In introductory level math classes, writing prompts can be used as part of weekly homework assignments to encourage students to think more deeply about the subject at hand. These writing prompts present scenarios related to recently learned material in a new context and require students to submit a short written response online. Writing prompts…

Challenging mathematics problems were posed as a substantial part of homework in an elective combinatorics course. The intent was to encourage undergraduate students' exploration as well as develop their technical writing skills. The bulk of students' grades on these problems rested on a three-page reflective write-up using a rubric on…

Modeling projects in differential equations and engineering courses create an authentic activity and an opportunity to attain the holy grail of "deeper" learning. However, what do we mean by "deeper" learning and how do we create an environment that encourages that? This article describes a proposal and case study in using…

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…

Mathematical modeling allows flexibility for a project-based experience. We share details of our regular capstone course, successful for virtually 100% of our math majors for almost two decades. Our research-like approach in this course accommodates a variety of student backgrounds and interests, and has produced some award-winning student…

A growing body of mathematics education research points to the importance of fostering students' mathematical creativity in undergraduate mathematics courses. However, there are not many research-based instructional practices that aim to accomplish this task. Our research group has been working to address this issue and created a formative…

Standards-based grading, in which grading should be designed to communicate to students their current level of mastery with regards to well-articulated standards, is becoming popular at the K-12 level. As yet, the literature addressing standards-based grading at the university level is scarce. In this paper, I document my attempts to put into…

This case study details the integration of an online grading platform in a Calculus program. Initially implemented to increase the efficiency and quality of grading written assessments in a large undergraduate program, the effects were many and surprising. Two main concerns surfaced that we needed to address, namely: (1) consistency in grading;…

Liberal arts mathematics courses can provide non-majors the opportunity to connect mathematical topics with areas of personal interest. This article describes two end-of-unit writing assignments (on voting and graph theory) that have been structured so that each student is able to synthesize course material in a unique way, while ensuring a…

One goal of our Discovering the Art of Mathematics project is to empower students in the liberal arts to become confident creators of art and imaginative creators of mathematics. In this paper, we describe our experience with using string art to guide liberal arts students in exploring ideas of calculus. We provide excerpts from our inquiry-based…

Over the last 10 years faculty members in the Department of Mathematical Sciences at the United States Air Force Academy have incorporated individual oral exams into mathematics courses. We have experimented with various approaches, shared results and ideas with other department members, and refined our techniques. We have found that this…

As an often recommended but under-utilized pedagogical strategy, writing in mathematics has many benefits for students. However, creating and grading worthwhile writing projects can be more time-consuming than utilizing more traditional forms of assessment. This paper provides a concrete example of a writing project prompt, questions, directions,…

This article discusses a writing project that offers students the opportunity to solve one of the most famous geometric problems of Greek antiquity; namely, the impossibility of trisecting the angle [pi]/3. Along the way, students study the history of Greek geometry problems as well as the life and achievements of Carl Friedrich Gauss. Included is…

In the early 1990s, in an effort to enhance their majors' ability to communicate mathematical ideas, the Mathematics Department at Bellarmine University added a capstone course, "Readings in Mathematics," to the curriculum of each degree program in the department. We provide an overview of the course, noting its unique aspects, with…

Most instructors desire to create a learning environment conducive to deep learning. However, in courses where grades are based upon the accumulation of points, students may focus on collecting points rather than on learning and achieving the course objectives. We discuss an alternative points-free course design based on the development of clear…