They might answer correctly when an adult gives them a cue. They might count to find the answer. They might hesitate for several seconds before responding. They might know the fact one day and forget it the next.

So when we say a student “knows” a math fact, what do we really mean?

In our last conversation with Dr. Brian Poncy, we explored why math facts matter, the difference between strategies and automatic retrieval, and why students eventually need to move beyond counting and other effortful strategies.

But once we recognize that a student needs stronger fluency, another question becomes just as important:

How do we actually build it?

In this continuation of our conversation, Heather Brand, Director of Instructional Strategy at Made for Math, sits down with Dr. Brian Poncy to explore what effective math fact practice really looks like. From flashcards and Cover-Copy-Compare to explicit timing, set size, retrieval practice, and data-based decision-making, Dr. Poncy explains why effective practice is much more than simply giving a student more problems.

Table of Contents

Flashcards Aren’t as Simple as They Look

When most people hear “math fact practice,” flashcards probably come to mind.

Show the card.

Ask for the answer.

Move to the next card.

Simple, right?

According to Dr. Poncy, not quite.

Flashcards are not actually the intervention themselves. They are simply the vehicle used to deliver an intervention.

What matters is what happens during each learning trial.

A student sees a problem. They respond. They receive immediate feedback. If they are incorrect, the teacher provides the appropriate model or cue and gives the student another opportunity to respond.

For example, instead of immediately asking a student:
“What is 3 + 6?”

A teacher might first model:
“3 + 6 is 9.”

Then the student is asked to respond:
“What is 3 + 6?”

If the student answers correctly, they receive feedback and move on. If they do not, the teacher provides the answer and gives them another opportunity to respond.

That distinction matters.

If we simply flash a card and wait for an answer, we may not be providing the instructional support a student needs to learn the fact.

As Dr. Poncy explains, the flashcard isn’t the intervention. The instructional routine surrounding it is.

And there is another important consideration: the number of cards matters.

Showing a student 20 flashcards twice in five minutes does not automatically mean they received effective practice. Without appropriate feedback, set sizes, repetition, and opportunities to respond, simply increasing the number of problems may accomplish very little. 

When Is a Math Fact Actually “Known”?

This leads to an important question:

When can we say that a student knows a math fact?

A student might eventually produce the correct answer, but that does not necessarily mean the fact is automatic.

Dr. Poncy describes using different categories based on how quickly a student can retrieve a fact:

• 0–1 second: Mastered
• 1–3 seconds: Developing
• 3+ seconds: Not yet mastered

The exact timing is less important than the underlying idea: not all correct responses represent the same level of learning.

A student who instantly responds to 2 + 3 is in a very different place from a student who eventually says 5 after several seconds of thinking or counting.

That means we shouldn’t simply mark every correct answer as “known” and move on.

Instead, we can use the student’s response time to decide what happens next.

Practice Should Change as the Student Changes

One of the biggest themes throughout this conversation is that effective intervention is not static.

The practice routine should change based on what the student demonstrates.

For facts that are close to automatic, students can practice retrieving them with fewer cues and larger sets.

For facts that are still developing, the teacher can use procedures such as a time-delay approach: give the student an opportunity to retrieve the answer independently, but provide the answer if they do not respond within the allotted time.

For facts that are truly unknown, the set should become much smaller, with more explicit cues, feedback, and repetition.

In other words:
The student tells you what to do next.

As students become more fluent, the cues can become less noticeable, the rate of presentation can increase, and the set size can grow.

As Dr. Poncy explains, the goal is to gradually decrease the amount of support surrounding the response until the student can retrieve the answer independently.

This is one reason that one-to-one intervention can look very different from a whole-class practice activity.

A teacher working individually with a student can constantly adjust:
“You know this one. Let’s see if you can retrieve it without my cue.”

And then, a few cards later:
“This one still feels medium. Let’s practice so we can help it feel easy to remember.”

The intervention becomes responsive rather than scripted.

What is an effective set size?

 
Small Sets Can Make a Big Difference
 
Another key piece of effective fact practice is set size.

It can be tempting to give students a large collection of facts and ask them to practice all of them.
But for students who are struggling, that can create more difficulty without creating more learning.

Instead, Dr. Poncy describes shrinking the set.

A student might work with only four or six facts that need additional practice while continuing to retrieve facts that are already becoming automatic.

As those facts become fluent, new facts can be introduced.

This creates a cycle:
Teach → Practice → Assess → Adjust → Add → Reassess

The goal is not to keep students working on the same tiny set forever. The goal is to use small sets to build success and then gradually expand the student’s repertoire.

At Made for Math, we refer to this idea as focus facts: narrowing the student’s practice to the facts that actually need the most attention.
 

Timing Isn’t the Problem. Timing the Wrong Thing Is.

Timed math practice can be a controversial topic.

