Ten seconds pass. Then twenty.

For many parents, this moment sparks a difficult question.

Is my child struggling because they do not understand math, or because basic facts never became automatic?

It is a simple scenario, but the answer is anything but simple. Depending on who you ask, whether a teacher, parent, or researcher, you may hear very different explanations.

To unpack this, Heather Brand, Operations Manager at Made for Math, sat down with Dr. Brian Poncy, Professor and Director of the School Psychology Program at Oklahoma State University, co-author of Effective Math Interventions: A Guide to Improving Whole-Number Knowledge and creator of the Facts on Fire program. With extensive experience researching and supporting students with learning challenges, Dr. Poncy brings a practical and research-backed perspective to one of the most debated topics in math education.

Table of Contents

Why Math Facts Matter More Than You Think

Let’s start with something most adults take for granted.

When you see 3 + 4, the answer likely just appears. There is no effort and no visible steps.

But when you see 8 + 7, you might think through it. Maybe you recall that 7 + 7 equals 14 and then add one more.

These are two completely different mental processes.

Dr. Poncy explains this through the distinction between declarative and procedural knowledge. Declarative knowledge refers to facts that can be instantly retrieved. Procedural knowledge refers to the strategies used to figure something out.

Both are essential. However, they do not play equal roles in learning.

Declarative knowledge provides the foundation. Procedural knowledge builds on top of it.
 

Why Memorizing Math Facts Still Matters

The conversation around memorizing math facts often becomes polarizing. But the real issue is not whether memorization is good or bad. It is understanding what memorization actually does for a learner.

Math facts act as building blocks.

When students have a strong set of facts they can quickly retrieve, they are able to focus on higher-level thinking. They can compare strategies, understand patterns, and apply their knowledge to more complex problems.

Without that foundation, even simple tasks become demanding. A student may know a strategy, but they are forced to pause and work through each small step. Their attention is divided, and the learning process slows down.

As Dr. Poncy explains, if students are constantly using strategies like “make ten” to solve problems like 8 + 7, they are spending cognitive energy on something that should already be automatic. That energy should instead be directed toward understanding and applying mathematical concepts.

The Role of Automaticity in Learning

A key idea that emerges in this conversation is automaticity.

When foundational skills are automatic, students can direct their attention to new learning. When those skills are not automatic, everything feels harder.

This is often described as a working memory issue. However, Dr. Poncy offers a different perspective.

Rather than viewing this as a limitation within the child, it is more accurate to see it as a gap in automaticity. Students have not yet built fluency with the prerequisite skills needed to take on more complex tasks.

This distinction is important because it changes how we respond.

If we assume a fixed limitation, expectations may be lowered. If we recognize a skill gap, we can adjust instruction and provide the support needed to build fluency.
 

Why Some Students Struggle More Than Others

In many classrooms, instruction moves quickly and introduces multiple concepts at once. For students who already have strong foundational skills, this may not create a problem.

But for students who do not, it can be overwhelming.

Dr. Poncy points out that much of what we see as struggle is actually the result of how instruction is designed. When too many components are introduced at the same time, students without the necessary prerequisite skills are left behind.

Over time, these students may begin to disengage. Not because they lack motivation, but because repeated difficulty has made learning feel frustrating and inaccessible.
 

Building Skills the Right Way

Effective instruction does not try to teach everything at once. Instead, it breaks learning into smaller components and builds them gradually.

This means identifying the foundational skills students need, such as recognizing numbers, understanding quantity, and using basic math vocabulary. These are not small details. They are essential building blocks.

Once those pieces are in place and automatic, they can be combined with procedures. At that point, students are able to apply strategies more effectively because they are not overwhelmed by the basics.

Dr. Poncy describes this as creating a chain of skills. Each link must be strong for the next to hold.

When instruction follows this approach, students experience success more quickly. That success builds confidence and increases their willingness to engage.
 

Rethinking How Concepts Are Learned

There is a common belief that students should learn concepts before memorizing facts. While this sounds logical, learning does not actually work this way.

Concepts develop over time. They are not taught in isolation.

