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…

This paper is a practical how-to guide to help you start using active learning or to have greater success and more fun with it. We categorize active learning techniques as Think, Pair, Share, Composite, Group, Move, or Lead and discuss how to implement activities in each category, along with advice on creating engaging, effective, and equitable…

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 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…

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…

This paper shares a flexible activity for engaging people in mathematical inquiry that does not depend on fixed prior knowledge built on a famous property of Möbius strips. The discussion includes the implementation of the activity and its extensions, facilitator moves and common participant thinking, suggestions for adaptation and integration…

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…

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…

In this paper, we invite the reader to think deeply about professional development opportunities for faculty. The focus of this professional development is to improve teaching and learning by including more inquiry in the mathematics classroom. Building on theories of teaching and learning, we develop the idea of "teaching procedures"…

In this paper, we present an overview of a series of 1-credit applied problem solving courses. The goal of these courses was to help students develop their oral and written communication skills, ability to work as a team, and general problem solving skills through preparation and participation in the Mathematical Contest in Modeling (MCM) and…

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…

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.…

Historically, math education at the high school and introductory college levels has focused on computational skills. With the advancement of computational technologies, problemsolving and other higher-order thinking skills should become the focal point. This article discusses ways in which the University of Minnesota has integrated problem-solving…

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…