We offer ways that the inspection paradox can be usefully presented, even in the most elementary statistics courses, and provide guidance about how it can be revisited subsequently in the same course and in succeeding courses. Numerous situations in which the inspection paradox might occur are mentioned, and mathematically simple demonstrations…

This paper describes a project assigned in a multivariable calculus course. The project showcases many fundamental concepts studied in a typical course, including the distance formula, equations of lines and planes, intersection of planes, Lagrange multipliers, integrals in both Cartesian and polar coordinates, parametric equations, and arc length.

This paper discusses a concept that we call "'m'-tile means," which are the arithmetic mean of data values that break a data set into "m"-1 equal parts. Studying "m"-tile means can engage students' critical thinking skills and demonstrate the concepts underlying commonly used measures of central tendency, and so they…

The design and initial implementation of a project-based directed study course in mathematical research and communication is described. The intention of the course is to expose students to the foundation of mathematical research through inquiry-based learning. Students are asked to approach an exercise in topology as though it is an open problem.…

With this paper, we share an activity for the undergraduate mathematics classroom called "The Harp Project" that leverages the aesthetic nature of both the mathematical and the musical arts. This project was conceived as a STEAM/PBL project with the added feature that it was carried out in pieces by an entire class. Anecdotal evidence…

We believe that developing cultural competencies can help students learn mathematics and conversely that learning mathematical content can help students learn about themselves and others. Using frameworks introduced by Rendón (2009) and Gutiérrez (2018), we present a five-part bundle of activities for undergraduate differential equations course…

The main problem for teachers working with students who have various disadvantages is that many of them lack extrinsic motivation and they can get discouraged very easily as they hate feeling less capable than their peers. As a film enthusiast, the author appllied and won an Education Innovation Teacher Challenge grant to run a film-related…

Transforming an observable phenomenon into a tractable model is a challenging process, from determining the appropriate modeling scale to making realistic simplifying assumptions. However, many modeling texts are anchored around problems that have already been synthesized into a digestible format, which inhibits an opportunity to engage students…

In this article, the author presents a Desmos activity where students adjust the measures of angles in radians to reposition a laser and a mirror so the beam passes through three stationary targets. This Radian Lasers activity can be extended to simulate project-based learning (PBL), a pedagogical approach for applying concepts and skills from…

Digital technologies and the instructional contexts in which they are embedded can increase students' access to meaningful learning opportunities. Although there is a tradition of designing and integrating digital tools in secondary-grades project-based science instruction to enhance learners' access to disciplinary learning, the elementary grades…

In a recent article, Crider recommends ending a course with a memorable learning experience, called an epic finale, instead of a final exam. Here, we give the details of epic finales given in four mathematics courses: Discrete Mathematics, Information and Coding Theory, Real Analysis, and Complex Analysis. We describe how to reconfigure a course…

Computer programming and mathematical algorithms are natural partners in the development of programming skills, logical thought, and a deeper understanding of mathematical concepts. We present the details of a course which blends the two at the sophomore level. This course is required of our mathematics majors, but attracts mathematics minors from…

Effective mathematics teaching elicits and uses evidence of student thinking to assess progress toward mathematical understanding and adjusts instruction continually to support and extend learning (National Council of Teachers of Mathematics, 2014). However, as teachers march through content in precalculus, they tend to rely heavily on traditional…

Students explore the relationship between thrill-seeking rides and their algebra 1 curriculum in an informative, engaging, student-centered lesson that was designed using a project-based-instruction (PBI) framework.

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…