I describe the motivation, structure, implementation, and student feedback of my mastery-based testing (MBT) system with a significant final exam component in Calculus I and II since 2016. Grades for each written assignment, quiz, and exam question were assigned on a Mastery/Progressing/Needs Improvement (M/P/NI) scale. Homework and quizzes could…

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…

At the college level, it can be difficult to engage students outside the classroom through the use of effective homework assignments. Although it is straightforward to create assignments that test the ability to carry out computations as discussed in class, it is more challenging to create assignments that encourage students to think more…

We describe a method that instructors can use to grade tests and assignments that can be used in follow-up inquiry-based activities in class to review material. The grading process is essentially a sorting of student assignment/test responses based on the instructor's conception of what makes responses acceptable. The instructor can assign a grade…

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…

Mathematics teachers need to teach students more than just a laundry list of mathematical skills. Many of us also want to train our students to use mathematical habits of mind. However, traditional grading schemes usually do not allow us to reward intellectual courage and modesty. In this paper, I report on my implementation of specifications…

Quantitative Reasoning for Professionals is a two-semester general education sequence that teaches basic and intermediate algebra through the lens of quantitative reasoning. In this course sequence, we emphasize communication and inference-making while teaching practical algebra skills for students in programs such as business, nursing, and social…

We report on a large-scale implementation of mastery-based grading in a General Education Introductory Statistics course at California State University Los Angeles. In Fall 2018, the course had 80 sections of approximately 30 students each and was taught by 37 instructors who ranged from long-time, experienced instructors to brand new teaching…

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…

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…

In this paper, I present a homework system that supports a flipped classroom environment using only a textbook for students' first contact with the material. Motivated by David Pengelley's homework system, each unit of material has four key components: Core Assignments, Conceptual Assignments, In-class Worksheets, and Follow-up Assignments. The…

In the age of the internet, it is increasingly difficult to write homework assignments in a way that encourages students to struggle with a problem on their own without seeking answers from other sources. This is especially true in lower-level courses, where students often start with the attitude of "I can't do this." In this article, I…

Addressed toward course coordinators and departmental leaders interested in redesigning an undergraduate mathematics course, we highlight the steps our team at the University of Maryland, College Park has taken in bringing active learning to our Precalculus course. We provide examples of ways in which we have coordinated active learning across…

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…

My goal in crafting homework in calculus is twofold: to provide scaffolding for students to develop a theoretical understanding of calculus concepts and to incorporate good mathematical exposition, including justification and proof when appropriate. I achieve these goals by creating weekly homework sets that students work on in groups of three or…