We studied aspects of undergraduate STEM majors' mathematical reasoning as they engaged in mathematically modeling a predator-prey scenario. The study used theoretical viewpoints on quantitative reasoning to inform scaffolding moves that would assist modelers in overcoming blockages to their mathematization of real-world problems. Our contribution…

This paper is written as a guide for any instructor seeking to develop the mathematical modeling process or open-ended problem solving in their courses. We describe a pedagogical approach to create mini modeling problems to develop the modeling process. These are problems that fall between traditional homework problems and open-ended modeling…

The manuscript describes a community-based mathematical modeling task that was implemented in a Calculus I classroom to engage students in mathematical modeling. Twenty-five undergraduate students engaged in this activity. These students selected a context that they found interesting, posed questions, developed constraints, came up with solution…

We joined an initiative to engage faculty and undergraduate students in research by scheduling regular early college-level mathematics research presentations with pre- and post-lecture exercises. While our program featured six talks that were predominantly in the mathematical biosciences, the concept of creating themed topics for presentations can…

There is growing awareness of the need for mathematics and computing to quantitatively understand the complex dynamics and feedbacks in the life sciences. Although several institutions and research groups are conducting pioneering multidisciplinary research, communication and education across fields remain a bottleneck. The opportunity is ripe for…

Relating mathematics learned in the classroom to real situations increases student motivation and enhances learning. In this paper, we provide an example of a classroom application of calculus to physiology in two courses: "Differential Equations" and "Calculus I for Biology and Medicine." We designed and implemented a project…

This article provides an overview of a modeling sequence that culminates in student reinvention of a bifurcation diagram. The sequence is the result of years of classroom-based research and curriculum development grounded in the instructional design theory of Realistic Mathematics Education. The sequence of modeling tasks and examples of student…

In this paper, we tell a story of iterative design and continual improvement of an asynchronous technological resource, pencasts, to support development of students' modeling skills while studying at home. Our students were typically engineering majors, enrolled in differential equations as a prerequisite for their subsequent engineering courses.…

This article describes our modeling approach to teaching the one-dimensional heat (diffusion) equation in a one-semester undergraduate partial differential equations course. We constructed the apparatus for a demonstration of heat diffusion through a long, thin metal rod with prescribed temperatures at each end. The students observed the physical…

A great deal of educational literature has focused on problem-based learning (PBL) in mathematics at the primary and secondary level, but arguably there is an even greater need for PBL in college math courses. We present a project centered around the Humans versus Zombies moderated tag game played on the Utah State University campus. We discuss…

James Madison University faculty team-teach an interdisciplinary mathematical modeling course for mathematics and biology students. We have used two different project-based approaches to emphasize the mathematical concepts taught in class, while also exposing students to new areas of mathematics not formally covered in class. The first method…

In this paper, we discuss active learning in College Algebra at Georgia Gwinnett College. This approach has been used in more than 20 sections of College Algebra taught by the authors in the past four semesters. Students work in small, structured groups on guided inquiry activities after watching 15-20 minutes of videos before class. We discuss a…