Some students have had negative experiences with timed tests, and it is understandable that educators and parents may worry that timing will create anxiety.

But Dr. Poncy makes an important distinction:

Timing itself isn’t necessarily harmful. Poorly implemented timing can be.

If a student is asked to complete a large number of problems they have not yet learned, timing can turn the experience into repeated failure.

The student learns:

“I can’t do this fast enough.”

Over time, that experience can create anxiety around timed math.

But timing can look very different when students are practicing skills they have already learned and are ready to make more fluent.

Instead of asking a student to race through problems they don’t know, an interventionist can first establish accuracy, build fluency, and then use timing to measure growth.

Dr. Poncy describes this as part of a student’s learning history. If a student has repeatedly experienced timing as a situation where they fail, we may need to rebuild that history by creating successful experiences with timed practice.

And that can be surprisingly motivating.

A student who once hated being timed may eventually start asking:

“Can you time me?”

The difference isn’t necessarily the timer.

The difference is whether the student has been set up to experience success.

How Do We Know When a Student Is Ready for Timing?

This brings us to one of the most practical questions in the conversation:

When is a student ready for explicit timing?

Dr. Poncy describes research comparing explicit timing with tape problems and found an important threshold.

Students who were below 10 digits correct per minute did not show the same growth from time practice. Students who were above that level responded similarly with explicit timing and tape problems.

The takeaway isn’t that every child must hit one magic number before receiving any timed practice.

Instead, the data can help us ask a better question:

Is the student responding quickly enough that explicit timing will actually provide useful practice opportunities?

If a student is only producing a handful of correct responses per minute, giving them a one-minute timing may not be the most efficient intervention.

They may need more explicit instruction, smaller sets, stronger cues, and immediate feedback first.
Once their rate of responding increases, timing may become a much more efficient way to practice.
 

Rates of Responding Matter

 
This idea of rate of responding comes up again and again in Dr. Poncy’s explanation.

Imagine one student who solves 12 problems in a minute and another who solves 4.

Even if both students eventually get the answers correct, they are getting very different amounts of practice.

The student who responds more frequently is getting more opportunities to practice the skill.
That is one reason fluency matters so much.

We are not simply trying to make students faster for the sake of speed.

We are trying to increase the number of successful opportunities a student has to respond and learn within a given amount of instructional time.

For students who are behind, this matters enormously.

We don’t have unlimited instructional time.

The goal is to spend that time doing the things most likely to move the student forward.

What About Students Who Are Still Counting?

This is where the conversation connects directly back to Part 1.

A student might appear to be practicing math facts, but if they are still counting to solve every problem, what are they actually practicing?

Suppose a student sees:
8 + 7

and solves it by counting:
8, 9, 10, 11, 12, 13, 14, 15.

The student got the answer.

But they did not retrieve the fact.

They practiced counting.

That distinction is critical.

Dr. Poncy explains that interventionists need to look at how a student arrives at an answer, not simply whether the answer is correct.

A student might use an efficient strategy, such as a known double plus or minus one. Another student might still be counting.

Those students need different instruction.

The question isn’t simply:
“Can you get the answer?”

It is:
“What are you doing to get the answer?”

If the student is relying on an inefficient procedure, the goal may be to build the prerequisite knowledge that allows them to move toward retrieval.

Cover-Copy-Compare: Where Does It Fit?

Another intervention Dr. Poncy discusses is Cover-Copy-Compare.

The basic routine is straightforward:
1. The student looks at a modeled problem and answer.

2. They say it.

3. They cover it.

4. They write the problem and answer.

5. They uncover the model.

6. They compare their response to the correct answer.

This may look very different from flashcard practice, but Dr. Poncy explains that the underlying learning process is actually quite similar.

Both involve a stimulus, a response, and feedback.

The difference is that Cover-Copy-Compare is student-mediated, while flashcard drill allows an interventionist to respond much more flexibly to what the student is doing.

That makes Cover-Copy-Compare particularly useful in settings where one teacher is supporting multiple students.

A classroom might have one student practicing addition, another practicing subtraction, and another practicing multiplication—all working through appropriately selected routines at the same time.
The teacher doesn’t have to provide every learning trial individually.

Why Permanent Products Matter

There is another advantage to Cover-Copy-Compare: it leaves behind a permanent product.

When a student practices flashcards at home, a teacher may have no way of knowing how many times the student actually responded.

Did they practice for five minutes?

Did they practice for thirty seconds?

Did the parent give the answer immediately?

Did the student actually look at the problem?

There is no easy way to know.

With Cover-Copy-Compare, the completed work provides some evidence that the student engaged with the practice.

That makes it easier for teachers to monitor what is happening and make instructional decisions.

Making Math Practice Easier for Families

This also changes the way we think about homework.

Parents are often asked to practice math with their children, but if the parent doesn’t understand the intervention, homework can quickly become frustrating for everyone.

