Kien Lim

University of Texas at El Paso | UTEP · Department of Mathematical Sciences

The editorial staff of JHM works hard to make sure the scholarship disseminated in JHM is accurate and upholds professional ethical guidelines. However the views and opinions expressed in each published manuscript belong exclusively to the individual contributor(s). The publisher and the editors do not endorse or accept responsibility for them. Syn...

Two equations are presented in this article to communicate a particular understanding of karma. The first equation relates future experiences to past and present actions. Although the equation uses variables and mathematical symbols such as the integral sign and summation symbol, it reads more like a literal translation of an English sentence. Base...

The hammer-and-nail phenomenon highlights human tendency to approach a problem using a tool with which one is familiar instead of analyzing the problem. Pedagogical suggestions are offered to help students minimize their mathematical impulsivity, cultivate an analytic disposition, and develop conceptual understanding.

An exploratory study was conducted to investigate the use of magic activities in a math course for prospective middle-school math teachers. This research report focuses on a lesson using two versions of math magic: (1) the 5-4-3-2-1-½ Magic involves having students choose a secret number and apply six arithmetic operations in sequence to arrive at...

Use math videos and different types of inquiries to increase students' intellectual engagement.

Meaningful context motivates students to appreciate the usefulness of variables, expressions, equations, and symbolic transformations.

We are infusing inquiry-driven programming activities into algebra and physics courses with the objective of strengthening disciplinary understandings and providing all students a meaningful first experience with programming. The majority of students who complete 9th grade algebra fail to connect its syntactic and graphical representations to conce...

Counterintuitive results based on Simpson's paradox generate rich discussions about scoring and weighted averages.

Student errors are springboards for analyzing, reasoning, and justifying. To induce specific errors and help students learn, choose tasks that might produce mistakes.

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。

Algebra I is a gateway course for high school and college STEM. Ninth graders who develop mastery of Algebra I learning outcomes are well prepared to comprehend and succeed in the quantitative STEM courses such as physics. Those who do not are likely to encounter difficulty in subsequent STEM coursework. Our "iMPaCT-Math" activities can potentially...

iMPaCT-Math is an approximate acronym for Media-Propelled Computational Thinking for Mathematics Classrooms, which fairly reflects our ambitions - that engagement with graphical programming challenges that focus student attention towards exploring mathematics principles will propel students towards exploration of science, computational thinking and...

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...

The following is the abstract for the working group, which was a continuation of the one at the 2009 PME-NA Conference. 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 mat...

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 dis...

The following is the abstract for the working group on mathematical habits of mind, which was a continuation of the one conducted the previous year at the 2009 PME-NA Conference. 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...

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 play...

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 dis...

This is the abstract, which is in essence a description of the working group, followed by a call for presentations/participation. 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 docto...

Tasks that generate a need for mathematical intellect generate motivation and promote success in learning mathematics. Some specific tasks and ways to generate new ones are offered.

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...

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 instru...

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...

A Project NeXT panel, “Helping Students Develop Mathematical Habits of Mind without Compromising Key Concepts from the Syllabus,” was organized by Kristin Camenga, Houghton College, and Kien Lim, University of Texas at El Paso, at the San Diego Joint Mathematics Meetings. The panel addressed the tension between teaching all the mathematical concept...

As teachers, we are entrusted to teach the long list of mathematical concepts specified in the syllabus. In addition to the tension between depth and breadth, we need to incorporate into our lessons opportunities for students to develop mathematical thinking, called "habits of mind" by Cuoco, Goldenberg, and Mark and "ways of thinking" by Harel. A...

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 complem...

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...

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...

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.

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 re...

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-pr...

Thesis (Ph. D.)--University of California, San Diego, and San Diego State University, 2006. Includes bibliographical references (leaves 246-256).

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...

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...