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 article presents a mathematical modeling activity for students related to the process of memorization in which students collect their own data to drive their model development, parameterization, and validation. Engaging in the data collection gives them insight to critique and evaluate various models. This task is a low-floor high ceiling…

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…

Implementing inquiry-based modules within a course can be effective and enable instructor experimentation, without completely transforming an entire course. For instructors new to inquiry-based learning (IBL), we state hallmarks of the practice and point out the merits of strong IBL communities. An inquiry-based approach may alleviate some current…

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,…

Practices such as making connections between topics, prioritizing content, and identifying broad themes are essential to learning mathematics. This paper describes a project designed to integrate these synthesizing activities into an abstract algebra class. Students used a classroom wall to record and organize their collective learning and…

In an undergraduate analysis course taught by one of the authors, three prompts are regularly given: (i) What do we know? (ii) What do we need to show? (iii) Let's draw a picture. We focus on the third prompt and its role in helping students develop their confidence in learning how to construct proofs. Specific examples of visual models and their…

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…

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…

In recent years, I have cultivated an almost pathological resistance to grading. Here I explore the reasons why and describe how I eventually recovered. In particular, I propose that although grading, or more explicitly, effective assessment of student learning, is a challenging component of a mathematics instructor's job description, reflective…

This article discusses ways in which improvisational comedy games and exercises can be used in college mathematics classrooms to obtain a democratic and supportive environment for students. Using improv can help students learn to think creatively, take risks, support classmates, and solve problems. Both theoretical and practical applications are…

This article points out a simple connection between related rates and differential equations. The connection can be used for in-class examples or homework exercises, and it is accessible to students who are familiar with separation of variables.