This article describes the author's experience designing and implementing an inquiry-based learning (IBL) pedagogical approach to an upper-division undergraduate cryptology course. The author shares the course goals and how the IBL style supports their achievement. The article concludes with sample activities -- in-class exercises that touch on…

Nationwide, many students fail to complete the key mathematics courses that are required for most STEM majors, including Precalculus. This paper describes the rationale, implementation, and impact of the redesign of Precalculus at one regional west coast institution. Prior to the redesign, pass rates in Precalculus were modest (75.8% of all…

We discuss two proof evaluation activities meant to promote the acquisition of learning behaviors of professional mathematics within an introductory undergraduate proof-writing course. These learning behaviors include the ability to read and discuss mathematics critically, reach a consensus on correctness and clarity as a group, and verbalize what…

The Mathematics Department at Cornell University has recently secured a grant from the University to implement systemic change in how we teach courses that reach students at critical transition points in their mathematical development. In this article, we report on the changes made to our large multi-section first-semester calculus course in order…

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…

We discuss an innovative course model used in first-year calculus courses at a large North American research university, which we refer to as the "Blended Model." We argue that our model takes the best features of lectures, flipped classrooms, and traditional recitations, and gathers them into a cohesive, robust structure that benefits…

This study explores the impact of Peer-Assisted Reflection (PAR), a structured active learning strategy that emphasizes peer feedback and reflection, on students' perceptions of mathematical thinking, and of the roles their peers and their instructors play in their learning process. This study also examines the impact of PAR on the students'…

As students learn to problem solve in authentic situations, they must also develop metacognitive tools to manage and regulate their problem-solving process. To foster process-focused metacognition utilized by mathematical thinkers and problem solvers, inquiry-based learning classroom practices and an adapted version of portfolio problems were…

It is increasingly important for mathematics students to engage in active learning along with discussion of material with their peers. "Slopes" is a mobile application designed to visualize solutions to differential equations and support active learning in the classroom. We implemented group activities using "Slopes" into an…

This article addresses the logistics of implementing projects in an undergraduate mathematics class and is intended both for new instructors and for instructors who have had negative experiences implementing projects in the past. Project implementation is given for both lower- and upper-division mathematics courses with an emphasis on mathematical…

We explored the effectiveness of a flipped active learning pedagogy in a liberal arts mathematics course without video or interactive preparation. In both control and active learning classes, students were required to respond to a reading before class and take a quiz after class. During the active learning class, students worked together in groups…

Over the past 10 years, the authors of this paper have implemented a series of project-based and inquiry-based learning initiatives in the calculus sequence at our institution. These initiatives took place in a department with an existing strong culture supporting teaching innovation and improvement. In this paper, we describe three initiatives in…

Research has highlighted that inquiry-based learning (IBL) instruction leads to many positive student outcomes in undergraduate mathematics. Although this research points to the value of IBL instruction, the practices of IBL instructors are not well-understood. Here, we offer a characterization of a particular form of IBL instruction:…

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…

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…