Making Sense of Algebra: Developing Students' Mathematical Habits of Mind

"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

"One of the joys of Making Sense of Algebra is how clearly and practically the 'how' question is answered."
-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."
-David Wees, New Visions for Public Schools, New York City

Every teacher wants to help students make sense of mathematics; but what if you could guide your students to expect mathematics to make sense? What if you could help them develop a deep understanding of the reasons behind its facts and methods?

In Making Sense of Algebra, the common misconception that algebra is simply a collection of rules to know and follow is debunked by delving into how we think about mathematics. This "habits of mind" approach is concerned not just with the results of mathematical thinking, but with how mathematically proficient students do that thinking. Making Sense of Algebra addresses developing this type of thinking in your students through:

• using well-chosen puzzles and investigations to promote perseverance and a willingness to explore
• seeking structure and looking for patterns that mathematicians anticipate finding-and using this to draw conclusions
• cultivating an approach to authentic problems that are rarely as tidy as what is found in textbooks
• allowing students to generate, validate, and critique their own and others' ideas without relying on an outside authority.

Through teaching tips, classroom vignettes, and detailed examples, Making Sense of Algebra shows how to focus your instruction on building these key habits of mind, while inviting students to experience the clarity and meaning of mathematics-perhaps for the first time.

Discover more math resources at Heinemann.com/Math

E. Paul Goldenberg has led a wide range of projects during his 28 years at EDC, fostering love and enthusiasm for mathematics from early learners through adulthood. Among his projects is the comprehensive K-5 Think Math! program. Paul has taught every age and type of student, and raised four sons of his own. Along with Al Cuoco and June Mark, he has authored articles focused on a habits-of-mind approach to mathematics education. Dr. Goldenberg studied psychology, mathematics, and education at Brandeis and Harvard.

June Mark brings over twenty years of experience in research and development related to mathematics instructional materials, curriculum implementation, and mathematics teacher professional development. June received her BS (Mathematics) and BSE from the University of Pennsylvania and her Ed.M. from the Harvard Graduate School of Education. She has been involved in a numerous mathematics education projects, many centering on bringing high quality mathematics to underserved populations. Outside of work, she enjoys spending time with her family including her kids, Michael and Lena. June Mark is the coauthor of four Heinemann titles: Lesson Study in Practice: A Mathematics Staff Development Course (2010), A Mathematics Leaders Guide to Lesson Study in Practice (2010), The Fostering Geometric Thinking Toolkit (2008), Choosing a Standards-Based Mathematics Curriculum (2000) and Transition to Algebra: Make Algebra Make Sense (2014).

Jane M. Kang brings seven years of mathematics teaching experience at Charlestown High School in Boston to this project. She has a strong belief in reflection and classroom discussions as key elements to teaching mathematics. She received her B.A. in Chemistry, M.Ed. in International Education Policy, and M.A. in Mathematics for Teaching, all from Harvard University. Jane is also a serious musician, playing violin in various orchestras and ensembles in the Boston area.

Mary Fries is a former high school mathematics teacher and dean with an interest in innovative materials development and issues of equity in education - particularly critical mathematics education. She has a B.S. in Mathematics, an M.A. in Philosophy and Religion, and a C.A.G.S. in Mathematics Education. She lives in Boston and enjoys painting, yoga, and contemplating the nature of reality through spirituality and physics.

Cynthia J. Carter teaches mathematics to sixth and eighth grade classes that complete algebra 1 and study significant parts of geometry and algebra 2 by the end of eighth grade. She also teaches seventh grade classes that have historically struggled and are just beginning the transition to algebra. She holds an A.B. in a triple major in mathematics, economics, and urban studies from Brandeis University, and an A.M. and a.b.d. in psychology and social relations from Harvard University. Cindy has co-authored other books in mathematics and education, and has also worked as an econometrician, a mathematics teacher coach, and a mother of four wonderful boys.