Comprehending Problem Solving: Building Mathematical Understanding with Cognition and Language

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.

Ellin Oliver Keene has been a classroom teacher, staff developer, non-profit director and adjunct professor of reading and writing. For sixteen years she directed staff development initiatives at the Denver-based Public Education & Business Coalition. She served as Deputy Director and Director of Literacy and Staff Development for the Cornerstone Project at the University of Pennsylvania for 4 years. Ellin works with schools and districts throughout the country and abroad. Her emphasis is long-term, school-based professional development and strategic planning for literacy learning.

Ellin recently published The Literacy Studio: Redesigning the Workshop for Readers and Writers which is focused on an up-to-date conceptualization of Readers/Writers' workshop. She is the author of Engaging Children: Igniting the Drive for Deeper Learning (2018), is co-editor and co-author of The Teacher You Want to Be: Essays about Children, Learning, and Teaching (Heinemann, 2015); co-editor of the Not This, but That series (Heinemann, 2013 - 2018); author of Talk About Understanding: Rethinking Classroom Talk to Enhance Understanding (Heinemann, 2012), To Understand: New Horizons in Reading Comprehension (Heinemann, 2008), co-author of Comprehension Going Forward (Heinemann, 2011), co-author of Mosaic of Thought: The Power of Comprehension Strategy Instruction, 2^nd edition (Heinemann, 2007, 1^st edition, 1997) and author of Assessing Comprehension Thinking Strategies (Shell Educational Books, 2006) as well as numerous chapters for professional books and journals on the teaching of reading as well as education policy journals.

Arthur Hyde is the author or coauthor of the Heinemann titles Understanding Middle School Mathematics; Comprehending Math; Best Practice, Fourth Edition; and Mathwise. A professor of mathematics education at National-Louis University, 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 was Associate Director of Teacher Preparation. He continues to work frequently in elementary and middle school classrooms and conducts extensive professional development programs on mathematics and problem solving in Chicago and its surrounding school districts.