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Comprehending Problem Solving (eBook)

Building Mathematical Understanding with Cognition and Language

By Arthur Hyde
Foreword by Ellin Oliver Keene

Learn to leverage rich activities, language, and how children learn to create classrooms where deep mathematical understanding is achieved. Whether you aim to overhaul how your instruction or enhance the strategies you already use, this book will be an invaluable resource for the journey.


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Web/School Price: $17.50


Full Description

Nationally recognized mathematics educator and author Art Hyde takes a culminating look at his thirty years of experience working with teachers and students to answer the question:  In the Common Core era, what are the most successful practices for helping children solve mathematical problems with deep understanding?  The key , he argues, is providing positive experiences with meaningful mathematics centered around rich activities.  When students are given the opportunity to wrestle with appropriately difficult activities based on real life situations and intriguing contexts, they become excited about the math and willingly tackle problems with more zeal and accuracy than ever before.  The result is deeper understanding of the content and greater skill at doing mathematics.

Art draws on extensive research on how children learn and the relationship between reading and mathematical comprehension.   His braided model of problem solving in which cognition, language, and mathematics are woven together intentionally forms the basis of math activities that he and numerous elementary teachers around the country have used.  Look into the classrooms of some of these math teachers in this book, as they share their success stories illustrating the rewards of using these activities to foster deep mathematical understanding.

Arthur Hyde is a professor of mathematics education at National Louis University, where he received its Excellence in Teaching award. While teaching high school mathematics in Philadelphia, he developed a variety of creative methods for teaching math. He also obtained a doctorate in curriculum and instruction from the University of Pennsylvania, where he later directed its teacher-education programs. He has worked frequently in elementary classrooms, conducting extensive professional development programs on teaching mathematics and math problem solving in Chicago and its surrounding school districts. His previous books include: Best Practice, Fourth Edition (coauthored with Steven Zemelman and Harvey Daniels), Understanding Middle School Math, and Comprehending Math.

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Foreword by Ellin Oliver Keene

CHAPTER 1 Attending to Cognitive Processes
CHAPTER 2 Attending to Language Issues
CHAPTER 3 Broadening the Definition of Problem Solving
CHAPTER 4 Mathematical Modeling and Problem Solving
CHAPTER 5 Exploring the Braid Model of Problem Solving
CHAPTER 6 Planning for and Implementing the Braid Model

Appendix: Resources for Teaching Mathematics



Chocked full of pedagogical insights, real life classroom examples and juicy math problems, Art Hyde’s newest book offers elementary school teachers the frameworks and resources they need to catalyze students’ mathematical understanding. Integrating theories of cognition, comprehension, language learning and problem solving, the text offers readers the practical tools they need to vigorously engage all young learners as successful mathematicians.

Wendy Ward Hoffer, author of Minds on Mathematics

[Art] has helped those of us who considered ourselves math-phobic to shed the fear and even shame that came from our backgrounds with very inauthentic math instruction and embrace mathematical thinking as readily as we have embraced well-loved literature and writing the stories of our lives.

Ellin Oliver Keene, author of Mosaic of Thought, Second Edition

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Email if you would like to contact Arthur Hyde directly about professional development support.