Think about how young children learn to count. They are not first taught an abstract idea of quantity. They learn by counting objects, repeating numbers, and building familiarity through experience.

In the same way, math understanding grows as students build knowledge. Facts, vocabulary, and procedures all contribute to deeper conceptual understanding.

Rather than choosing between memorization and understanding, it is more accurate to see them as connected.

From Knowing to Doing: Why Fluency Changes Everything

If math facts are the foundation, the next question becomes clear.

How do students actually move from learning a skill to using it successfully?

Dr. Poncy points to a framework called the Instructional Hierarchy, which helps explain how learning develops over time and why some students get stuck along the way.

At its core, this hierarchy includes four stages: acquisition, fluency, generalization, and adaptation.

Students first need to respond accurately. Then they need enough practice to respond effortlessly. From there, they begin to apply that skill in slightly different ways, and eventually in entirely new contexts.

It sounds straightforward, but where things break down is when students are pushed to later stages before they are ready.

Why Students Get Stuck

A common pattern in math instruction is asking students to generalize before they are fluent.

For example, a student may be introduced to number lines as a tool for understanding addition. While number lines are incredibly valuable, they require a surprising number of underlying skills.

A student needs to recognize numbers quickly, understand what symbols mean, and count accurately without hesitation. If any of those pieces are not automatic, the number line becomes overwhelming instead of helpful.

In those cases, the solution is not more practice with the number line. It is stepping back and strengthening the missing pieces.

Sometimes that means simplifying the task dramatically. Instead of solving a full problem, a student might practice identifying the number that comes after five or quickly recognizing a numeral. These small skills may seem basic, but they are essential for everything that follows. 

Accuracy Is Not Enough

One of the biggest misconceptions in learning is that getting the right answer means a student has mastered a skill.

Accuracy is only the first step.

A student might be able to solve a problem correctly, but if it takes significant effort or relies on a long strategy, the skill is not yet fluent. And without fluency, it is unlikely to transfer to new situations.

Fluency is what allows students to move forward.

When a skill is fluent, it is fast, effortless, and requires little conscious thought. This frees up attention for higher-level thinking, like choosing strategies or solving more complex problems.

Without fluency, students remain stuck in effortful processing, which limits their ability to grow. 

Breaking Skills Into Two Paths

To better understand where students struggle, Dr. Poncy suggests looking at learning through two parallel tracks.

On one side are declarative skills, such as math facts, vocabulary, and symbol recognition. On the other side are procedural skills, such as strategies and problem-solving methods.

Students can be strong in one and weak in the other.

For example, a student might know their math facts but struggle to apply a procedure like multi-digit addition. Another student might understand a procedure but lack the fact fluency needed to carry it out efficiently.

Both situations lead to the same result. The student cannot fully generalize their learning.

The key is identifying which component is breaking down and addressing it directly.

Why Generalization Fails

When a student cannot apply a skill in a new context, it is often labeled as a lack of understanding.

But more often, it is a missing piece.

If a student knows their facts but has not practiced the procedure enough, they may not recognize when or how to use those facts. On the other hand, if they understand the procedure but lack fluency with facts, the process becomes too slow and effortful to sustain.

Generalization happens when both pieces come together.

This is why targeted practice matters. Instead of repeating the same full problem over and over, effective instruction isolates the specific skill that needs strengthening.

When that piece becomes fluent, the larger skill often improves quickly.
 

Teaching With Precision

This approach requires a shift in how we think about instruction.

Rather than relying on assumptions about what a student can or cannot do, Dr. Poncy emphasizes the importance of observing and measuring specific behaviors.

🔴What can the student do accurately
🟠What can they do fluently
🟡Where do they hesitate
🟢Where do they rely on strategies

These observations provide clear direction for instruction.

Instead of guessing, educators can break a skill into its components, assess each part, and teach exactly what is missing.

This level of precision is especially important for students who struggle the most. For them, efficient and targeted instruction is not just helpful, it is necessary.
 

What Mastery Really Looks Like

So what does it mean to truly master a math fact or skill?

According to Dr. Poncy, mastery is not just correct.

It is instant.

