Why Great Schools Should Embrace the “Science of Math”

Summary for Educators

Based on:

Original article: “Why Educators Should Embrace the ‘Science of Math’”

Author: Frederick M. Hess, interviewing Daniel Ansari

Source: Education Next | Date: October 23, 2026

THE BIG IDEA

The science of reading has transformed conversations about literacy instruction. Could a similar research-based movement improve mathematics teaching?

In an insightful interview with Frederick M. Hess, Daniel Ansari, a professor of psychology and education at Western University in Ontario and director of its Numerical Cognition Laboratory, argues that the answer is yes.

Decades of research in psychology, cognitive neuroscience, and education have revealed important insights into how children develop numerical understanding, learn arithmetic, and acquire mathematical fluency. Unfortunately, much of this knowledge never reaches classroom teachers.

Ansari believes the emerging “science of math” movement offers schools an opportunity to connect instructional practices more closely with evidence about how children learn.

However, he cautions against simply replicating the science-of-reading movement. Mathematics involves multiple developmental pathways, and learning algebra differs from learning geometry or arithmetic.

The central message is clear: Effective mathematics instruction should be guided by research, adapted to children’s developmental needs, and refined through professional judgment.

KEY TAKEAWAYS

1. Mathematical Understanding Begins With Number Sense

Children must understand that written numerals represent quantities before they can confidently perform calculations.

For example, recognizing the symbol 8 is different from understanding that it represents eight objects.

Teachers should help young students connect numbers with physical quantities, numerical relationships, and mathematical operations.

Weaknesses in these foundational concepts can create difficulties that persist into later grades.

2. Novice Learners Need Explicit Instruction

Ansari emphasizes that beginning mathematics students have limited prior knowledge on which to build.

Consequently, approaches that expect young learners to discover mathematical principles with minimal teacher guidance may be less effective than carefully structured instruction.

Classroom example: Before asking students to independently discover strategies for multiplying two-digit numbers, a teacher demonstrates the process, explains the reasoning, provides guided practice, and gradually releases responsibility.

Discovery and independent problem-solving become more appropriate as students develop expertise.

3. Mathematical Fluency Should Follow Understanding

Automatic recall of math facts is important because it reduces demands on working memory.

However, Ansari cautions against beginning instruction with timed speed drills.

Students should first understand arithmetic operations, develop accuracy through meaningful practice, and only then use timed activities to strengthen automatic recall.

For example, children might initially use fingers, counters, or number lines to understand addition before progressing toward fluent mental computation.

4. Conceptual Understanding and Procedural Knowledge Both Matter

Mathematics requires knowing how to perform calculations and understanding why mathematical relationships work.

A student might memorize the steps for subtraction without understanding its relationship to addition.

Effective instruction should develop both capabilities.

Importantly, researchers have not established a single developmental sequence in which conceptual knowledge must always precede procedural knowledge or vice versa.

5. Instructional Materials Should Minimize Distractions

Young children’s executive functioning abilities are still developing.

Highly decorated worksheets, unnecessarily colorful manipulatives, and visually complicated presentations may compete for students’ attention.

Instructional materials should direct attention toward mathematical relationships rather than irrelevant visual details.

A simple number line may sometimes be more helpful than an elaborate digital animation.

6. Early Identification Can Prevent Later Difficulties

Because mathematics learning is cumulative, early weaknesses can become increasingly serious.

Ansari highlights the work of educational psychologist Lynn Fuchs, whose research has contributed substantially to mathematics intervention and multitiered systems of support.

Schools should screen students for emerging mathematics difficulties and provide timely, targeted interventions rather than waiting for failure to become entrenched.

WHY IT MATTERS

American schools continue to struggle with mathematics achievement, and educators frequently disagree about the best instructional approaches.

Debates often pit traditional teaching against student-centered discovery, memorization against understanding, and standardized algorithms against multiple strategies.

Ansari’s perspective suggests that these familiar divisions can distract educators from a more productive question: What does credible research tell us about how children learn mathematics at different developmental stages?

The science of math does not prescribe one instructional technique for every child or grade level. Instead, it provides evidence that teachers can use to make better instructional decisions.

For principals, this means mathematics improvement cannot depend solely on purchasing a new curriculum or increasing instructional minutes.

It requires strengthening teachers’ knowledge of how mathematical understanding develops and providing opportunities to translate research into practice.

LEADERSHIP ACTIONS

Principals can help connect the science of math with classroom instruction through five practical strategies:

1. Review K–5 mathematics instruction. Examine whether students develop strong number sense before they are expected to master increasingly complex procedures.

2. Strengthen professional development. Introduce teachers to research on numerical cognition, explicit instruction, cognitive load, retrieval practice, and mathematical fluency.

3. Evaluate mathematics interventions. Determine whether struggling students receive systematic instruction targeting specific mathematical misconceptions rather than simply spending additional time completing similar problems.

4. Examine classroom practices. During observations, consider whether instructional approaches match students’ current knowledge and developmental readiness.

5. Build research-informed PLCs. Ask grade-level and departmental teams to identify one mathematics instructional practice, study the relevant research, test an improvement, and examine evidence of student learning.

One particularly promising faculty activity would be to select a common mathematical misconception, such as a misunderstanding of place value or fractions, and ask teachers to discuss how students develop that misconception and which instructional approaches can help correct it.

LEADER REFLECTION

School leaders might consider three important questions:

• How much of our mathematics instruction is based on credible learning research, and how much reflects tradition or personal preference?
• Are we asking students to memorize procedures before they understand the mathematics, or are we withholding useful explicit instruction in the hope that they will discover everything independently?
• What steps are we taking to ensure that teachers understand how mathematical knowledge develops from kindergarten through high school?

Ansari concludes with an especially important distinction: Researchers can identify instructional approaches that generally work, but teachers must determine how to apply that evidence in their particular schools.

The science of math should not replace teacher judgment. It should strengthen it.

That is a message every principal and mathematics department should take seriously.

Source: Frederick M. Hess, “Why Educators Should Embrace the ‘Science of Math,’” an interview with Daniel Ansari, Education Next, October 23, 2026.