About the Book
A schoolwide solution for students’ mathematics success!
Do you sometimes start to teach a mathematics concept and feel like you’re staring at a sea of bewildered faces? What happens when you discover students previously learned a calculation trick or a mnemonic that has muddied their long-term understanding? When "rules" seem to change from year to year, teacher to teacher, or school to school, mathematics can seem like a disconnected mystery for students. Clear up the confusion with a Mathematics Whole-School Agreement!
Expanded from the highly popular "Rules that Expire" series of NCTM articles, this essential guide leads educators through the collaborative step-by-step process of establishing a coherent and consistent learner-centered and equitable approach to mathematics instruction. Through this work, you will identify, streamline, and become passionate about using clear and consistent mathematical language, notations, representations, rules, and generalizations within and across classrooms and grades. Importantly, you’ll learn to avoid "rules that expire"—tricks that may seem to help students in one grade but hurt in the long run. Features of this book include:
• Abundant grade-specific examples
• Effective working plans for sustainability
• Barrier-busting tips, to-dos, and try-it-outs
• Practical templates and checklists
• PLC prompts and discussion points
When teachers unite across grades, students hit the ground running every year. Take the next step together as a team and help all your students build on existing understanding to find new success and most importantly, love learning and doing mathematics!
Table of Contents:
Foreword by Matthew R. Larson, and Robert Q. Berry III
About the Authors
Acknowledgments
Preface
Chapter 1: Jumping on Board: What is the Mathematics Whole School Agreement?
Chapter 2: Watching What We Say! Correct and Consistent Language
Chapter 3: Symbol Sense is Foundational: Noting the Importance of Precise Notation
Chapter 4: Mental Images that Last: Cohesive and Consistent Representations
Chapter 5: Why was I Taught That? Evaluating Rules that Expire
Chapter 6: Building Generalizations: Developing Instructional Strategies the MWSA Way
Chapter 7: Embodying the MWSA in Every Lesson: No Teaching by Telling!
Chapter 8: Getting to the Nitty Gritty: Building and Enacting the MWSA
Chapter 9: Sharing Successes from the Field: MWSA Heroes Tell their Stories!
References
Index
About the Author :
Barbara J. Dougherty is the past director of the Curriculum Research & Development Group and a professor in the College of Education at the
University of Hawai‘i at Mãnoa. She is a former member of the board of directors of the National Council of Teachers of Mathematics and is the
co-chair of the Mathematics/Special Education Workgroup, a partnership between the NCTM and the Council for Exceptional Children. She served
on the author panel for the What Works Clearinghouse Practice Guide on assisting elementary school students who have difficulty learning mathematics for the U.S. Department of Education Institute of Education Sciences. She is the author or coauthor of approximately 22 book chapters, 29 articles, and 36 books, including MPower: A Pathway to Understanding Algebra. Her research, funded by more than $11.5 million in grants, emphasizes supporting students who struggle in middle and high school, with a focus on algebra. She holds teaching certifications in middle and high school mathematics and K–12 special education.
Dr. Sarah B. Bush, a former middle school mathematics teacher, is a Professor of K–12 STEM Education and the Lockheed Martin Eminent Scholar Chair at the University of Central Florida. At the University of Central Florida, she is the Director of the Lockheed Martin/UCF Mathematics and Science Academy and is a program co-coordinator of the Mathematics Education PhD track. She teaches primarily graduate courses in mathematics education. She is a prolific writer who has authored 13 books and more than 100 journal articles and book chapters. Dr. Bush recently completed a term (2019–2022) as a member of the National Council of Teachers of Mathematics Board of Directors. She served as the lead writer and task force chair for NCTM’s Catalyzing Change in Middle School Mathematics: Initiating Critical Conversations. Dr. Bush was the recipient of the 2021 School Science and Mathematics Association (SSMA) Award for Excellence in Integrating Science and Mathematics and 2018 recipient of the Association of Mathematics Teacher Educators (AMTE) Early Career Award. Dr. Bush seamlessly integrates her practical experience as a middle school mathematics teacher in public schools with her innovative scholarship to serve as an instructional leader in the field of mathematics education and STE(A)M education. Dr. Bush co-wrote the Simplifying STEM: Four Equitable Practices to Inspire Meaningful Learning: PreK-5 and 6-12 books published by Corwin in early 2024.
