Education Commons^™

A Collection Of Lists Of Mathematical Habits Of Mind, Kien Lim

Kien H Lim

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.

Assessing Impulsive-Analytic Disposition: The Likelihood-To-Act Survey And Other Instruments, Kien Lim, Amy Wagler

Kien H Lim

The likelihood-to-act (LtA) survey is a 32-item instrument that measures impulsive and analytic dispositions in solving math problems. In this research report, we compare it to other instruments related to the impulsive-analytic construct such as Frederick’s Cognitive Reflection Test (CRT) and the Barratt Impulsive Scale in terms of mean scores, Cronbach alpha values, and correlation values. Both LtA-Impulsive and LtA-Analytic subscales have acceptable reliabilities of 0.79 and 0.83 respectively. The LtA-Analytic and LtA-Difference (analytic-impulsive difference) correlated well with other the Need for Cognition subscale and CRT scores. The correlations involving LtA-Impulsive subscale were unexpected and call for further investigation.

The Hammer-And-Nail Phenomenon In Mathematics Education, Kien Lim

Kien H Lim

"For a person with a hammer, everything looks like a nail" is a proverb that can be used to highlight the phenomenon that students tend to rely on familiar ideas as opposed to taking time to think about and analyse a problem. Presented in this theoretical paper is the usefulness of the hammer-and-nail metaphor, other related theoretical constructs, pedagogical causes of student impulsive behaviours, and pedagogical suggestions for addressing them.

Impulsive-Analytic Disposition In Mathematical Problem Solving: A Survey And A Mathematics Test, Kien H. Lim, Amy Wagler

Kien H Lim

The Likelihood-to-Act (LtA) survey and a mathematics test were used in this study to assess students’ impulsive-analytic disposition in the context of mathematical problem solving. The results obtained from these two instruments were compared to those obtained using two widely-used scales: Need for Cognition (NFC) and Barratt Impulsivity Scale (BIS). The exhibited correlations of the LtA scores with the NFC, BIS, and a math test provide evidence of the criterion validity of the analytic LtA items, and suggests further revision of the impulsive LtA items to improve the overall measurement validity of the LtA scale. Students LtA scores were found …

Planting The Seeds Of Computational Thinking: An Introduction To Programminsuitable For Inclusion In Stem Curriculag, Eric A. Freudenthal, Art Duval, Sarah Hug, Alexandria N. Ogrey, Kien H. Lim, Catherine Tabor, Rebeca Q. Gonzalez, Alan Siegel

Kien H Lim

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 …

Addressing The Multiplication Makes Bigger And Division Makes Smaller Misconceptions Via Prediction And Clickers, Kien Lim

Kien H Lim

This article presents a lesson that uses prediction items, clickers and visuals via PowerPoint slides to help prospective middle-school teachers address two common misconceptions: multiplication makes bigger and division makes smaller (MMB–DMS). Classroom research was conducted to explore the viability of such a lesson. Results show that the lesson was effective in creating awareness that multiplication does not always make bigger and division does not always makes smaller, uncovering students’ misconceptions, and providing opportunities for students to learn from mistakes. Students liked the activity for various reasons, such as getting to learn certain mathematical ideas, to think about the problems, …

Inferring Impulsive-Analytic Disposition From Written Responses, Kien Lim, Miguel Mendoza

Kien H Lim

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.

Continuing Discussion Of Mathematical Habits Of Mind, Annie Selden, Kien H. Lim

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 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.

Continuing Discussion Of Mathematical Habits Of Mind, Annie Selden, Kien H. Lim

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 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 …

The Role Of Prediction In The Teaching And Learning Of Mathematics, Kien Lim, Gabriela Buendía, Ok-Kyeong Kim, Francisco Cordero, Lisa Kasmer

Kien H Lim

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 …

Addressing Impulsive Disposition: Using Non-Proportional Problems To Overcome Overgeneralization Of Proportionality, Kien Lim, Osvaldo Morera

Kien H Lim

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 …

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, …

Mathematical Habits Of Mind: A Working Group At The 2009 Pme-Na Conference, Kien Lim, Annie Selden

Kien H Lim

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 …

Assessing Problem-Solving Dispositions: Likelihood-To-Act Survey, Kien Lim, Osvaldo Morera, Mourat Tchoshanov

Kien H Lim

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 …

Provoking Intellectual Need

Kien H Lim

Burning The Candle At Just One End: Using Nonproportional Examples Helps Students Determine When Proportional Strategies Apply, Kien H. Lim

Kien H Lim

Helping Students Develop Mathematical Habits Of Mind: A Joint Panel Session At The 2009 Jmm Conference, Kien Lim, Kristin Camenga

Kien H Lim

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.

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), Kien Lim, 庞雅丽, 赵锐

Kien H Lim

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。

Developing Mathematical Habits Of Mind, Selden Annie, Kien Lim

Kien H Lim

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.

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

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 …

Mathematics Teachers’ Knowledge Base: Preliminary Results, Guershon Harel, Kien Lim

Kien H Lim

Student learning depends on the teacher’s actions, which are, in turn, dependent on the teacher’s knowledge base—defined here by three components: knowledge of mathematics content, knowledge of student epistemology, and knowledge of pedagogy. The purpose of this study is to construct models for teachers’ knowledge base and for their development in an on-site professional development project.