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Modeling with Mathematics

Authentic Problem Solving in Middle School

By Nancy Butler Wolf
Foreword by Max Ray-Riek

Help your students develop the ability to model and analyze complex situations mathematically. Through detailed examples  and hands-on activities, learn how instruction focused on mathematical modeling engages all students regardless of their prior history of success or failure in math.

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“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.

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