I present a unit on voting theory and social choice taught as the beginning of a liberal arts mathematics course for undergraduates. In this unit, students voted on the final grade calculation formula and topics to cover during the semester and then analyzed the results using various voting systems. I believe that by allowing my students to…

Undergraduate students who have just completed an introductory statistics course often lack deep understanding of variability and enthusiasm for the field of statistics. This paper argues that by introducing the commonly underemphasized concept of measurement error, students will have a better chance of attaining both. We further present lecture…

Debates about how undergraduate mathematics should be taught are informed by different views of what it is to learn and to do mathematics. In this qualitative study 10 students enrolled in an advanced undergraduate course in mathematics shared their views about how they best learn mathematics. After participating in a semester-long course in…

This article reports on techniques of teaching abstract algebra which were developed to achieve multiple student objectives: reasoning and communication skills, deep content knowledge, student engagement, independence, and pride. The approach developed included a complementary combination of inquiry-based learning, individual (not group) homework…

This paper reports on the experience of STEM and mathematics faculty at four different institutions working collaboratively to integrate learning theory with curriculum development in a core undergraduate linear algebra context. The faculty formed a Professional Learning Community (PLC) with a focus on learning theories in mathematics and…

Two first-year engineering mathematics courses used computer-aided assessment (CAA) to provide students with opportunities for formative assessment via a series of weekly quizzes. Most students used the assessment until they achieved very high (>90%) quiz scores. Although there is a positive correlation between these quiz marks and the final…

We surveyed fifty leading undergraduate business schools concerning their statistics requirements. We report on many aspects including credit-hours required, topics covered, computer integration, faculty background, teaching pedagogy, textbooks, and recent and proposed changes. (Contains 8 tables.)

There is general agreement in Australia and beyond that quantitative skills (QS) in science, the ability to use mathematics and statistics in context, are important for science. QS in the life sciences are becoming ever more important as these sciences become more quantitative. Consequently, undergraduates studying the life sciences require better…

The processes of learning mathematics are immensely complex and we largely lack insights into these processes. This is especially problematic when it comes to tertiary mathematics education, which has been much less researched than primary and secondary mathematics education. It is thus far from possible to clarify all relevant issues related to…

This paper reports a teaching experiment in which two students engaged in tasks that challenged them to describe a final state for a variety of infinite iterative processes. The results from the study indicate that the students used multiple reasoning strategies for addressing these tasks. Refinements in the students' reasoning occurred as…

Slow faculty uptake of research-based, student-centered teaching and learning approaches limits the advancement of U.S. undergraduate mathematics education. A study of inquiry-based learning (IBL) as implemented in over 100 course sections at 4 universities provides an example of such multicourse, multi-institution uptake. Despite variation in how…

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…

The purposes of this study were to investigate (a) undergraduate students' reasoning about the concepts of confidence intervals (b) undergraduate students' interactions with "well-designed" screencast videos on sampling distributions and confidence intervals, and (c) how screencast videos improve undergraduate students' reasoning ability…

As student-centered approaches to teaching and learning are more widely applied, researchers must assess the outcomes of these interventions across a range of courses and institutions. As an example of such assessment, this study examined the impact of inquiry-based learning (IBL) in college mathematics on undergraduates' subsequent grades…

The Mat-Rix-Toe project utilizes a matrix-based game to deepen students' understanding of linear algebra concepts and strengthen students' ability to express themselves mathematically. The project was administered in three classes using slightly different approaches, each of which included some editing component to encourage the…