Reflections on Modeling and Teaching Modeling

Solomon Garfunkel’s delightful reflection on the 40th anniversary of COMAP [2022] reminded us that our book, How to Model It: Problem Solving for the Computer Age [Starfield, Smith, and Bleloch 1990], has passed its 30th anniversary and is still going strong. We appreciate the opportunity to reflect on the ideas that prompted the book, our modeling philosophy, and the implications and applications of our ideas. These ideas have, of course, evolved since the book was written, becoming more organized and explicit. We hope that they will help reinvigorate the movement to emphasize the development of modeling thinking.

We focus first on the background and philosophy behind the book and our thoughts on the principal aspects and core features of modeling. We then discuss our pedagogical approach to developing modeling thinking skills and their implementation in mathematical and computational thinking courses. Finally, we offer some insights and lessons learned.