This paper discusses several linear algebra activities designed to help enhance students' skills in collaborating, exploring mathematics, and linking together abstract and visual ways of approaching mathematics. Most of these activities are short, accessible, engaging, and easy to incorporate into any classroom. In addition, we discuss some…

According to the MAA Instructional Practices Guide, deep learning requires student engagement with content both inside and outside the classroom. Hence, mathematics instructors must work to engage students in the learning experience. Higher education research often equates engaged learning and active learning, but what does engaged learning mean…

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…

National studies continue to indicate that the graduating STEM student body is not representative of the diversity of the U.S. population. In addition to, or in the absence of, institutional change, instructors must learn how to implement equity-focused pedagogical changes in order to better support their students. This article describes my…

As calculus instruction moves further from lecture-based instruction toward student-centered pedagogy, support services must align with the changing goals for the course. This paper describes the work of a department as they collectively design and redesign a co-requisite Calculus I course, in an effort to better promote students' academic and…

In this study, we evaluate an innovative method to improve the teaching of linear algebra. The use of peer instruction in conjunction with a seminar strategy and supported by didactic engineering is proposed as a means to facilitate the mastery of abstract concepts, the undertaking of innovative research in problem solving, and the practical…

In a recent article, Crider recommends ending a course with a memorable learning experience, called an epic finale, instead of a final exam. Here, we give the details of epic finales given in four mathematics courses: Discrete Mathematics, Information and Coding Theory, Real Analysis, and Complex Analysis. We describe how to reconfigure a course…

This mixed-methods study examined prospective elementary teachers' (N = 32) mathematical knowledge and mathematics self-efficacy while learning about the Singapore Modeling Method in a university mathematics course. Pre- and post- quantitative data were collected via two content knowledge assessments and one belief survey, and qualitative data…

Homework is prevalent in mathematics courses, as are cumulative final exams. This study incorporated the memory science concepts of the "testing effect" and "spacing effect" in the homework and final exam of college mathematics courses. By replacing some new homework problems with review problems, students had additional…

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…

In this work, we studied the use of open education resources (OER) in the form of online modules combined with an open textbook as it relates to student performance and perceptions in a Linear Algebra course. In this approach, we compared student performance and perceptions from three sections of this intermediate level mathematics course. One was…

What if your students could access "any" resource during a test? How would they react? How would "you" react? This paper presents some results from a trial of allowing students access to notes, calculators, and any device connected to the internet, which occurred during a midterm in a second-year ordinary differential equations…

In the calculus classroom, integrating applications with the theoretical and procedural conveys the relevance of the material. Since Newton and Leibniz developed calculus in the context of physics and astronomy, applications in these fields tend to predominate. To engage and excite our students, pedagogical considerations must include broader…

Income inequality is a central social justice concern, and hence excellent motivation for real-world applications in mathematics classrooms at every level. We describe the "Mathematics for Social Justice" course at Saint Michael's College, giving a specific example of one of the typical social justice projects for the course, and showing…

During the Spring 2020 semester, universities transitioned to online instruction to slow the spread of COVID-19. During this time, mathematics support/tutoring centers also moved their services online. We discuss best practices for online tutoring from the literature and the shared experiences of 28 tutoring center leaders who transitioned to…