This paper reports on a research project that investigated the effects of a flipped instructional approach on student attitudes and achievement in a lower division university-level Finite Mathematics course. The project employed a mixed-methods design that included content exams, an attitude survey, open-ended student responses, observations, and…

To further understand student thinking in the context of combinatorial enumeration, we examine student work on a problem involving set partitions. In this context, we note some key features of the multiplication principle that were often not attended to by students. We also share a productive way of thinking that emerged for several students who…

Mathematicians use example generation to test and verify mathematical ideas; however, the processes through which undergraduates learn to productively generate examples are not well understood. We engaged calculus students in a teaching experiment designed to develop skills in productively generating examples to learn novel concepts. This article…

Flipping the classroom refers to moving lectures outside of the classroom to incorporate other activities into a class during its standard meeting time. This pedagogical modality has recently gained traction as a way to center the learning on students in mathematics classrooms. In an effort to better understand the efficacy of this approach, we…

The flipped classroom approach was implemented across three semesters of a College Algebra course. This paper is part of a larger design and development research study and focuses on student perceptions of the flipped classroom teaching approach. Qualitative methodology was used to describe how students perceived the instruction of their College…

Equivalence relations and partitions are two interconnected ideas that play important roles in advanced mathematics. While students encounter the informal notion of equivalence in many courses, the formal definition of an equivalence relation is typically introduced in a junior level transition-to-proof course. This paper reports the results of a…

In this paper, we share the results of our recent study of a quantitative literacy course with a service-learning component. Our study aims to answer the question: How did student attitudes shift as a result of participating in this course? We present and analyze statistics from pre- and post-surveys in five classes (N = 78) taught by two…

Reviewing numerous textbooks, we found that in both differential and integral calculus textbooks the authors commonly assume that: (i) students can generalize associations between representations in two dimensions to associations between representations of the same mathematical concept in three dimensions on their own; and (ii) explicit…

This article describes the initial development of a qualitative system dynamics model as part of the periodic review of a mathematics course. In an effort to enhance the learning experience of undergraduate computing students (for whom the course is a compulsory part of their curriculum) a small sample of students were interviewed regarding their…

This article examines the transition process of 14 international teaching assistants (TAs), who teach mathematics courses in U.S. college contexts. In particular, this study documents several major aspects of changes in their teaching, including their curriculum choice and instructional practices over time. This study reveals how the institutional…

This paper presents an assessment tool which can be used during the first weeks of calculus to measure students' visual thinking skills. We have developed and applied this instrument in classes for the last three years, tabulating results and interviewing students on a regular basis. We discuss our findings and provide hints to using the…