Karen S. Karp is a mathematics educator who focuses on the intersection of mathematics education and special education. She is a former professor at Johns Hopkins University and at the University of Louisville where she is professor emerita. Early in her career she received a Development Award from the Joseph P. Kennedy, Jr. Foundation to support more seamless integration between general education and special education. She is the author or co-author of numerous publications including Assisting Students Struggling with Mathematics: Intervention in the Elementary Grades and Elementary and Middle School Mathematics. Karen was on the writing team of the NCTM/CEC Joint position statement on Teaching Mathematics to Students with Learning Disabilities. In 2024, she chaired the Topic Study Group on Teaching Mathematics to Students with Special Needs at the International Congress on Mathematical Education in Australia. She holds teaching/administrative certifications in elementary education, secondary mathematics, K-12 special education, and K-12 educational administration.
Review :
"Dougherty, Bush, and Karp are offering you their entire playbook for scaling effective teaching beyond individual teachers to an entire school. Their Math Pact will support everyone in a school, even people who wish they were more comfortable with math, to help students learn math in ways that make sense and endure across grades."
"This book brilliantly connects research-informed practices to empower stakeholders in engaging students in meaningful mathematics through
a vertically articulated Mathematics Whole School Agreement! Building on the impact of the Rules That Expire series, the authors lay out an easy to implement approach to share, connect, and represent mathematical ideas across classrooms to intentionally and explicitly bring about change prior, during, and after instruction."
"These books provide effective steps and strategies toward students being able to make powerful, purposeful connections across grade levels and across a wide variety of mathematical concepts."
"How can you ensure you have equitable instruction that strengthens students’ beliefs that they can understand and use mathematics in a variety of contexts? A starting point is to have a Mathematics Whole School Agreement (MWSA) in which there is a unified approach to how mathematics is communicated in a consistent manner across grade levels and courses. With this collective approach, disjointed approaches that lead to confusion and gaps in conceptual understanding will be gone. The Math Pact: Achieving Instructional Coherence Within and Across Grades, High School is your guide to creating and implementing your own MWSA."
"If you have anything to do with transforming mathematics teaching and learning at your school, then stop everything right now and read this book. Dougherty, Bush, and Karp’s The Math Pact strategically navigates the complex topic of creating and cultivating cohesive mathematics instruction by introducing readers to their Mathematics Whole School Agreement and specific elements that ensure schoolwide success. Building on their renowned Rules That Expire work, this book takes readers through the essential components of best practices of mathematics teaching. This should be a required read for any mathematics leadership program."
"This is a long-awaited publication that will help preservice teachers, educators, and administrators of all levels and curriculum coordinators abolish the use of tricks and magic in mathematics instruction. For years we have inadvertently led students down a dead-end street in their math instruction by teaching them expiring rules, tricks, and cutesy sayings that may help them perform short-term on a test but leave them conceptually damaged in the long run."
"Finally, a practical guide to ensuring equitable, coherent instruction for all students in your school district! Broader than collaboration and more effective than a PLC, establishing a Mathematics Whole School Agreement (MWSA) is a common sense approach to taking the next step beyond having a common curriculum."
"Maya Angelou said, ′Do the best you can until you know better. Then, when you know better, do better.′ The Math Pact is a practical guide that supports us in collectively taking responsibility for helping each and every one of our students to become problem solvers, critical thinkers, and capable and confident doers of mathematics. The detailed vignettes and suggestions are vivid guideposts for a journey of self reflection and collective decision making with colleagues about really critical components of mathematics instruction. It will leave you both ′knowing better′ and collectively ′doing better′ for your students. No matter your level of experience, there is something new to learn here! I think it would work beautifully with pre-service teachers, new teachers, and veteran teachers. I even picked up some new things on my read that I hadn’t really thought about in my nearly 30 years in the classroom."
"The Math Pact is the perfect resource for groups who are seeking to put students first and create cohesive, thoughtful agreements to support students’ learning of mathematics. The Math Pact leverages the NCTM Mathematics Teaching Practices to encourage mathematics teaching that is grounded in effectiveness and puts learning at the forefront of decision making. As a mathematics teacher educator, I appreciate the stress on the precision and consistency with mathematical vocabulary, notation, and meaning-making. The strategies stressed in The Math Pact align with the collaborative and professional nature of teaching—that is, teachers work best when they are working as a cohesive team. Sending the same message to students is appreciated by teachers, administrators, coaches, students, and parents.
The structure of The Math Pact offers opportunities for learning communities to reflect and foster change through learning, discourse, and action. From overarching ideas such as "no teaching by telling" to more intricate details, such as considering the frequency, purpose, and nature of homework assignments, The Math Pact provides insight into a myriad of mathematical issues that allow teams to construct Mathematics Whole School Agreements that consider the nature and needs of their students and promote efficiency and consistency."
