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…

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…

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…

This article presents a task providing college students opportunities to build on their high school knowledge of trigonometry to explore parametric equations and inverse trigonometric relationships within a contextual learning ladder problem.

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…

Graphs about Us (GaU) is an activity for building classroom community within mathematics classrooms. Through the creation and analysis of graphical representations of data about the students' lives in and out of school, this activity aims to allow each student to feel seen and validated in the class, create shared knowledge of students'…

We present a free student-facing tool for creating 3D plots and smartphone-based virtual reality (VR) visualizations for STEM courses. Visualizations are created through an in-browser interface using simple plotting commands. Then QR codes are generated, which can be interpreted with a free smartphone app, requiring only an inexpensive Google…

Many students who enroll in a first course in linear algebra major in STEM disciplines other than mathematics. Teachers who serve such students may find it difficult to provide authentic problems from these broader areas that ignite students' interest in linear algebra. In this paper, we highlight an interdisciplinary learning activity that…

Students enrolled in introductory math courses, such as college algebra, deserve to do more than find answers and fix mistakes. We present one interactive digital activity, the Cannon Man "Techtivity," which we developed to provide opportunities for students to develop an understanding of function, beyond just applying a rule, such as…

This paper offers instructional interventions designed to support undergraduate math students' understanding of two forms of representations of Calculus concepts, mathematical language and graphs. We first discuss issues in students' understanding of mathematical language and graphs related to Calculus concepts. Then, we describe tasks, which are…

This manuscript proposes the use of the "I notice, I wonder" routine in college mathematics classrooms to address issues of diversity, equity, and inclusion. Examples are given of prompts that incorporate meaningful conversations about real-world issues affecting our students or about issues of inclusion, access, and representation in…

The Gauss-Lucas Theorem is a classical complex analysis result that states the critical points of a single-variable complex polynomial lie inside the closed convex hull of the zeros of the polynomial. Although the result is well-known, it is not typically presented in a first course in complex analysis. The ease with which modern technology allows…

In this article we discuss relationships between the cyclic group Z[subscript 12] and Western tonal music that is embedded in a 12-note division of the octave. We then offer several questions inviting students to explore extensions of these relationships to other "n"-note octave divisions. The answers to most questions require only basic…

We present a mathematical activity called graph talks as a new pedagogical routine to intertwine social justice issues and mathematics. Adapted from "number talks," graph talks involve students analyzing, interpreting, and discussing real-life data represented in graphs. Graphs may be strategically selected to both highlight a relevant…

Finite Mathematics has become an enormously rich and productive area of contemporary mathematical biology. Fortunately, educators have developed educational modules based upon many of the models that have used Finite Mathematics in mathematical biology research. A sufficient variety of computer modules that employ graph theory (phylogenetic trees,…