Like many math educators, I have spent much of my career bound to traditional methods of instruction and assessment. In recent years, motivated by a growing understanding that such approaches may not result in equitable or inclusive classroom environments, my teaching philosophy has shifted radically. In this article, I describe how I transformed…

This paper reflects on a teaching experiment and presents details of a pedagogical technique where students periodically write down their clearest interpretation of the conditions imposed on various discrete mathematical subjects they are learning in class. Through iterations, students generate a more complete understanding of the material, one…

How can we teach inquiry? In this paper, I offer practical techniques for teaching inquiry effectively using activities built from routine textbook exercises with minimal advanced preparation, including rephrasing exercises as questions, creating activities that inspire students to make conjectures, and asking for counterexamples to reasonable,…

In this article, I present a collection of puzzles appropriate for use in a variety of undergraduate courses, along with suggestions for relevant discussion. Logic puzzles and riddles have long been sources of amusement for mathematicians and the general public alike. I describe the use of puzzles in a classroom setting, and argue for their use as…

"Find the extreme values of the function." "At what rate is the distance between A and B increasing after 12 seconds?" Prompts like these can be heard in most first-semester calculus courses. Unfortunately, these cues also tend to prompt students' eyes to glaze over with thoughts of "When will I ever use this?" This…

What began as a small group of professors gathering to discuss implementation of Inquiry-Based Learning (IBL) in our classes has developed into a strong regional community of practice. Through a generous grant and a lot of hard work, we created the Greater Upstate New York IBL consortium with a mission to create, grow, and maintain a community of…

Surface area and volume computations are the most common applications of integration in calculus books. When computing the surface area of a solid of revolution, students are usually told to use the frustum method instead of the disc method; however, a rigorous explanation is rarely provided. In this note, we provide one by using geometric…

With the goal of improving student success, the chancellor of the California State University (CSU) system issued an executive order that required all CSU campuses to eliminate remedial math courses as of Fall 2018 and place all first-year students into appropriate General Education (GE) mathematics/quantitative reasoning courses. The Mathematics…

Calculating Laplace transforms from the definition often requires tedious integrations. This paper provides an integration-free technique for calculating Laplace transforms of many familiar functions. It also shows how the technique can be applied to probability theory.

A new transition course centered on complex topics would help in revitalizing complex analysis in two ways: first, provide early exposure to complex functions, sparking greater interest in the complex analysis course; second, create extra time in the complex analysis course by eliminating the "complex precalculus" part of the course. In…

The authors have been teaching mathematics and economics for more than 15 years at two nonresidential colleges in New York City: Metropolitan College of New York and Bronx Community College, which is part of the City University of New York (CUNY). Until the first week of March 2020, the authors were teaching all their classes in-person. With the…

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…

The article provides a possible option of how first-year students of Russian universities adapt to mastering higher mathematics. The purpose of the research is the development of methodological approaches to designing an online course that recaps school math material in a short period. The concept of individualization of educational activities is…

String art can be easily used in introductory calculus to capture the interest of students, to motivate mathematical investigations, and to deepen mathematical understanding.

In this article we present three group activities designed for math students: a balloon-twisting workshop, a group proof of the irrationality of p, and a game of Math Bingo. These activities have been particularly successful in building enthusiasm for mathematics and camaraderie among math faculty and students at Kenyon College.