In the calculus classroom, integrating applications with the theoretical and procedural conveys the relevance of the material. Since Newton and Leibniz developed calculus in the context of physics and astronomy, applications in these fields tend to predominate. To engage and excite our students, pedagogical considerations must include broader…

The goal of this paper is to promote the use of R and Python as high-level, free, open-source programming environments that can be used as a computational and visualization tool for teaching differential equations. Both R and Python also allow for creating reproducible dynamic documents using Markdown, which combines live code, plain text, and…

Income inequality is a central social justice concern, and hence excellent motivation for real-world applications in mathematics classrooms at every level. We describe the "Mathematics for Social Justice" course at Saint Michael's College, giving a specific example of one of the typical social justice projects for the course, and showing…

We describe the design and implementation of lessons in undergraduate abstract algebra that integrate applications to teaching high school mathematics. Each lesson consists of a pre-activity, class activity, homework set, assessment questions and detailed instructor notes. The included applications intend to bridge advanced mathematics concepts to…

We present a question bank consisting of over 250 multiple-choice and true--false questions covering a broad range of material typically taught in an introductory undergraduate course in numerical analysis or computational science. The questions are ideal for polling students during lectures by means of a student response system that uses…

In the context of national collaborative efforts to increase the prevalence of active learning strategies in undergraduate precalculus and calculus classrooms, we discuss the context, strategy, and processes used at one university to create change within a mathematics department. We highlight the use of a unified active learning approach and the…

An interactive open-source calculus textbook is compared to a popular commercial textbook. Structured as a non-inferiority study, use of the open-source textbook does not harm student outcomes, and there is evidence that the open-source textbook is better than the commercial textbook in promoting post-course enjoyment of mathematics and confidence…

In this paper I will outline the process I have developed for conducting applied mathematics research with undergraduates and give some examples of the projects we have worked on. Several of these projects have led to refereed publications that could be used to illustrate topics taught in the undergraduate curriculum.

Rouché's Theorem is a standard topic in undergraduate complex analysis. It is usually covered near the end of the course with applications relating to pure mathematics only (e.g., using it to produce an alternate proof of the Fundamental Theorem of Algebra). The "winding number" provides a geometric interpretation relating to the…

As an interdisciplinary team, we set out to create an applied statistics course that would cover the traditional introductory statistics topics in a consistent framework of social justice. The goal was to motivate students to understand and learn math while deepening their understanding of the interplay, at local and global levels, between social…

Many students experience mathematics as a neutral entity, without understanding its impact on social justice and equity. Students must understand that mathematics and statistics are powerful tools for creating social change, and that students themselves are capable to enact positive social change through their mathematical abilities. In this…

We hope to initiate a discussion about various methods for introducing Cauchy's Theorem. Although Cauchy's Theorem is the fundamental theorem upon which complex analysis is based, there is no "standard approach." The appropriate choice depends upon the prerequisites for the course and the level of rigor intended. Common methods include…

A deficit perspective is a propensity to locate the source of academic problems in deficiencies within students, their families, their communities, or their membership in social categories (such as race and gender). While the deficit perspective is a common topic of discussion in K-12 mathematics education, it is a much rarer topic of discussion…

We describe some classic experiments on the Möbius strip, the projective plane band, and the Klein bottle band. We present our experience with freshmen college students, college teachers, high school students, and Mathematics Education graduate students. These experiments are designed to encourage readers to learn more about the properties of the…

In this paper, we will describe the experience of the authors in using process-oriented guided inquiry learning (POGIL) in calculus at four institutions across the USA. We will briefly examine how POGIL compares to and fits in with other kinds of inquiry-based learning approaches. In particular, we will first discuss the unique structure of a…