“Making Sense of Algebra is a vivid application of the ‘habits of mind’ perspective that has become a trademark of these EDC authors. It helps put flesh on the mathematical practice standards. More than algebra, it is about mathematical ways of thinking, problem solving, and seductively accessible entrees into adventurous new mathematical territories. Unlike many discussions of mathematical practices, its rhetoric is quickly and abundantly brought alive by concrete and inventive examples, at various levels of mathematical sophistication, and with motivational insightfulness. This book has much to offer teachers of middle and high school algebra who wish to implement the Common Core Standards for all of their students.”
—Hyman Bass, Samuel Eilenberg Distinguished University Professor of Mathematics & Mathematics Education, University of Michigan
“Making Sense of Algebra provides a window onto algebra as a realm for posing questions, noticing structure, and reasoning with a variety of tools. Presenting a range of problems designed to help students develop ‘mathematical habits of mind,’ this book is an essential guide for teachers of algebra who want to engage their students as thinkers, especially those who struggle.”
—Deborah Schifter, Education Development Center, coauthor of Connecting Arithmetic to Algebra
“One of the joys of Making Sense of Algebra is how clearly and practically the ‘how’ question is answered. Not only are we provided with wonderful ‘low threshold, high ceiling’ examples, but we are also shown how to transfer these examples directly to algebra lessons along with insightful and honest guidance on advantages and disadvantages, pitfalls and opportunities, important ideas, and connections to algebraic thinking.”
—Steven Leinwand, American Institutes for Research, author of Accessible Mathematics
“Paul Goldenberg and his colleagues have done a fantastic job of connecting mathematical ideas to teaching those ideas. A teacher who may be unfamiliar with multiple models of describing mathematical ideas is presented in an engaging and interesting way with many different representations that can help extend their knowledge of mathematics. Similarly the authors offer practical advice a teacher can use to support their students in developing their understanding. The authors present a coherent argument of why puzzles should have a place in math classrooms and how these puzzles can help struggling learners re-engage with mathematics.”
—David Wees, formative assessment specialist in mathematics, New Visions for Public Schools, New York City
“As a teacher who uses the Transition to Algebra curriculum, Making Sense of Algebra is the perfect companion. It does much more than the title suggests; it helps teachers make sense of the mathematical thinking students are developing in their classes. With the inclusion of ideas for incorporating cognitive development and processing, executive functioning, and interventions for students with mathematical difficulties, Making Sense of Algebra is a great addition to any special education math teacher’s book shelf.”
—Andrew Gael, special education teacher, New York City, blogs at The Learning Kaleidoscope
“Rare is the resource that offers first-person accounts of teacher experience and insight, accompanied by broad and deep knowledge of the research literature. This book fits the bill, and does so with clarity, warmth, and humor. A good example is the chapter ‘A Geometric Look at Algebra,’ in which the authors use the geometry of the number line to integrate conceptions of operations in arithmetic with operations in algebra. Recent research is very clear: a facility with number-line representations of the magnitude of rational numbers is foundational to success in learning algebra.”
—Mark Driscoll, Education Development Center, author of Fostering Algebraic Thinking
