Making the Most of Modeling Tasks

While there is disagreement among mathematics educators about some aspects of its meaning, mathematical modeling generally involves taking a real-world scenario and translating it into the mathematical world (Niss, Blum, and Galbraith 2007). The complete modeling process involves describing situations posed in problems with mathematical concepts, relationships, diagrams, and symbolic expressions; manipulating and reasoning about those representations to derive new information; making predictions based on the results; and verifying predictions in the original problem situation (Lesh and Doerr 2003; Lesh and Zawojewski 2007). During the process of modeling, students apply what they already know as well as build and deepen their mathematical understanding of new mathematical content. For these reasons, modeling is important, which may be why the Common Core State Standards for Mathematics (CCSSI 2010) emphasizes the topic as not only a conceptual category in the high school curriculum but also a Standard for Mathematical Practice. As such, mathematical modeling should be part of mathematics learning, starting in the early grades. This implies that modeling is not an area of mathematics to be taught in isolation, but one that should permeate across content in the curriculum for all grades. In this article the authors consider the opportunities that students have to engage in tasks that strongly support modeling practices as well as those in which modeling is less visible. They describe examples of two types of tasks from existing curricula and online resources to illustrate their potential for supporting students in their modeling endeavors.