Designing Coherent Math Systems with Pivotal Progressions™
Every student deserves math instruction that builds understanding and nimble mathematical skills over time. Pivotal Progressions™ help systems focus on the mathematical ideas that matter most to keep all students moving forward in a rapidly changing future.
Explore the ReportKeeping all students in the math.
Math is more than a set of procedures—it’s a way of thinking that helps students make sense of the world, solve problems, and open doors to future opportunity.
Every student deserves consistent access to math instruction that builds deep understanding over time—not just the ability to get correct answers, but the ability to reason, connect ideas, and apply their learning in new situations. When systems get this right, students develop confidence, persistence, and the skills needed for college, careers, and life.
But this level of learning doesn’t happen by chance. Designing a Coherent System for K–5 Mathematics explores what must intentionally be in place to support how mathematical understanding actually develops.
A Way Forward: Introducing Pivotal Progressions™
The Challenge: Why Current Approaches Fall Short
Across the country, school systems have made significant investments in curriculum, assessments, and Multi-Tiered Systems of Support (MTSS). Yet many leaders see the same persistent challenges:
- Students who appear successful in the moment but struggle later
- Intervention systems that feel disconnected from grade-level learning
- Unclear signals about when students need support—and what support will help
- Wide variation in student experience and teaching quality across classrooms and schools
These challenges are not just about effort. They are about design. Too often, systems are organized around performance levels or isolated skills, rather than the underlying mathematical ideas students must develop to keep progressing.
Pivotal Progressions™ offer a clearer, more coherent approach to designing math systems that keep students in the math no matter where they start.
Why We Created a Coherence Framework for K–5 Mathematics
Pivotal Progressions™ identify the small number of high-leverage conceptual shifts in each grade that unlock access to future mathematics. Rather than treating all standards as equally important, Pivotal Progressions™ help systems focus on what matters most:
- The ideas that shape how students think, not just what they can do
- The learning that compounds over time
- The concepts that, if underdeveloped, create barriers in later grades
When these ideas are strong, students accelerate. When they are fragile, gaps compound—even if students appear successful in the short term.
Get Started
Pivotal Progressions™ are part of a broader, system-level approach to coherence:
A small set of clearly defined progressions creates shared priorities across classrooms, schools, and roles.
Progressions show how understanding develops—not just what students should know at a single point.
These are predictable moments in instruction where student thinking becomes visible, allowing educators to gather meaningful evidence without over-testing.
Additional support is organized around the concepts students need to develop—not just where they are placed in a system.
Curriculum, instruction, assessment, and intervention all reinforce the same learning goals, creating a more connected experience for students and educators.
The Difference We Can Make Together
Improving math outcomes isn’t about adding more initiatives—it’s about doing less better and creating coherence around what matters most.
When systems align around a shared understanding of how students learn mathematics, improvement becomes more focused, more sustainable, and more impactful. Students experience math as a connected journey. Educators gain clarity and confidence. Leaders can make high-impact decisions that last.
Let’s work together to design a math system where every student stays in the learning—and moves forward with confidence.
Schedule a conversation with our team to explore how Pivotal Progressions™ can help you achieve your goals.
Meet the Designers & Contributors
Dr. Shelbi Cole
Juri Tyrrell
Michael Dang
Amber Walker
George Werres
Ginny James
About Dr. Shelbi Cole
Before joining Leading Educators, Dr. Cole was a Math Director at Student Achievement Partners, leading national projects in partnership with states, districts, nonprofits, and curriculum developers. She previously served as Director of Mathematics for the Smarter Balanced Assessment Consortium, leading the multi-state collaborative in developing an assessment system from the ground up following the release of the Common Core State Standards. Dr. Cole currently serves as the chair for the Inclusion and Accessibility in Educational Assessment Special Interest Group for the American Educational Research Association (AERA) and is a member of the Smarter Balanced Technical Advisory Committee.
Dr. Cole began her career as a high school math teacher and holds a Ph.D. in Educational Psychology from the University of Connecticut. Outside of work, she enjoys boating near Tampa Bay and spending time with her four children.
About Juri Tyrrell
Her work contributes to four key grant goals: improving student outcomes in mathematics through stronger achievement and mathematical self-efficacy; enhancing mathematics instruction by increasing teacher self-efficacy and practice in prioritized areas; building durable schools with systems to sustain teacher development and student achievement; and developing a more coherent, connected professional learning system for continuous district improvement.
Juri focuses on building sustainable and coherent professional development that ensures ongoing, job-embedded, curriculum-focused, and differentiated professional learning with supported schools and partners. Drawing on her deep knowledge of standards-aligned instruction and master-level coaching skills, she guides adult learning grounded in observation, data, and student artifacts.
Juri holds a bachelor's degree from the University of Texas Pan American. When not working, she enjoys spending quality time with her family at the beach, cheering on one daughter at flag football games, and watching her other daughter enjoy sushi.
About Michael Dang
As an instructional coach, he supports teachers to strengthen their practice, facilitates collaboration in teams, and develops vision and strategy with school leaders to solve complex problems. Prior to Leading Educators, he served as a classroom teacher the 8 years. Michael has taught CC Math 7, CC Math 8, Science 7, Algebra 1, Computer Science, and Introduction to Design in diverse classrooms and earned National Board Certification in Math.
Additionally, Michael worked as a UX Researcher for web-based B2C platforms and service design. He is particularly passionate about solving problems in the edtech space using the Design Process.
About Amber Walker
Originally from Somerset, NJ, Amber received her Bachelor of Arts in International Affairs and Economics from Northeastern University. She continued her education at Stanford University, earning a Master of Arts in Education with a concentration in Secondary Mathematics. She is currently pursuing her Doctorate of Education at the University of San Francisco.
Outside of work, Amber enjoys cooking, exploring the food scene in cities across the world, traveling, hiking, and yoga.
About George Werres
Prior to joining the LE staff, he worked at Teach for America training and supporting instructional coaches and corps members. During his 12 years in the classroom, he spent the majority of his time teaching 3rd and 4th grade, and he spent multiple years as a Director of Curriculum and Instruction supporting grades 3-8. LE has a special place in his heart, as he was also a member of LE’s 2012 Cohort.
George has a Masters in Elementary Education and BS in Psychology from Indiana University. He lives in New Orleans and is active in multiple Stonewall Sports leagues. He enjoys playing video games and walking his dog, Rex, on the bayou.
George Werres in the news
About Ginny James
Before joining Leading Educators, Ginny worked as the Special Education Manager for KIPP SoCal, supporting teachers to provide inclusive, strengths-based instruction for students in both general and special education settings. She started her career as a teacher at the University of Chicago Charter School serving students with various learning needs. She then worked as an Instructional Coach for the Academy of Urban School Leadership coaching and providing professional learning to teachers within the Chicago Public School district.
Ginny holds a master's degree in childhood and special education from New York University. She currently lives in Long Beach, CA where she and her husband share their love of travel, sports, and food with their 2 daughters.
