ACSI Research Fellow Program

In recent years, the education community has witnessed a significant shift in literacy instruction through the widespread adoption of the Science of Reading. Grounded in cognitive science and decades of research, this movement has reshaped how educators approach reading instruction—prioritizing explicit, systematic teaching of foundational skills. Mathematics is now at a similar turning point. Across K–12 education, there is growing recognition that math instruction should align with the science of how students learn. 

This is where the Science of Math comes in. 

The Science of Math is a research-informed framework that emphasizes explicit, systematic, and coherent instruction designed to build deep and lasting mathematical understanding. At its core, it integrates several essential and interconnected elements: conceptual understanding, procedural fluency, number sense, mathematical reasoning, and problem-solving. These are not isolated skills taught in silos; rather, they work together to develop students who can think flexibly, reason logically, and apply mathematics with confidence. 

A strong foundation begins with conceptual understanding—helping students grasp why mathematical processes work. Without this foundation, students may be able to follow procedures but struggle to transfer their knowledge to new or unfamiliar contexts. At the same time, conceptual understanding must be paired with procedural fluency and number sense. Students need consistent, meaningful practice so that foundational skills become accurate, efficient, and increasingly automatic. 

Cognitive science helps explain why this balance is so critical. Students’ working memory is limited, and when too many new ideas or strategies are introduced at once, cognitive overload can occur. This is especially true for novice learners. Research supports the use of explicit instruction—clear modeling, guided practice, and a gradual release of responsibility—before expecting students to independently generate strategies. While discovery-based learning has value, a poorly designed discovery -first approach can unintentionally increase cognitive load, which may lead to a gap in understanding. The developmental needs and prior knowledge of the students must be considered first. 

Another key component is mathematical reasoning. Students should be encouraged to explain their thinking, justify their solutions, and make connections across mathematical ideas. This not only deepens understanding but also strengthens critical thinking skills that extend beyond the math classroom. 

Similarly, problem-solving should be intentionally structured. Effective instruction provides opportunities for students to apply their learning in both real-world and abstract contexts, explore multiple strategies, and engage in mathematical modeling. Over time, this fosters perseverance and flexibility. 

An often-overlooked aspect of mathematics instruction is math language and vocabulary development. When students can clearly articulate their thinking using precise mathematical terminology, they are better equipped to engage in meaningful discourse and evaluate the reasoning of others. 

You may also hear the term productive struggle. While it is important for students to engage with challenging tasks, not all struggle leads to learning. Research indicates that struggle is most beneficial when it is appropriately scaffolded. Without sufficient background knowledge, tasks can exceed students’ cognitive capacity. Effective instruction strikes a careful balance—providing support while still encouraging independent thinking. 

Ongoing formative assessment and targeted feedback are also essential. Frequent checks for understanding allow teachers to identify misconceptions and adjust instruction in real time. Feedback should address not only correctness, but also strategy use and the development of mathematical thinking. 

For teachers and school leaders, these research-based insights point to several important priorities. High-quality math instruction should follow a coherent progression of skills, emphasize depth over breadth, limit the number of strategies introduced at one time, and prioritize mastery before expanding to additional approaches. 

Professional learning is equally important. When educators understand principles from cognitive science, such as managing cognitive load, sequencing instruction effectively, and supporting novice learners, they are better equipped to make informed instructional decisions and create classrooms where all students can succeed. 

Aligned with these principles, Purposeful Design Publications’ 3rd edition mathematics curriculum is standards-driven and grounded in a biblical worldview that connects mathematical truth to God’s design, equipping students for discernment. It integrates rigorous standards with explicit, systematic instruction based on the Science of Math, promoting conceptual understanding, procedural fluency, and meaningful problem-solving. This approach supports both academic excellence and character development, equipping students for lifelong learning. 

We invite you to join us for our Grades 4–6 Math Launch Party on May 19 at 9:30 AM MST. During this event, we’ll highlight how the curriculum aligns with the Science of Math, walk through key updates and enhancements, and provide a live demonstration of our new Digital Teacher Edition, powered by Edusfere—along with an exclusive preview of an engaging standalone module focused on financial literacy. 

References 

Achieve the Core. (n.d.). Focus, coherence, and rigor: The major shifts in mathematics. https://achievethecore.org 

Hankins, D. K. (2026, April 6). Math needs its “Science of reading” moment (opinion). Education Week. https://www.edweek.org/teaching-learning/opinion-math-needs-its-science-of-reading-moment/2026/04  

Leinwand, S., Brahier, D. J., Huinker, D., Berry, R. Q., Dillon, F. L., Larson, M. R., ... & Smith, M. S. (2014). Principles to actions: Ensuring mathematical success for all. NCTM, National Council of Teachers of Mathematics. 

National Mathematics Advisory Panel. (2008). Foundations for success: The final report of the National Mathematics Advisory Panel. U.S. Department of Education. https://www2.ed.gov 

National Research Council. (2001). Adding it up: Helping children learn mathematics. National Academy Press. https://doi.org/10.17226/9822 

U.S. Department of Education, Institute of Education Sciences, What Works Clearinghouse. (2010). Developing effective fractions instruction for kindergarten through 8th grade (NCEE 2010-4039). https://ies.ed.gov