This paper introduces the concept of logical consistency in students' thinking in mathematical contexts. We present the Logical in-Consistency (LinC) instrument as a valuable assessment tool designed to examine the prevalence and types of logical inconsistencies among undergraduate students' evaluation of mathematical statements and accompanying…

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…

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…

Escape the Math Room is a fun, interactive, sequence of puzzles designed to encourage mathematical collaboration, team work, and ingenuity. Using advanced mathematical topics in an accessible way, Escape the Math Room appropriately challenges students ranging from high school to advanced undergraduate. The activity can be adjusted by adding or…

The Mathematical Sciences Department at Shenandoah University focused on increasing the participation of women in the mathematics program by fostering a welcoming learning community and promoting double majors. Data from the past decade is presented. During this time, the program saw an increase in women undergraduate mathematics majors from 11%…

This article is a discovery-based instructional resource for faculty to use as a capstone course or exploratory project for undergraduates who are familiar with (but not necessarily fluent in) calculus, linear algebra, complex variables, and geometry. The explorations flow from a simple change in sign: in the complex numbers a + bi, where…

Sonia Kovalevsky Days (SK Days) are nationally-held outreach events that are commonly organized by local chapters of the Association for Women in Mathematics (AWM) to encourage young women to continue their study of mathematics. The AWM Student Chapter at Worcester Polytechnic Institute hosted virtual renditions of SK Day for middle school girls…

This paper describes a course designed to introduce students to mathematical thinking and a variety of lower level mathematics topics using baseball while satisfying the goals of quantitative reasoning. We give suggestions for sources, topics, techniques, and examples so any mathematics teacher can design such a course to fit their needs. The…

In this paper, we briefly introduce three theoretical frameworks for mathematical identity and why they matter to practitioners teaching undergraduate mathematics courses. These frameworks are narrative identities, communities of practice, and figured worlds. After briefly describing each theory, we provide examples of how each framework can be…

Though posters have been used as a pedagogical tool in a variety of fields, the literature suggests that the use of posters as an educational assessment tool by the mathematics community has been limited. This is unfortunate given the numerous potential benefits of a poster, including the development of oral communication skills and the ability to…

This article presents a reflection on a teaching experience involving the use of the Brügner tangram, an interesting but little-known manipulative material. It details an activity conducted as part of an undergraduate mathematics education course for prospective primary school teachers. The main objective of this paper is to present the…

Point-set topology is among the most abstract branches of mathematics in that it lacks tangible notions of distance, length, magnitude, order, and size. There is no shape, no geometry, no algebra, and no direction. Everything we are used to visualizing is gone. In the teaching and learning of mathematics, this can present a conundrum. Yet, this…

This article provides conceptual ideas, data, and exercises, for integrating original sources of recent, state of the art, world-class life science research in the undergraduate mathematics curriculum and classroom. To this end, this article shows how one of the main goals of calculus in the life sciences, fitting parameters to data and assessing…

Course-based Undergraduate Research Experiences (CUREs) were originally developed by biologists to answer the call for undergraduate curriculum reform and expose more students to authentic research experiences [Wei and Woodin. 2011. Undergraduate research experiences in biology: Alternatives to the apprenticeship model. "CBE Life Sciences…

The design and initial implementation of a project-based directed study course in mathematical research and communication is described. The intention of the course is to expose students to the foundation of mathematical research through inquiry-based learning. Students are asked to approach an exercise in topology as though it is an open problem.…