This article describes the author's experience designing and implementing an inquiry-based learning (IBL) pedagogical approach to an upper-division undergraduate cryptology course. The author shares the course goals and how the IBL style supports their achievement. The article concludes with sample activities -- in-class exercises that touch on…

Faculty professional development is an important lever for change in supporting instructors to adopt research-based instructional strategies that engage students intellectually, foster learning-supportive attitudes and habits of mind, and strengthen their persistence in mathematics. Yet the literature contains few well-rationalized models for…

The mathematical egg hunt is a hands-on activity designed to help students understand mathematical relations in an Introduction to Proofs course. This activity gives students the opportunity to practice selecting which ordered pairs do and do not belong to a given relation in a moderately competitive egg hunt. It is designed to be low-stakes, yet…

In this reflection of teaching, we describe a series of activities that introduce the Taylor series through dynamic visual representations with explicit connections to students' prior learning. Over the past several decades, educators have noted that curricular materials tend to present the Taylor series in a way that students often interpret as…

This article presents several activities suitable for a transition to proofs course. In addition, this article surveys literature in support of active learning in the transition to proofs course and discusses how these activities have been successfully implemented in one such course.

The Euclidean Discus Toss is an active and tactile learning activity that models the extended Euclidean algorithm with a frisbee relay. The extended Euclidean algorithm involves both iterative and recursive programming and is regularly taught throughout the mathematics and computer science curricula. The Euclidean Discus Toss invites students to…

In this paper, we discuss mathematical modeling opportunities that can be included in an introductory Differential Equations course. In particular, we focus on the development of and extensions to the single salty tank model. Typically, salty tank models are included in course materials with matter-of-fact explanations. These explanations miss the…

The typical trigonometry, precalculus, or calculus student might not agree that logarithms are hot stuff, but we drew motivation from chili peppers to help students get a better taste for logarithms. The Scoville scale, which ranges from 0 to 16,000,000, has been the sole quantitative metric to measure the pungency (spiciness) of peppers since its…

According to the MAA Instructional Practices Guide, deep learning requires student engagement with content both inside and outside the classroom. Hence, mathematics instructors must work to engage students in the learning experience. Higher education research often equates engaged learning and active learning, but what does engaged learning mean…

Teaching Mathematics to tertiary students can be a challenge to educators, mainly because they must deal with learners' varying levels of readiness. Some of the factors attributing to the variability are learners' perceptions of mathematics, their previous learning experiences, and fear of failure. We implemented a teaching approach to facilitate…

It is increasingly important for mathematics students to engage in active learning along with discussion of material with their peers. "Slopes" is a mobile application designed to visualize solutions to differential equations and support active learning in the classroom. We implemented group activities using "Slopes" into an…

As part of a departmental reform project, a large University converted a "Precalculus College Mathematics" lecture-based course for 97 students into an active learning flipped classroom for first-year engineering students. The curriculum was designed specifically to provide applications of pre-calculus in various engineering subjects.…

Collegiate mathematics instructors are moving away from traditional lecture-based teaching practices to accommodate the pedagogies that support more active student learning. As part of the movement, groupwork has been increasingly implemented. At the same time, mathematics classrooms have become increasingly diverse and also in the distribution of…

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…

This paper introduces lessons designed to incorporate applications to teaching high school mathematics in an undergraduate Discrete Mathematics course. Because many prospective high school teachers do not take courses that are specifically designed for teachers, providing materials aimed at teacher preparation that can be easily integrated into…