This paper presents a semester-long bottle design project for an undergraduate Numerical Analysis course. Students implement numerical methods in MATLAB to design and 3D print a bottle. Employing mathematical methods to compute features of their designs enhances students' understanding of numerical techniques in design applications. Student…

This paper shares a flexible activity for engaging people in mathematical inquiry that does not depend on fixed prior knowledge built on a famous property of Möbius strips. The discussion includes the implementation of the activity and its extensions, facilitator moves and common participant thinking, suggestions for adaptation and integration…

Team-Based Learning (TBL) is a cooperative learning strategy blending elements of flipped learning, inquiry-based learning, and problem-based learning. Although used quite frequently in other disciplines, use of this strategy in mathematics has been limited. In this article, we describe how TBL can be implemented in math courses with adherence to…

Financial literacy is ideally suited to be integrated into mathematics courses and taught in an interdisciplinary manner. Students learn best and are motivated when tackling real-world meaningful questions. This article shares how elementary mathematics was applied to better understand the debate about raising the minimum wage and the United…

We consider the use of projects in math courses as a mechanism for promoting coding, communication, and interdisciplinary application of math skills. Final projects play an important role, but we also discuss several alternate types of projects. We describe a model that incorporates projects at all stages across the undergraduate mathematics…

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…

We discuss teaching and learning situations that surfaced when computer programming and mathematics were brought together in a course where students write computer code to explore mathematics problems. Combining programming and mathematics creates a rich ecosystem which, on top of traditional mathematics activities (writing solutions, proofs,…

In a series of group activities supplemented with independent explorations and assignments, calculus students investigate functions similar to their own derivatives. Graphical, numerical, and algebraic perspectives are suggested, leading students to develop deep intuition into elementary transcendental functions even as they lay the foundation for…

In this article we present three group activities designed for math students: a balloon-twisting workshop, a group proof of the irrationality of p, and a game of Math Bingo. These activities have been particularly successful in building enthusiasm for mathematics and camaraderie among math faculty and students at Kenyon College.

This paper aims to illustrate a design cycle of inquiry-based mathematics activities. We highlight a series of questions that we use when creating inquiry-based materials, testing and evaluating those materials, and revising the materials following this evaluation. These questions highlight the many decisions necessary to find just the right tasks…

Calculus students' difficulties in understanding integration have been extensively studied. Research shows that the difficulty lies with students understanding of the definition of the definite integral as a limit of a Riemann sum and with the idea of accumulation inherent in integration. We have created a set of manipulatives and activities…

Applying the Mathematical Knowledge for Teaching framework, we discuss the components of teacher knowledge that might be useful in supporting mathematical inquiry, and examine ways in which we strive to develop this knowledge within a middle grades mathematics program for undergraduate students who are prospective teachers. Using sample activities…

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…

We discuss the pedagogical redesign of a liberal arts mathematics course that enrolls roughly 3000 students per year. Flipping the classroom is a prominent feature of the new pedagogical approach. We describe the nature of this redesign, course resources, and how students are assessed for both preparation and understanding. We also indicate how…

This article presents a problem-based approach that prepares students for future learning in the classroom. In this approach, students complete problem-based activities before coming to class to familiarize themselves with the topics to be covered. After the discussion on how the use of these activities relate to the learning and transfer…