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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 …

Impulsive-Analytic Disposition: Instrument Pilot Testing, Kien H. Lim, Osvaldo F. Morera

Kien H Lim

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 …

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 …

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. In the Proceedings of PME-NA 31, we provided an overview of …

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, …

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

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

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

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 …

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, …