Designing Coherent Math Systems with Pivotal Progressions™
Keep every student progressing in math no matter where they start with Pivotal Progressions™, the high-leverage conceptual shifts in each K–5 grade that unlock access to future mathematics, developed by Leading Educators.
Keeping all students in the math.
Every student deserves 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 to future questions in new situations. When systems get this right, students develop confidence, persistence, and the skills needed for a rapidly changing world.
This kind of learning doesn’t happen by chance. Designing a Coherent System for K–5 Mathematics explores what must intentionally be in place to develop students’ mathematical understanding over time.
Introducing Pivotal Progressions™
Central Question: How can we more effectively see and understand where students are in their math journey?
Imagine two kindergartners solving 5 + 3. Both say 8. One counts every object from the beginning. The other starts at 5 and counts on: “6, 7, 8.”
Same answer. But something important is different in their thinking. The second student is beginning to understand 5 as a quantity they can work from—not simply a number they reach while counting.
If an educator, tutor, or parent can’t recognize these pivotal shifts in understanding, how do they know what supports each student needs to keep moving forward?
That’s the thinking behind Pivotal Progressions™, an emerging concept that works alongside standards to map how mathematical ideas build on one another and enable future mastery.
Where Current System Approaches Fall Short
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.
Too often, advancement is organized around performance levels or isolated skills, rather than the underlying mathematical ideas students must develop to keep progressing.
What Our Coherence Framework for K–5 Mathematics Offers
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.
Explore With Us
Come Learn With Us! Webinar on October 22
Want to hear more about this concept directly from the lead designers and educators who are using it right now? Join us for “Pivotal Progressions™ for K-5 Mathematics: Keeping All Children in the Learning”, an interactive dialogue on how having a deeper understanding of how conceptual knowledge builds over time can enable better support for students.
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.
Schedule a conversation with our team to explore how Pivotal Progressions™ can help you achieve your goals.
Meet the Designers & Contributors
Dr. Shelbi Cole
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 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.
