Education Commons^™

Preparing Teachers To Apply Research To Mathematics Teaching: Using Design-Based Research To Define And Assess The Process Of Evidence-Based Practice, Sarah Van Ingen

Sarah van Ingen

Persistent lack of mathematics achievement and disparity in achievement has led to the publication of research findings related to equitable teaching practices. Although the publication of such research provides insights about approaches for potentially increasing equity in mathematics education, teachers must be able to apply what has been learned from these studies to their classroom teaching practices. Despite the widespread expectation that teachers use research-supported teaching strategies to meet the needs of their diverse classrooms, the research to practice gap persists. Little research is currently available to guide mathematics teacher educators in how to prepare future teachers to apply research …

Are There Any Winners In High-Stakes Testing? A Qualitative Case Study Exploring Student, Parent And Teacher Attitudes Towards Naplan Numeracy Tests In Years 3 And 5, Gregory S. C. Hine

Gregory S.C. Hine

A Mathematical Perspective On Educational Research

Cathy Kessel

No abstract provided.

Experiences Of Adults With Developmental Disability And Teacher In An Applied Mathematics Based Money Club., Anthony M. Rodriguez

Anthony M. Rodriguez

This study investigates the experiences of young adults with developmental disability and their math teacher. Together, they explore mathematics, finance, and self within a six week program of instruction titled the Money Club. This includes how adults with developmental disability reason, apply, perceive, and solve applied mathematics problems in finance.

"I'Ve Come Too Far, I'Ve Worked Too Hard!": Reinforcement Of Support Structures Among Black Male Mathematics Students, Clarence L. Terry Sr, Ebony O. Mcgee

Clarence "La Mont" Terry, Sr.

Along with the growth and refinement of our shared discourses on equity, the community of education researchers focused on Black males has developed lenses with which to examine the risk and protective factors related to Black males’ participation in and experiences with mathematics. In this paper, the authors focus on the importance of the “supports” associated with mathematically high-­achieving Black high school students in urban high schools. Using Critical Race Theory and narrative analysis, the authors report findings from semi-structured interviews of mathematically-successful Black male students (n = 12) from four urban high schools. Analysis of key themes suggests that …

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 …

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, …

Provoking Intellectual Need

Kien H Lim

The Awm-Nsf Mathematics Education Research Travel Grants, Cathy Kessel

Cathy Kessel

No abstract provided.

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, …

Teaching Mathematical Problem Solving: An Analysis Of An Emergent Classroom Community, A. Arcavi, C. Kessel, L. Meira, J. Smith

Cathy Kessel

No abstract provided.