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Aaron Wootton – PRIMUS, 2024
We introduce learning modules in cryptography that can be crafted to motivate many abstract mathematical ideas, and we illustrate with a sample module. These modules can be used in a variety of ways, such as the core for a cryptography course or as motivating topics in other courses such as abstract and linear algebra or number theory.
Descriptors: Technology, Mathematical Concepts, Learning Modules, Mathematics Instruction
Cody L. Patterson; Paul Christian Dawkins; Holly Zolt; Anthony Tucci; Kristen Lew; Kathleen Melhuish – PRIMUS, 2024
This article presents an inquiry-oriented lesson for teaching Lagrange's theorem in abstract algebra. This lesson was developed and refined as part of a larger grant project focused on how to "Orchestrate Discussions Around Proof" (ODAP, the name of the project). The lesson components were developed and refined with attention to how well…
Descriptors: Mathematics Instruction, Algebra, Validity, Mathematical Logic
Keith Brandt – PRIMUS, 2024
This paper describes a project assigned in a multivariable calculus course. The project showcases many fundamental concepts studied in a typical course, including the distance formula, equations of lines and planes, intersection of planes, Lagrange multipliers, integrals in both Cartesian and polar coordinates, parametric equations, and arc length.
Descriptors: Mathematics Instruction, Calculus, Equations (Mathematics), Design
Gabriel Gianni Cantanelli; Barbara A. Shipman – PRIMUS, 2024
Through galleries of graphs and short filmstrips, this paper aims to sharpen students' eyes for visually recognizing continuous functions. It seeks to develop intuition for what visual features of a graph continuity does and does not allow for. We have found that even students who can work correctly with rigorous definitions may not be able to…
Descriptors: Mathematics Instruction, College Mathematics, Undergraduate Study, Visual Aids
Michael D. Hicks – PRIMUS, 2024
Analogy has played an important role in developing modern mathematics. However, it is unclear to what extent students are granted opportunities to productively reason by analogy. This article proposes a set of lessons for introducing topics in ring theory that allow students to engage with the process of reasoning by analogy while exploring new…
Descriptors: Mathematics Instruction, Mathematical Logic, Logical Thinking, Algebra
Hortensia Soto; Jessi Lajos; Alissa Romero – PRIMUS, 2024
We describe how an instructor integrated embodiment to teach the Fundamental Homomorphism Theorem (FHT) and preliminary concepts in an undergraduate abstract algebra course. The instructor's use of embodiment reduced levels of abstraction for formal definitions, theorems, and proofs. The instructor's simultaneous use of various forms of embodiment…
Descriptors: Mathematics Instruction, Algebra, Undergraduate Students, Mathematical Concepts
Suzanne Dorée; Jennifer Quinn – PRIMUS, 2024
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…
Descriptors: Active Learning, Learning Activities, Mathematics Instruction, Sequential Approach
Gary A. Olson; Heather Lynn Johnson; Rebecca Robinson; Robert Knurek; Kristin A. Whitmore – PRIMUS, 2024
Inverse and injective functions are topics in most college algebra courses. Yet, current materials and course structures may not afford students' conceptual understanding of these important ideas. We describe how students' work with digital activities, "techtivities," linking two different looking graphs that represent relationships…
Descriptors: College Mathematics, Algebra, Mathematics Instruction, Mathematical Concepts
Roneet Merkin – PRIMUS, 2024
This paper reports on a novel corequisite design and implementation for College Algebra at Florida International University. The corequisite course uses online, just-in-time, prerequisite assignments delivered on an open-educational platform. Students get help from near-peer learning assistants inside a math emporium environment. The course…
Descriptors: Required Courses, College Mathematics, Algebra, Mathematics Instruction
T. Clark – PRIMUS, 2024
A standard element of the undergraduate ordinary differential equations course is the topic of separable equations. For instructors of those courses, we present here a series of novel modeling scenarios that prove to be a compelling motivation for the utility of differential equations. Furthermore, the growing complexity of the models leads to the…
Descriptors: Mathematics Instruction, Undergraduate Study, College Mathematics, Equations (Mathematics)
Building a Student-Centered Assessment Community: Motivations, Experiences, Supports, and Challenges
Justin Barhite; Benjamin Braun; Courtney George; Angela Hanson; Hunter Lehmann; Camille Schuetz; Chloe Urbanski Wawrzyniak – PRIMUS, 2024
Over the past three years, a community of faculty and graduate teaching assistants has developed within the University of Kentucky Mathematics department centered around the use and development of student-centered assessment methods. In this article, we discuss the environmental factors that contributed to the growth of this community, our…
Descriptors: Evaluation, Measurement Techniques, Faculty, Teaching Assistants
Diamond, Harvey – PRIMUS, 2023
This paper presents a series of basic computational problems that are mathematically and/or graphically appealing, and provides an idea of places one might go in trying to understand what is happening, integrating mathematics, computation, and graphics. The real point of this paper is to make a case, through those examples, for computation as an…
Descriptors: Mathematics Instruction, Computation, College Mathematics, Undergraduate Study
Yu, F. – PRIMUS, 2023
A productive understanding of rate of change concept is essential for constructing a robust understanding of derivatives. There is substantial evidence in the research that students enter and leave their Calculus courses with naive understandings of rate of change. Implementing a short unit on "what is rate of change" can address these…
Descriptors: Mathematics Instruction, College Mathematics, Calculus, Mathematical Concepts
Jenny Cox; Scott Kaschner; Mary Krohn – PRIMUS, 2024
The number of undergraduates placing into developmental or "remedial" coursework continues to increase. This rise is concerning because developmental or "remedial" coursework creates barriers for many students. This mixed method study examines a holistic approach to placement. After one-on-one interviews with mathematics…
Descriptors: Undergraduate Students, College Faculty, Intervention, Remedial Mathematics
David P. Bunde; John F. Dooley – PRIMUS, 2024
We present a detailed description of a Cryptography and Computer Security course that has been offered at Knox College for the last 15 years. While the course is roughly divided into two sections, Cryptology and Computer Security, our emphasis here is on the Cryptology section. The course puts the cryptologic material into its historical context…
Descriptors: Technology, Coding, Computer Security, Mathematics Education