Science and Mathematics Education Commons^™

Connecting Confidence To College Mathematics And High School Ability Tracks, Kaleb Wourms

Honors Projects

Ability tracking within mathematics education is commonplace in American high schools. Some feel that students’ ability tracks act as a predictor for their success in university mathematics. Research has shown that many factors, such as socioeconomic status and more, have substantial effects on student success. The purpose of this study was to further investigate variables related to success in university mathematics. Confidence in mathematics is one factor in student performance that is particularly under-researched. This research investigated the relationship between ability tracking in high school mathematics, student confidence level, and performance in university mathematics. Data was gathered via a survey. …

Mathematics Teacher Developers’ Views Of A Demonstration Class, Ginger Rhodes, Allyson Hallman-Thrasher, Kyle T. Schultz

Education Faculty Articles

This article examines the professional vision of mathematics teacher developers during a professional development experience that featured observations of a content course for elementary teachers. The researchers examined whether these mathematics teacher developers viewed the demonstration class as an analysis class, a site for reflection and analysis, or a model class, an example of teaching to be emulated. Results indicated participants could hold either view and, in some cases, both. Each view provided opportunities for professional growth, but particular aspects of the experience promoted an analysis class view.

We Would If We Could: Examining Culturally Responsive Teaching Self-Efficacy In A Middle School Mathematics Methods Course, Jamaal R. Young, Jemimah L. Young, Brandon L. Fox, Earl R. Levingston Jr., Alana Tholen

Northwest Journal of Teacher Education

Despite mounting evidence of the pedagogical importance of culturally responsive teaching, many teachers do not implement culturally responsive practices in their classrooms. The purpose of this study was to investigate pre-service mathematics teachers’ culturally responsive teaching and outcome expectancy in order to inform teacher preparation in mathematics methods courses. Participants completed the Culturally Responsive Teaching Self-efficacy Scale (CRTSE) and the Culturally Response Teaching Outcome Expectancy (CRTOE) Scale. Results suggest that middle school mathematics teachers were only moderately efficacious in their ability to implement culturally responsive teaching practices, despite strong beliefs in the instructional utility of culturally responsive teaching practices.

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.

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.

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 …

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

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 …