To date, the way that academic misconduct is manifested in undergraduate mathematics coursework has been unexamined in the literature, with the consequence that policy and preventive education can fail to address it appropriately. This paper describes the particular features of the responses expected in mathematical tasks and provides concrete…

Beginning a teaching career and working to prepare and support beginning teachers is a roller-coaster of successes and puzzling moments. In this article, author Cassandra (Cassie) Seiboldt shares how she learned to manage her first years of teaching by purposefully planning through anticipating student thinking and solutions, and the positive…

Many large universities, community colleges and some smaller four-year colleges are turning to hybrid or online instruction for remedial and entry level mathematics courses, often assessed using online exams in a proctored computer lab environment. Faculty face the task of choosing questions from a publisher's text bank with very little, if any,…

Storytelling has proved to be an effective way of passing on information from one generation to the next. Whether the information relates to history, culture, health, or morality, the story provides a framework so that complex ideas can be better understood and retained. In this article, we consider the role of narrative in the design and…

We discuss two proof evaluation activities meant to promote the acquisition of learning behaviors of professional mathematics within an introductory undergraduate proof-writing course. These learning behaviors include the ability to read and discuss mathematics critically, reach a consensus on correctness and clarity as a group, and verbalize what…

We propose a divisibility criterion for elements of a generic Unique Factorization Domain. As a consequence, we obtain a general divisibility criterion for polynomials over Unique Factorization Domains. The arguments can be used in basic algebra courses and are suitable for building classroom/homework activities for college and high school…

A key motivational tactic in undergraduate mathematics teaching is to launch topics with fundamental questions that originate from surprising or remarkable phenomena. Nonetheless, constructing a sequence of tasks that promotes students' own routes to resolving such questions is challenging. This note aims to address this challenge in two ways.…

This document includes two technical appendices that accompany the full report, "Increasing Community College Transfers: Progress and Barriers." The two appendixes include: (1) Data and Methods; and (2) Figures and Tables. [For the full report, "Increasing Community College Transfers: Progress and Barriers," see ED608004.]

In this paper, we propose an elementary proof of Niven's Theorem in which the tangent function will have a primary role.

An important step to achieving a sustainable department culture that encourages innovation in teaching is the alleviation of the isolation that teaching faculty experience. Decreasing this isolation should be accomplished in a manner that respects all instructors' classroom practices while simultaneously exposing faculty to new ideas. In this…

The complexity in understanding the [epsilon-delta] definition has motivated research into the teaching and learning of the topic. In this paper I share my design of an instructional analogy called the Pancake Story and four different questions to explore the logical relationship between [epsilon] and [delta] that structures the definition. I…

Answering a call by the "Common Vision" for instructional material to "establish stronger connections with other disciplines" and "work with professional-level technology tools," the present article shows how various aspects of fitting circles to data fit in existing courses from basic calculus to advanced calculus.

This article describes a method for using the United States Census data to open a differential equations course. The question of finding a model for the United States population data gives students a first experience with creating a model using differential equations, and also understanding derivatives, what they mean, and how to calculate them in…

This paper describes an activity using a dog treat ball to introduce systems of first-order differential equations. Beads are placed in the first of two hemispherical chambers of a food-dispensing dog toy. As the ball is turned, students track the number of beads in the first chamber, the second chamber, and the exterior of the ball. Students…

Even though K-12 mathematics educators have embraced the role of graphing calculators and computers, student use of technology in tertiary mathematics has been slow to implement in the USA context. Enter March 2020, a global health crisis, and the shift to online and remote learning. The immediate and dramatic cessation of in-person modes of…