About the Book
A school-wide 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
Acknowledgements
Preface
Chapter 1: Jumping on Board: What is the Mathematics Whole School Agreement?
Chapter 2: Watching What We Say! Using 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 :
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.
Barbara J. Dougherty is a former professor at the University of Hawai‘i where she was Director of the Curriculum Research & Development Group. Her research foci include determining ways to better support students who are struggling in mathematics and teaching algebra for understanding. She is the author or co-author of multiple publications including Assisting Students Struggling With Mathematics: Interventions in the Elementary grades and MPower: A Pathway to Understanding Algebra. Barbara was the co-chair of the joint NCTM/CEC task force and on the writing team of the NCTM/CEC joint position statement on Teaching Mathematics to Students with Learning Disabilities. She has been principal investigator or co-principal investigator of National Science Foundation and U. S. Department of Education grants that have provided funding to develop intervention modules for middle and high school and progress monitoring tools. She holds current teaching certifications in middle and high 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.
Review :
"If you have anything to do with transforming mathematics teaching and learning at your school, then stop everything right now and read this book. Karp, Dougherty, and Bush’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 the authors’ 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."
"Just for a moment, imagine the positive and impenetrable mathematics energetic forcefield that could be created in a school if every teacher strategically and collaboratively decided upon agreements around mathematics vocabulary, notations, representations, and the
overarching philosophy about how mathematics should be taught? Guess what! You do not have to imagine! No more reteaching, revising previously taught material, and explaining that "Well, in my classroom, we do it, say it, notate it this way." Because let’s face it, those messages confuse students and families and can frustrate teachers. Grab this book, gather your colleagues, and get started in creating a unified and comprehensive whole school agreement that will positively enrich your students’ mathematics learning experiences!"
"As a fan of the "Rules That Expire" and "Whole School Agreement" articles, I consider this resource a welcome addition to my professional library! In this practical, easy-to-follow book, the authors provide educators with an extremely thorough and useful "go to guide" on establishing a Mathematics Whole School Agreement (MWSA). For those not familiar with the NCTM articles that initiated the movement, this resource defines what an MWSA is and why each school should establish one. More important, educators learn how to create and implement an MWSA, and the role each school and district stakeholder plays in implementation. This user-friendly resource provides teachers, teacher leaders, parents, and administrators with a comprehensive blueprint that includes research-informed practices, vignettes, grade-specific examples, and tools to encourage reflection."
"The Math Pact is a critical guide that takes stakeholders on a journey to create a Mathematics Whole School Agreement (MWSA). This journey begins with a look inward at mathematics instruction in their schools and then moves onward to compare their practices to best practices. Stakeholders arrive at their MWSA when they can ensure a unity of message that promotes coherent and effective instruction within their school and even across their district."
"The Math Pact is an essential resource for educators looking to develop and support a coherent schoolwide approach to the teaching and learning of mathematics. The authors provide clear guidelines with examples and references to numerous resources that will support you and your colleagues as you develop a shared vision for you and your students in mathematics education."
"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."
"The Math Pact will surely be hailed a seminal work in the field for years to come! The authors outline a crystal-clear, research-supported case for a unified approach to mathematics instruction. The embedded reflection opportunities and suggested parent communications make a Mathematics Whole School Agreement possible for everyone."
"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."
"Wow! The Math Pact will lead the movement to help educators and students overcome the idea that math is a mysterious set of "tricks and shortcuts." The Mathematics Whole School Agreement process provides the steps, language, representations, and knowledge to build, implement, and sustain equitable learning outcomes for all students! The power to make change is in our collective hands and hearts! This book needs to be in the hands of all teachers, district leaders, and stakeholders."
"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."
"This is the perfect balance of inspiration and practical guidance! The inspiration motivates me to work harder at collaboration with peers, building common commitment. The practical guidance helps me put the ideas into action around what specific changes will improve mathematics teaching and learning."
