ABSTRACT
This chapter provides a rationale for changing the structure of the mathematics classroom and a methodology to enable students to reason mathematically in our ever-advancing world. Mathematical understanding and procedural skills are what all educators desire to develop in their students. The key to developing both conceptual understanding and procedural fluency is for students to engage in rich mathematical tasks. The Common Core State Standards further explain that modeling mathematically involves making assumptions, approximations, simplifying complex situations, reflecting on results, and modifying results as necessary. Textbook word problems often deter students from the mathematical practices because the problems follow a predictable format. Modeling mathematics is more complex. In addition to meeting the demands of the standards, modeling mathematics is supported by the current research on teaching and learning mathematics. Project-based learning involves students engaging in an extended process of inquiry in response to a complex question, problem, or challenge.
