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…

Ciphers based on rotor machines were the state-of-the-art in the mid-1900s, with arguably the most famous being the German Enigma. We have found that students have great interest in the Enigma and its cryptanalysis, so we created our own rotor cipher that is simulated with shifting tables and can be cryptanalyzed. Ours and the historic rotor…

This article includes a case study describing our innovative teaching technique of assigning reading journals in a first semester calculus course (Calculus I), as well as an exposition about and recommendations arising from our subsequent experiences implementing similar methods in Junior and Senior mathematics courses. In the primary case study…

In calculus courses, instructors often use the end-of-section problems in a textbook in homework assignments or other course assessments. As a result, these problems influence the teaching and learning of calculus. In this study, we examine the levels of cognitive demand of these problems in a mainstream calculus textbook and classify them within…

Students often view their role as that of a replicator, rather than a creator, of mathematical arguments. We aimed to engage our students more fully in the creation process, helping them to see themselves as legitimate proof creators. In this paper, we describe an instructional activity (i.e., the "group proof activity") that is…

Service-learning provides a versatile pedagogical platform that can improve the academic performance of participating students and open space for a discussion of issues of social justice within a mathematics classroom. We describe our Precalculus course with a service-learning component, in which university students regularly tutor algebra…

History of mathematics courses based on original source materials are becoming increasingly common. However, are they more suitable for particular types of students? Here we compare two such upper-level courses, with a similar structure and using the same textbook, taken by liberal arts students at Colorado College and mathematics specialists at…

The percentage of college students receiving unproductive grades in introductory mathematics courses is a concern for post-secondary institutions across the country. Many factors can be targeted as potential explanations for this lack of success, yet none of these issues are more noteworthy than the fact that many students enter college…

Although modeling is an integral process in applied mathematics, students rarely encounter modeling opportunities in their calculus courses. We introduce a laboratory experience as a starting point for calculus students to investigate multivariable functions. A layered system of coffee and milk serves as a physical model for temperature gradients…

We describe the process of adjusting the balance between computer-based learning and peer interaction in a college algebra course. In our first experimental class, students used the adaptive-learning program ALEKS within an emporium-style format. Comparing student performance in the emporium format class with that in a traditional lecture format…

This paper describes, as an alternative to the Moore Method or a purely flipped classroom, a student-driven, textbook-supported method for teaching that allows movement through the standard course material with differing depths, but the same pace. This method, which includes a combination of board work followed by class discussion, on-demand brief…

This paper summarizes the experiences of two mathematics faculty members who participated in an in-house study abroad program. Descriptions of math courses taught abroad are given, as well as how students were recruited, courses were designed, and the environment was incorporated. Tips for mathematics faculty wanting to offer study abroad are…

In the age of the internet, it is increasingly difficult to write homework assignments in a way that encourages students to struggle with a problem on their own without seeking answers from other sources. This is especially true in lower-level courses, where students often start with the attitude of "I can't do this." In this article, I…

The purpose of this paper is to explain a newly implemented interactive delivery model for students at the Colorado School of Mines (Mines) repeating Calculus for Scientists & Engineers I during the spring of 2017. Since calculus is a necessary component for so many STEM degrees, it will continue to be a gateway to obtaining such degrees and…

The flipped classroom model interchanges the roles of in-class and out-of-class time to allow students more time to engage with cognitively demanding tasks when expert help from their instructor is more available. An extensive body of literature supports the effectiveness of this model. In contrast, I present a case study of a less-successful…