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…

San Diego State University recently embarked on a major initiative to revitalize the Precalculus, Calculus 1, and Calculus 2 sequences. In addition to program features such as course coordination, a new active learning component led by graduate teaching assistants (GTAs) was added to each of the Precalculus, Calculus 1, and Calculus 2 courses, and…

As calculus instruction moves further from lecture-based instruction toward student-centered pedagogy, support services must align with the changing goals for the course. This paper describes the work of a department as they collectively design and redesign a co-requisite Calculus I course, in an effort to better promote students' academic and…

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…

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…

Although the number of bachelor's degrees in the U.S. awarded to women has gone up, engagement of women in science, technology, engineering, and mathematics (STEM) continues to be low. This paper presents a project-based learning program, informed by education research best practices, designed to provide research experiences to female students…

Inquiry-based learning is a topic of growing interest in the mathematical community. Much of the focus has been on using these methods in calculus and higher-level classes. This article describes the design and implementation of a set of inquiry-based learning activities in a Math for Liberal Arts course at a small, private, Catholic college.…

This article reports on techniques of teaching abstract algebra which were developed to achieve multiple student objectives: reasoning and communication skills, deep content knowledge, student engagement, independence, and pride. The approach developed included a complementary combination of inquiry-based learning, individual (not group) homework…

"WeBWorK," an online homework system, can be be used to deliver daily reading questions to students. The author studied its use for this purpose with a lower division Introduction to Programming course and an upper division Probability and Statistics course. In the lower division course, "WeBWorK" significantly improved peer…

In this article, we present a large list of low-threshold active teaching methods categorized so the instructor can efficiently access and target the deployment of conceptually based lessons. The categories include teaching strategies for lecture on large and small class sizes; student action individually, in pairs, and groups; games; interaction…

Describes student historical research and student classroom presentation of the results of that research. Feedback from the student surveys verifies that active-learning mathematics history can motivate students to learn mathematics. (Author/DDR)