How to Build a Course in Mathematical–Biological Modeling: Content and Processes for Knowledge and Skill

Abstract

Biological problems in the twenty-first century are complex and require mathematical insight, often resulting in mathematical models of biological systems. Building mathematical–biological models requires cooperation among biologists and mathematicians, and mastery of building models. A new course in mathematical modeling presented the opportunity to build both content and process learning of mathematical models, the modeling process, and the cooperative process. There was little guidance from the literature on how to build such a course. Here, I describe the iterative process of developing such a course, beginning with objectives and choosing content and process competencies to fulfill the objectives. I include some inductive heuristics for instructors seeking guidance in planning and developing their own courses, and I illustrate with a description of one instructional model cycle. Students completing this class reported gains in learning of modeling content, the modeling process, and cooperative skills. Student content and process mastery increased, as assessed on several objective-driven metrics in many types of assessments.

Keys to a Successful Student‐Centered Classroom: Three Recommendations

“…For example, students in an ecology course showed higher scores on exams consisting of questions that asked students to apply, evaluate, and synthesize what they had learned (higher-order congition; Bloom 1956), than students in a previous teacher-centered course on exams testing only factual recall. This is consistent with other findings about the synergy of thoughtfully-structured cooperative work (Hoskinson 2010, Ramaekers et al 2011, Welsh 2012. Students also reported that collaboration helped them learn "much" or "very much" in anonymous surveys, both while our courses were in progress and after their conclusions (Barger, Hoskinson, Martin, unpublished data).…”

The Math–Biology Values Instrument: Development of a Tool to Measure Life Science Majors’ Task Values of Using Math in the Context of Biology

“…In response to these calls, there have been efforts to better integrate math into biology curricula. Such reforms include incorporating the teaching of quantitative skills (e.g., via modules or in-class research experiences) into biology courses ( Robeva et al , 2010 ; Speth et al , 2010 ; Thompson et al , 2010 ; Colon-Berlingeri and Burrowes, 2011 ; Madlung et al , 2011 ; Wightman and Hark, 2012 ; Makarevitch et al , 2015 ; Hoffman et al , 2016 ), redesigning mathematics courses for biology majors to include biology examples ( Edelstein-Keshet, 2005 ; Metz, 2008 ; Chiel et al , 2010 ; Duffus and Olifer, 2010 ; Watkins, 2010 ; Rheinlander and Wallace, 2011 ; Thompson et al , 2013 ), and designing fully integrated math–biology courses and majors ( Depelteau et al , 2010 ; de Pillis and Adolph, 2010 ; Duffus and Olifer, 2010 ; Hoskinson, 2010 ; Usher et al , 2010 ; Thompson et al , 2013 ; Hester et al , 2014 ). The goal of such reforms is to ensure that students develop quantitative skills that will prepare them for careers in the field of modern biology.…”

Bridging physics and biology teaching through modeling

“…4,19,20 Yet, despite the occasional use of the term "model" in our science classrooms (e.g., Bohr model, Standard Model of particle physics, Lotka-Volterra predator-prey model), models and modeling are rarely given explicit treatment, except in particular curricula emphasizing them. [21][22][23] Below, we provide operational definitions of models (products) and modeling (practices) that are broadly applicable across the sciences. By identifying the many similarities and few differences between modeling in physical and life sciences, we present a way to bridge the teaching of physics and biology through scientific practices that are fundamental to both disciplines.…”