Math modeling is a unique and powerful part of mathematics that is underutilized in contemporary classrooms. Teachers of all grade levels may utilize such modeling problems to better serve the students in their classrooms, with related analytical problem-solving activities that contribute to learners meeting the highest of learning standards. With…

Too often, mathematics and science are taught in isolation from each other and from meaningful problems that matter to students. This book draws on the authors' experiences with teacher colleagues, including time spent in their classrooms co-developing and refining lessons. The core of their approach is to encourage learners to pursue solutions to…

This curated collection covers a selection of PRIMUS articles published over a roughly 12-year period that focus on modeling and applications. The collection includes sections on individual projects, courses with a significant modeling component, and modeling and applications in extracurricular settings and throughout the curriculum.

In this paper, we present an overview of a series of 1-credit applied problem solving courses. The goal of these courses was to help students develop their oral and written communication skills, ability to work as a team, and general problem solving skills through preparation and participation in the Mathematical Contest in Modeling (MCM) and…

In this paper, we share our collaboration across the disciplines of mathematics and mathematics education to develop and implement a mathematical modeling task for prospective secondary mathematics teachers. Through this collaboration, we identified three key components of mathematical modeling: the "what," "how," and…

Connections among the mathematics, science, and engineering disciplines have been recognized and affirmed in national standards. For example, the application of mathematical ideas and skills within science has been highlighted in national science standards for over 20 years. More recently, the Next Generation Science Standards (NGSS; NGSS Lead…

The Coronavirus outbreak allows for a number of possible applications to classroom teaching (biology, computer science, Earth science, physics, statistics), as well as student research. A number of simple models reproduce fairly well the case numbers (total confirmed cases) of the Coronavirus pandemic in specific regions. These models may also be…

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…

The integration of biology with mathematics and computer science mandates the training of students capable of comfortably navigating among these fields. We address this formidable pedagogical challenge with the creation of transdisciplinary modules that guide students toward solving realistic problems with methods from different disciplines.…

This paper introduces a course design for a post-Calculus undergraduate course on mathematical modeling for the life sciences. The course includes differential equations, discrete, and cellular automata approaches (among others) to modeling questions in the life sciences, as well as a variety of biological topics. The course focuses on model…

In this personal essay, I explain how my use of visual modelling has the capacity to broaden constructionism in five important ways. (1) It introduces new techniques for students to describe and document, in a personal way, what they are actually doing in modelling. (2) It introduces the big ideas of mathematical modelling and computational…

Biological systems exhibit strong dynamic variations; for example, a system may have a tendency towards either a steady state, periodic behaviour or chaotic oscillations. These findings, explained by dynamic systems theory, have allowed researchers to formally relate a wide variety of systems, such as the theory of rumour propagation, glucose…

Learning to create, use, and evaluate models is a central element of becoming a scientist. In physics, we often begin an analysis of a complicated system with highly simplified or toy models. In introductory physics classes, we tend to use them without comment or motivation. Some students infer that physics is irrelevant to their understanding of…

Inspired by the approach first employed by C.S. Holling in his classic "disc experiment," this article provides a sequence of learning activities that increase students' understanding of the mechanisms behind saturating effects in predator-prey scenarios. The proposed lesson is recommended for inclusion in courses that address…

In times of rapid technological innovation and global challenges, the development of science, technology, engineering and mathematics (STEM) competencies becomes important. They improve the personal scientific literacy of citizens, enhance international economic competitiveness and are an essential foundation for responsible citizenship, including…