Modeling with Mathematics (Print eBook Bundle) by Nancy Butler Wolf.
Modeling with Mathematics (Print eBook Bundle)
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Modeling with Mathematics (Print eBook Bundle)

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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Full Description

“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

“This is the book that math teachers and parents have been waiting for. Nancy provides a comprehensive step-by-step guide to modeling in mathematics at the middle school level.”
—David E. Drew, author of STEM the Tide: Reforming Science, Technology, Engineering, and Math Education in America

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.

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.

Contents

Foreword

Chapter 1 Introduction: Modeling with Mathematics

  • What is Mathematical Modeling?
  • The Process of Modeling?
  • Why Modeling?
  • Mathematical Autonomy

Chapter 2 Rich Mathematical Modeling Tasks

  • Characteristics of Rich Modeling Tasks
  • Word Problems versus Modeling Tasks
  • Finding Rich Mathematical Modeling Tasks

Chapter 3  Investigation and Problem Identification

  • Getting Started: Student Autonomy
  • The Teacher's Role
  • More Problem Identification: Old MacDonald's Farm
  • 1000 Paper Cranes: Getting Started

Chapter 4 Mathematical Formulation of the Model, Data Collection, and Finding a Solution

  • Formulating a Model
  • Multiple Representations
  • The 1000 Cranes Problem: Formulating the Model and Collecting Data
  • Conclusion

Chapter 5 Interpreting the Solution and Comparing with Reality

  • The Importance of Interpretation
  • Interpreting the Solution
  • Examples of Students Interpreting Solutions
  • Conclusion

Chapter 6 Communicating and Implementing the Solution

  • Communicating the Solution
  • Multiple Representations
  • Implementing the Solution
  • 1000 Cranes Work

Chapter 7 Assessment of Mathematical Modeling

  • Goals of Assessment
  • Informal Assessment
  • Formal Assessments

Chapter 8 Conclusion

Samples

Companion Resources

Reviews

“Mathematical modeling is one of the hottest topics in the school curriculum. And one of the least understood. 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

“This is the book that math teachers and parents have been waiting for. Writing in clear and entertaining prose, Nancy provides a comprehensive step-by-step guide to modeling in mathematics at the middle school level. She shows that the new math standards need not be intimidating or confusing. Instead, students will learn how modeling relates directly to real life problems and decisions through a series of terrific examples. Unlike most books about mathematical modeling, this book is both thorough and accessible, focused and fun. A tour de force!”

—David E. Drew, author of STEM the Tide: Reforming Science, Technology, Engineering, and Math Education in America

“Nancy’s book is an excellent guide for middle school teachers who want to incorporate mathematical modeling in their classrooms. It provides both theoretical and practical discussions on how teachers can change their teaching so that their students become more independent and thoughtful problem solvers.”

Judith E. Jacobs, Past President of the Association of Mathematics Teacher Educators

“Between the stories, the examples, the extensive citing of research, and the way Nancy describes her own transformation as a teacher, I’m confident that you’ll be excited and ready to try modeling tasks with your students as soon as you finish this book.”

—Max Ray-Riek, author of Powerful Problem Solving

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Speakers

Email planningservices@heinemann.com if you would like to contact Nancy Butler Wolf directly about professional development support.