In introductory math courses such as precalculus, students often have difficulty with assignments that require explanations or synthesizing knowledge. When students receive low scores on such assignments, instructors often wish to help students understand the material they struggled with. A common strategy is to allow the students to revise and…

Homework completion and self-regulatory ability have both been extensively studied to examine their impact on learning achievement. Moreover, the reciprocal nature of how these two qualities affect one another is also an area of research. While evidence shows that voluntary completion of assigned homework predicts self-regulation in students, a…

This article reports on a reconceptualization of the Precalculus course experience at Florida International University. We discuss the details of the redesign process--unified within a faculty learning community (FLC) model--along with a broader change in the course sequence leading up to Calculus. We provide data, including the comparison between…

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…

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…

We present an analysis on the differential effects of incentivizing homework in an introductory mathematics course at the United States Military Academy. We found that including homework as part of a student's overall course average (incentive) led to a significantly higher performance (achievement) on homework assignments. However, doing homework…

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…

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…

The use of writing to learn mathematics at the university-level is a pedagogical tool that has been gaining momentum. The setting of this study is a second-year differential equations class where written assignments have been incorporated into the course. By analyzing survey results and students' written work, we examine the extent to which…