This paper explores the viability and development of the first edition of the researcher's mathematical card game, Groups, as a learning tool for elementary group theory, a topic in abstract algebra. "Groups" was play-tested by six undergraduate students in late 2016 who provided feedback on "Groups" from both utility-centric…

This paper explores the ways students perceive the transfer of learned knowledge to new situations -- often a surprisingly difficult prospect. The novel aspect compared to the traditional transfer studies is that the learning phase is not a part of the experiment itself. The intention was only to activate acquired knowledge relevant to the…

This study addresses the problem of mathematics teachers' resistance to problem-solving models that align with constructivist perspectives because they feel pressure to utilize more teaching approaches that focus on preparing students for high-stakes tests. The purpose of this qualitative study was to explain how ninth grade mathematics students…

In order to improve student success within developmental programs, we conducted a study of 1st year students taking required, developmental mathematics courses at a large, urban public university. Findings suggest that merely the number of years of mathematics that students take in high school is not a precise indicator of student readiness and…

The purpose of this study was to discover what teaching strategies were utilized by Special Day Class (SDC) teachers to prepare their 9-12 grade students to pass a course in Algebra 1 and the mathematics section of the California High School Exit Exam (CAHSEE). This study used a mixed methodology involving a quantitative survey and qualitative…

This study investigates the responses to prior knowledge errors that Calculus I instructors make when assessing students. Prior knowledge is operationalized as any skill or understanding that a student needs to successfully navigate through a Calculus I course. A two part qualitative study consisting of student exams and instructor interviews was…

The ability to flexibly solve problems is considered an important outcome for school mathematics and is the focus of this paper. The paper describes the impact of a three-week summer course for students who struggle with algebra. During the course, students regularly compared and contrasted worked examples of algebra problems in order to promote…

This study examined practices of teachers in Wake County Public Schools' (WCPSS) middle school Algebra I classes. Regression analyses of standardized state testing results allowed for identification of the most effective and least effective Algebra I teachers. The study used surveys, observations, and focus group interviews to compare and contrast…