Modeling with Mathematics: Authentic Problem Solving in Middle School

“Nancy’s in-depth look at mathematical modeling offers middle school teachers the kind of practical help they need for incorporating modeling into their classrooms.”
―Cathy Seeley, Past President of NCTM, author of Faster Isn’t Smarter and Smarter Than We Think

Modeling is Math at its Most Powerful

We all use math to analyze everyday situations we encounter. Whether we realize it or not, we’re modeling with mathematics: taking a complex situation and figuring out what we need to make sense of it. In Modeling with Mathematics, Nancy Butler Wolf shows that math is most powerful when it means something to students. She provides clear, friendly guidance for teachers to use authentic modeling projects in their classrooms and help their students develop key problem-solving skills, including:

• collecting data and formulating a mathematical model
• interpreting results and comparing them to reality
• learning to communicate their solutions in meaningful ways.

Support for Incorporating Modeling Into Your Instruction

This kind of teaching can be challenging because it is open-ended: it asks students to make decisions about their approach to a scenario, the information they will need, and the tools they will use. But Nancy proves there is ample middle ground between doing all of the work for your students and leaving them to flail in the dark.

Through detailed examples and hands-on activities, Nancy shows how to guide your students to become active participants in mathematical explorations who are able to answer the question, “What did I just figure out?” Her approach values all students as important contributors and shows how instruction focused on mathematical modeling engages every learner regardless of their prior history of success or failure in math.

Max Ray-Riek is a curriculum writer at Illustrative Mathematics and is the lead author of Powerful Problem Solving: Activities for Sense Making with the Math Practices. He previously worked for The Math Forum, focusing on fostering problem solving, communication, and valuing student thinking. Max is a former secondary mathematics teacher who regularly presents at regional and national conferences.

Watch Max and Suzanne Alejandre talk about giving students effective feedback.

Follow him on Twitter @maxmathforum.

 

 

Nancy Butler Wolf, Ph.D., is a national math consultant and curriculum developer who has served as a member of NCTM’s Illuminations Writing Group. She has over 30 years of classroom teaching experience and has presented at various conferences on mathematical modeling and algebraic reasoning.