In this paper, I analyze the impact of culture and metaphor on cryptology education. I will compare and contrast the historically grounded metaphors of cryptology-is-warfare and encryption-is-security to a set of counter-metaphors: cryptology-is-privacy and encryption-is-communication. Using this explicit understanding of conceptual metaphor, I…

This paper describes Alkaline, a size-reduced version of Kyber, which has recently been announced as a prototype NIST standard for post-quantum public-key cryptography. While not as simple as RSA, I believe that Alkaline can be used in an undergraduate classroom to effectively teach the techniques and principles behind Kyber and post-quantum…

This article reports on a reconceptualization of the Precalculus course experience at Florida International University. We discuss the details of the redesign process--unified within a faculty learning community (FLC) model--along with a broader change in the course sequence leading up to Calculus. We provide data, including the comparison between…

We offer an analysis of calculus assessment items that highlights ways to evaluate students' application of important meanings and support their engagement in generative ways of reasoning. Our central aim is to identify characteristics of items that require students to apply their understanding of key ideas. We coordinate this analysis of…

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.

Traditional lecturing is the dominant method of teaching mathematics in undergraduate mathematical courses in many countries, whereas active student-centered approaches such as inquiry-based learning have been shown in some instances to be more effective. Most teaching resources (inquiry-based tasks) available at the tertiary level are related to…

This article presents a mathematical modeling activity for students related to the process of memorization in which students collect their own data to drive their model development, parameterization, and validation. Engaging in the data collection gives them insight to critique and evaluate various models. This task is a low-floor high ceiling…

Several major themes related to rethinking assessment emerged from a search of the papers published in "PRIMUS." Authors explored ways to change the stakes of assessments, often with outcomes-based grading and testing structures. They explored changing the "structure" of assessments by considering media beyond written exams and…

Many mathematics departments have transition to proof (TTP) courses, which prepare undergraduate students for proof-oriented mathematics. Here we discuss how common TTP textbooks connect three topics ubiquitous to such courses: logic, proof techniques, and sets. In particular, we were motivated by recent research showing that focusing on sets is…

Placement policies are intended to match students with appropriate courses in order to improve student success, but how do you evaluate these policies? In this article, we evaluate four placement policies at Towson University by considering three categories of outcomes: long-term outcomes such as graduation and retention rates, short-term or…

The pedagogical discussion between the merits of traditional learning versus online learning provides much discussion from both camps. Following the Coronavirus of 2019 pandemic in the spring of 2020, undergraduate students enrolled in the freshman Single Variable Calculus course at the United States Military Academy at West Point were forced to…

Through a multi-year, national calculus study, researchers have recently identified seven characteristics of successful college calculus programs. We identified these seven characteristics by visiting five doctoral-granting mathematics departments with successful calculus programs and uncovering the common traits among them. These seven traits…

We discuss an innovative course model used in first-year calculus courses at a large North American research university, which we refer to as the "Blended Model." We argue that our model takes the best features of lectures, flipped classrooms, and traditional recitations, and gathers them into a cohesive, robust structure that benefits…

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, we describe the evolution of calculus instruction at a mid-sized, career-oriented, comprehensive public university. Changes in practice, that began with a single faculty member implementing technology as a tool for student inquiry, have spread to other department faculty via support from an internal grant, workshops, and the use of…