If a student has to pause, think through steps, or use a strategy to arrive at an answer, the skill is not yet automatic.

This applies to more than just math facts. It includes vocabulary, symbols, and even strategies themselves.

The goal is for students to retrieve information quickly and effortlessly so they can focus on new learning.
 

The Power of Retrieval Practice

One of the most effective ways to build this kind of mastery is through retrieval practice.

This means asking students to produce an answer without relying on prompts or supports. Over time, cues are reduced so the student must rely on memory alone.

This process strengthens recall and helps move skills from effortful to automatic.

Without this step, students may appear to know something when supports are present, but struggle to access it independently later.
 

Making Connections That Stick

As students build fluency, they are better able to see connections across math.

For example, understanding that 3 + 6 and 6 + 3 are related can lead to deeper insights about fact families. From there, students can connect addition to subtraction, and eventually to multiplication and division.

These connections are often described as conceptual understanding. But they do not happen by chance.

They are carefully built through explicit instruction, repeated practice, and opportunities to apply learning in new ways.

Students are not discovering these patterns out of thin air. They are being guided to recognize and use them.
 

When Strategies Get in the Way

Strategies like counting and skip counting can be helpful early on. But when overused, they can actually slow down learning.

If a student relies on counting to solve a problem like 7 × 8, the process becomes long and error-prone. There is too much distance between the problem and the answer, making it harder for the brain to connect the two.

In some cases, students may even begin to memorize incorrect answers because of counting errors along the way.

The goal is not to eliminate strategies entirely, but to ensure they are stepping stones rather than permanent solutions.

At a certain point, students need to move from strategy-based thinking to automatic recall.
 

Using Time Wisely

For students who are already behind, time matters.

When students spend large amounts of time using inefficient strategies, they are not just struggling in the moment. They are losing opportunities to build the skills that will move them forward.

Instruction must be targeted, efficient, and focused on what will have the greatest impact.

When foundational skills become automatic, everything else becomes more accessible.

Learning math is not about choosing between facts, strategies, or concepts.

It is about understanding how they work together.

Students need accurate knowledge. They need fluency. They need opportunities to apply what they know. And they need instruction that builds each piece intentionally.

When those elements are in place, something powerful happens.

Students stop feeling stuck.
They start making connections.
And math begins to make sense.

From Strategy to Automaticity

By this point, a clear pattern has emerged.

Early strategies like counting play an important role in helping children enter mathematics. They give students a way to make sense of numbers and begin solving problems.

But they were never meant to be permanent.

When students remain dependent on counting, every new problem places more demand on their attention. Each step has to be tracked, each count has to be remembered, and the process becomes increasingly fragile.

Over time, this creates a bottleneck.

Instead of building momentum, students feel like math is getting harder and slower. Not because the concepts are beyond them, but because the tools they are using are no longer efficient enough to support their growth.

If counting is the starting point but not the destination, what actually helps students move from effortful strategies to fluent retrieval?

As Dr. Poncy has emphasized throughout this conversation, automaticity is not something that happens by chance. It is built intentionally through structured practice, thoughtful instruction, and a clear understanding of how skills develop over time.

Students need opportunities to:
🟣Accurately learn a skill
🔵Practice it until it becomes fluent
🟢Apply it in different contexts
🟡Strengthen their ability to retrieve it independently

This process requires more than exposure. It requires deliberate design.

Memorizing math facts is not about speed for the sake of speed. It is about freeing up the brain to do more meaningful work.

When students have automatic access to foundational skills, they can think more clearly, solve problems more effectively, and engage more confidently in math.

This is not about choosing between memorization and understanding.

It is about recognizing that fluency is what makes deeper thinking possible.

What Comes Next

In the next part of this conversation, Heather and Dr. Poncy take a deeper look at what it really takes to build math fact fluency.

They explore what Dr. Poncy calls “getting facts on fire” and why helping students reach true automaticity is far more intentional and systematic than many people realize.

Because when facts become automatic, everything changes.

Students think faster.
They make stronger connections.
And math starts to feel possible again.

You can connect with Dr. Brian Poncy here.

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