In mathematics education, the research on proof by contradiction (PBC) often claims that this activity is more difficult for students than direct proof, or simply difficult in general. Many hypotheses have been offered to support or explain this belief, yet they span a disorientingly wide swath of journal articles, conference papers,…

An online intro-to-proof course provided an unexpected opportunity for a series of email exchanges that yielded insights into one student's mathematical thinking and the ambiguous role of mathematical jargon in miscuing this student's reasoning. The jargon deals with the notation [limit value of a function], which encapsulates multiple conceptual…

Developed as an integral component of many higher education programs, internships provide a multitude of benefits for participating students. However, there is a lack of tools designed to measure internship-related learning outcomes. Therefore, this article will present the process of constructing and validating a scale that can be used to…

Recent research on entering college student assessment instruments and placement practices has been critical. Critics suggest that commonly used assessment instruments are inaccurate, misused, and lack predictive validity. This article describes valid criticisms and appropriate uses of assessment instruments. It also lists challenges and provides…

Generative large language models (LLMs) like ChatGPT can quickly produce informative essays on various topics. However, the information generated cannot be fully trusted, as artificial intelligence (AI) can make factual mistakes. This poses challenges for using such tools in college classrooms. To address this, an adaptable assignment called the…

In this practice brief, we offer recommendations for practitioners supporting low-income students, first-generation college students, students of color, and/or students who are academically underprepared. We focus specifically on practices related to students' psychosocial well-being. Our recommendations are based on a multiyear, mixed methods…

The development of proficiency in the practices used by scientists and engineers is considered an important student outcome of laboratory instruction. We developed tasks to assess students' use and development of selected scientific and engineering practices in the general chemistry laboratory using an adapted evidence-centered design approach. In…

Students often view their role as that of a replicator, rather than a creator, of mathematical arguments. We aimed to engage our students more fully in the creation process, helping them to see themselves as legitimate proof creators. In this paper, we describe an instructional activity (i.e., the "group proof activity") that is…

In this article we describe the "Learning Environments and Well-Being Research Project," a collaborative initiative between a research institute and a health promotion unit at a leading Canadian university. The purposes of this project are, first, to conduct research about how classroom environments within higher education settings can…

Courses: Interpersonal Communication, Relational Communication Objective: This article teaches students to explain and evaluate Knapp's Relational Staircase Model through the creation of personalized greeting cards for each relational stage. The in-class activity encourages students to be creative and succinct in capturing the essence of an…

This paper describes, as an alternative to the Moore Method or a purely flipped classroom, a student-driven, textbook-supported method for teaching that allows movement through the standard course material with differing depths, but the same pace. This method, which includes a combination of board work followed by class discussion, on-demand brief…

We describe some classic experiments on the Möbius strip, the projective plane band, and the Klein bottle band. We present our experience with freshmen college students, college teachers, high school students, and Mathematics Education graduate students. These experiments are designed to encourage readers to learn more about the properties of the…

The nine-point circle theorem is one of the most beautiful and surprising theorems in Euclidean geometry. It establishes an existence of a circle passing through nine points, all of which are related to a single triangle. This paper describes a set of instructional activities that can help students discover the nine-point circle theorem through…

Developing a new assessment requires the expertise of both content experts and assessment specialists. Using the example of an assessment developed for Ontario's Colleges Mathematics Assessment Program (CMAP), this article (1) describes the decisions that must be made in developing a new assessment, (2) explores the complementary contributions of…

Students tend to believe that RateMyProfessors.com (RMP) is an unfailingly valid measure of teaching effectiveness, and in fact viewing that site prior to taking a course can have a direct influence on their future evaluations of faculty. The authors describe an activity whose objective is to have students analyze different types of validity using…