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…

Storytelling has proved to be an effective way of passing on information from one generation to the next. Whether the information relates to history, culture, health, or morality, the story provides a framework so that complex ideas can be better understood and retained. In this article, we consider the role of narrative in the design and…

We describe the use of student-generated video content to assess students' engagement with, and understanding of, problem-solving skills. In this framework, students are tasked with using technology to create videos that show them working through, and explaining solutions to, challenging calculus exercises. The videos are then posted online,…

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…

Research has shown that the types of tasks assigned to students affect their learning. Various authors have described desirable features of mathematical tasks or of the activity they initiate. Others have suggested task taxonomies that might be used in classifying mathematical tasks. Drawing on this literature, we propose a set of task types that…

In this paper I discuss my experience in using the inverted classroom structure to teach a proof-based, upper level Advanced Calculus course. The structure of the inverted classroom model allows students to begin learning the new mathematics prior to the class meeting. By front-loading learning of new concepts, students can use valuable class time…

In this note, we report on an implementation of discovery-oriented problems in courses on Real Analysis and Differential Equations. We explain a type of task design that gives students the opportunity to conjecture, refute and prove. What is new is that the complexity in our problems is limited and thus the tasks can also be used in homework…

Specifications grading is a version of mastery grading distinguished by giving students clear specifications that their work must meet, and grading most things pass/fail based on those specifications. Mastery grading systems can get quite elaborate, with hierarchies of objectives and various systems for rewriting and retesting. 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…

A common challenge among mathematics professors is to structure a course so that students are motivated to complete enough work to master the material without creating an unmanageable grading workload. We will discuss a strategy that the author devised to successfully confront this challenge (after many other failed attempts): using online surveys…

This paper is written to provide ideas and guide faculty who want to design a mathematical modeling course for undergraduate mathematics majors and minors. We discuss course goals, assignments, and projects that can be used to help students gain experience relevant for careers and mathematical modeling opportunities. The authors designed this…

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…

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…

On a typical day in a university precalculus classroom, as students arrive, they settle into their small groups and begin sharing their ideas and questions from the homework assigned the previous night. It can be quite challenging to create a learning environment in which students engage in mathematical thinking outside class and are prepared to…

"WeBWorK" CLASS combines the best features of online homework and digital whiteboards to create a system that provides instructors with information on students' problem-solving processes, as well as their final answer. The system's utilization of tools that can sort students based on correct and incorrect homework and quiz answers and…