In this note, I argue for and discuss my experiences with explicitly incorporating principles of critical and creative thinking in a transitions course which serves mathematics, mathematics education, and statistics majors. I describe several specific assignments and classroom tasks designed to enhance critical and creative thinking. I also…

Almost all finite groups encountered by undergraduates can be represented as multiplicative groups of concise block-diagonal binary matrices. Such representations provide simple examples for beginning a group theory course. More importantly, these representations provide concrete models for "abstract" concepts. We describe Maple lab…

Mastery grading is an approach to grading in which students are assigned term grades based on whether they meet certain enumerated objectives, rather than accumulating points. In this note, I describe my experiences using a mastery system, which I call techniques grading, which applies the insights behind the standards-based and specifications…

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…

Workshops can be a powerful tool to support students as they develop proof-writing skills. In a workshop, each student writes a proof, provides feedback on other students' work, and reflects on critiques from peers. Workshops can be used in any class that emphasizes writing proofs or other forms of mathematical writing. They are highly efficient…

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…

This paper aims to illustrate a design cycle of inquiry-based mathematics activities. We highlight a series of questions that we use when creating inquiry-based materials, testing and evaluating those materials, and revising the materials following this evaluation. These questions highlight the many decisions necessary to find just the right tasks…

In the Spring of 2011, two of the authors of this paper taught number theory courses at their respective institutions. Twice during the semester, students in each class submitted proofs of two to three theorems to be peer reviewed by students in the other class. Each student wrote anonymous and formal referee reports of the submitted theorems,…

Over the last four years of the senior capstone seminar at Western Carolina University, we have redesigned the course substantially to comply with our institutional Quality Enhancement Plan for engaged student learning and to follow the guidelines proposed by the Mathematical Association of America's Committee on Undergraduate Programs in…