continue the discussion of various views and aspects of mathematical habits of mind begun at PME-NA 31, (b) to explore avenues for research, (c) to encourage research collaborations, and (d) to interest doctoral students in this topic. In the Proceedings of PME-NA 31, we provided 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. Below we provide a summary of the discussions held at PME-NA 31. We invite returning participants, as well as other mathematics educators who are interested in mathematical habits of mind, especially those who have conducted research related to habits of mind, to our discussions.

]]> Annie Selden et al. Inferring Impulsive-analytic Disposition from Written Responses http://works.bepress.com/kien_lim/21 http://works.bepress.com/kien_lim/21 Mon, 29 Nov 2010 20:50:35 PST Impulsive disposition refers to one’s proclivity to spontaneously proceed with an action that comes to mind without checking its relevance. Analytic disposition refers to one’s proclivity to analyze a problem situation and establishes a goal to guide one’s actions. An instrument, called the likelihood-to-act survey, was developed to measure students’ impulsive-analytic disposition. In this study, we sought to test and refine this instrument by analyzing 92 participants’ written responses to open-ended questions that were adapted from items in the likelihood-to-act survey. We found relatively strong correlations between participants’ disposition scores for written responses and those from the likelihood-to-act survey.

]]> Kien H. Lim et al. The role of prediction in the teaching and learning of mathematics http://works.bepress.com/kien_lim/20 http://works.bepress.com/kien_lim/20 Tue, 13 Jul 2010 13:33:34 PDT The prevalence of prediction in grade-level expectations in mathematics curriculum standards signifies the importance of the role prediction plays in the teaching and learning of mathematics. In this article, we discuss benefits of using prediction in mathematics classrooms: (1) students’ prediction can reveal their conceptions, (2) prediction plays an important role in reasoning and (3) prediction fosters mathematical learning. To support research on prediction in the context of mathematics education, we present three perspectives on prediction: (1) prediction as a mental act highlights the cognitive aspect and the conceptual basis of one’s prediction, (2) prediction as a mathematical activity highlights the spectrum of prediction tasks that are common in mathematics curricula and (3) prediction as a socio-epistemological practice highlights the construction of mathematical knowledge in classrooms. Each perspective supports the claim that prediction when used effectively can foster mathematical learning. Considerations for supporting the use of prediction in mathematics classrooms are offered.

]]> Kien H. Lim et al. Mathematics Education A Collection of Lists of Mathematical Habits of Mind http://works.bepress.com/kien_lim/19 http://works.bepress.com/kien_lim/19 Sat, 05 Jun 2010 13:09:46 PDT Mathematical habits of mind and general habits of mind have been identified in the field by various authors such as Al Cuoco and colleagues, Driscoll and colleagues, and Costa and colleagues. Different list of habits of mind that are relevant to teaching and learning of mathematics education are compiled.

]]> Kien H. Lim Mathematics Education Addressing Impulsive Disposition: Using Non-proportional Problems to Overcome Overgeneralization of Proportionality http://works.bepress.com/kien_lim/18 http://works.bepress.com/kien_lim/18 Mon, 31 May 2010 18:10:40 PDT Impulsive disposition is an undesirable way of thinking where one spontaneously applies the first idea that comes to mind without checking its relevance. In this research, we explore (a) the possibility of helping pre-service teachers improve their disposition, from being impulsive to being analytic, in one semester, and (b) the effect of using non-proportional situations. This study involves two sections of a mathematics course for pre-service teachers for Grades 4-8. The lessons were designed whenever possible to elicit students’ impulsive disposition so that they could become cognizant of it and make conscious attempts to overcome it. Some test items were designed to be superficially similar but structurally different to those they had experienced in class or homework. Pre-post-end test results show that pre-service teachers’ tendency to overuse ratios and proportions can be reduced in one semester and that the use of non-proportional problems can minimize impulsive responses.

]]> Kien H. Lim et al. Mathematics Education Mathematical Habits of Mind: A Working Group at the 2009 PME-NA Conference http://works.bepress.com/kien_lim/16 http://works.bepress.com/kien_lim/16 Fri, 12 Mar 2010 10:57:10 PST 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 et al. Series of Presentations on Mathematical Habits of Mind 通过数学任务提高美国职前教师的数学成熟性 (Advancing pre-service teachers’ mathematical sophistication via mathematical tasks) http://works.bepress.com/kien_lim/15 http://works.bepress.com/kien_lim/15 Tue, 15 Dec 2009 17:06:54 PST 2008年5月22日，香港数学教育学会在香港浸会大学举行了研讨会。本文以该研讨会上的发言为蓝本，区分了以下四种差异：（1）约定俗成的数学与学校数学之间的差异；（2）理解方式与思维方式之间的差异；（3）成熟的学习者与被动的学习者之间的差异；（4）知识传授与知识参与这两种教学模式之间的差异。文章还讨论了Harel提出的教学原则以及数学任务的设计与它们在课堂中的使用，并呈现了具体的案例来说明如何设计数学任务以实现特定的学习与教学目标，如激发学生学习某一特定概念的需要，促进理想的思维方式，阻止不合适的思维方式以及评估学生的概念性理解。

]]> Kien H. Lim et al. Assessing Problem-Solving Dispositions: Likelihood-To-Act Survey 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 et al. Mathematical Habits of Mind 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.

]]> Kien H. Lim et al. Mathematics Education Provoking Intellectual Need 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 Burning the candle at just one end: Using nonproportional examples helps students determine when proportional strategies apply 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 Helping Students Develop Mathematical Habits of Mind: A Joint Panel Session at the 2009 JMM Conference 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 et al. Series of Presentations on Mathematical Habits of Mind Advancing pre-service teachers’ mathematical sophistication via mathematical tasks 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. A Chinese version of this paper (通过数学任务提高美国职前教师的数学成熟性) is published in the Journal of Mathematics Education.

]]> Kien H. Lim Mathematics Education Mathematical Knowledge for Pre-service Teachers 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. 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.

]]> Kien H. Lim Mathematics Education Developing Mathematical Habits of Mind 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 et al. Mathematics Education Characterizing Students’ Thinking: Algebraic Inequalities and Equations 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 Improving Students’ Algebraic Thinking: The Case of Talia http://works.bepress.com/kien_lim/2 http://works.bepress.com/kien_lim/2 Tue, 23 Oct 2007 16:09:05 PDT 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.

]]> Kien H. Lim Mathematics Education Students’ Mental Acts of Anticipating in Solving Problems involving Algebraic Inequalities and Equations http://works.bepress.com/kien_lim/1 http://works.bepress.com/kien_lim/1 Wed, 10 Oct 2007 15:32:49 PDT
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, ways of understanding, and ways of thinking—is used to analyze students’ acts of foreseeing and predicting.

This research has three objectives: (a) to categorize students’ ways of thinking associated with foreseeing and predicting, (b) to identify the relationships between these ways of thinking and students’ ways of understanding inequalities/equations, and (c) to explore the potential for advancing students’ ways of thinking associated with foreseeing/predicting. To accomplish these goals, fourteen 11th graders enrolled in various mathematics courses were interviewed. Four of them participated in one-on-one teaching interventions. Non-directive tasks were used to elicit students’ anticipatory behaviors.

In this study, five ways of thinking associated with foreseeing were identified: impulsive anticipation, tenacious anticipation, explorative anticipation, analytic anticipation, and interiorized anticipation. Three ways of thinking associated with predicting were identified: association-based prediction, comparison-based prediction, and coordination-based prediction. In addition, five ways of understanding inequalities/equations (I/E) were identified: I/E-as-a-signal-for-procedure, I/E-as-a-static-comparison, I/E-as-a-proposition, I/E-as-a-constraint, and I/E-as-a-comparison-of-functions. Students’ ways of thinking associated with foreseeing/predicting were found to be related to the quality of their solutions as well as the sophistication of their ways of understanding inequalities/equations.

One learner’s improvement was summarized in terms of the change in the sub context (Cobb, 1985) in which she operated, from manipulating symbols in the pre interview to reasoning with symbols in the post-interview. Her operating in the sub-context of working with numbers helped her to achieve this transition. This finding underscores the importance of using numbers as a platform for algebra students to explore algebraic expressions and symbolic structures.

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