Dr. Poncy makes an important point: parents and children can both develop negative learning histories around homework.

The solution isn’t necessarily to eliminate practice at home.

Instead, we can send home practice that the student already knows how to do successfully.

The child knows the routine.

The parent knows what to do.

The student can experience success.

And suddenly, homework doesn’t have to mean a 45-minute battle.

It can be a short, structured practice activity that gives families an opportunity to celebrate progress together.

A Powerful Example: Four Digits to Twenty-Six

One of the most compelling examples Dr. Poncy shares comes from an intervention study with a third-grade student with an intellectual disability.

The student began at approximately four digits correct per minute with about 33–50% accuracy.

After six days of intervention, she reached 26 digits correct per minute.

The total intervention time was only about 24–36 minutes.

What changed?

Not the child.

The instruction changed.

The intervention used small sets and the same basic instructional components that can be used with other students: a stimulus, a response, feedback, and practice. But the amount of material and the level of support were adjusted to the student’s needs.

The example also highlights something important: growth in a small set of facts doesn’t automatically mean every math fact has been mastered.

The student would still need systematic instruction to introduce new items, interleave previously learned items, and support maintenance over time.

But the result demonstrates what can happen when instruction is matched to the student’s current performance.

Don’t Guess. Test Your Hypothesis.

This may be the most important message from the entire conversation.

There is no single intervention that will work perfectly for every student.

Instead, Dr. Poncy emphasizes data-based decision-making.

If a student is struggling, don’t immediately assume:

Instead, ask:

What exactly is the student doing?

Then develop a hypothesis.

Test it.

Change the instructional conditions.

Measure the result.

And use the student’s response to determine what to do next.

As Dr. Poncy explains, even when an intervention produces strong growth during a session, we still need to know whether that growth maintains across sessions and over time. We need to consider rates of learning, rates of forgetting, set size, repetition, spaced practice, and interleaving.
This is where assessment becomes more than a test.

Assessment becomes the tool that tells us how to teach.

What If a Student Still Can’t Master Math Facts?

Parents and educators sometimes ask whether there are students who simply cannot learn their math facts.

Dr. Poncy’s response is essentially this:

Don’t start there.

Start by asking what conditions allow the student to learn.

Maybe the student needs a smaller set.

Maybe they need more repetitions.

Maybe they need a different type of practice.

Maybe the facts need to be broken into smaller groups.

Maybe the student needs oral responding instead of writing.

Maybe the practice needs to focus on prerequisite skills first.

The important thing is to identify the conditions under which the student can be successful and then build from there.

This doesn’t mean every student will reach the same level of fluency or that every learning challenge can be solved with one intervention.

It means we should be careful about turning a student’s current performance into a prediction about their potential.

Put the student in conditions where they can succeed, and let their behavior tell you what they need next.

What About Common Math Fact Errors?

The conversation also addressed several errors that parents and teachers frequently see.

“My child knows the facts, but they ignore the operation sign.”

A student might see:
2 + 3

and answer 5.

Then see:
2 × 3

and still answer 5 because they are focusing on the numbers rather than the operation.
Dr. Poncy describes this as a potential discrimination or self-monitoring issue.

The first step is to determine which one it is.

Can the student discriminate between the signs when the problems are presented in isolation?

If so, the problem may be that they are not attending to the sign when the problems are mixed together.

That means the intervention should include interleaved practice so the student has to attend to the entire problem.

“My child keeps reversing numbers.”

Dr. Poncy shares an example from his own children, who struggled with number reversals when they were young.

The important lesson wasn’t simply that they needed more handwriting practice.

It was that much of their practice had included a model.

When the model disappeared, the error appeared.

That tells us something about the skill.

A student might be able to copy a number accurately but struggle to produce it independently.

Again, the solution is to isolate the skill, assess it, and provide the appropriate practice.

For a student who writes 42 when the answer is 24, the same principle applies.

Rather than simply giving more worksheets, isolate the skill and practice the specific pattern that is causing difficulty.

The goal is always to determine what the student can do, where the breakdown occurs, and what instructional condition helps them succeed.

The Goal Isn’t Speed. It’s Automaticity.

It can be easy to read a conversation about timing, digits correct per minute, and fluency and come away thinking that math intervention is all about making children faster.

It isn’t.

The goal is automaticity.

We want students to be able to retrieve foundational information without spending all of their attention figuring it out.

We want them to have enough fluency that they can use those facts while solving more complex problems.

And we want practice to be efficient enough that students get the greatest possible benefit from the instructional time available.

That requires more than repetition.

It requires intentional repetition.

Let the Student Tell You What They Need

Throughout this conversation, Dr. Poncy returns to the same central idea:

Don’t decide what a child can or cannot do based on assumptions.

Measure.
Observe.
Hypothesize.
Intervene.
Evaluate.
Adjust.

A student’s performance tells us something about the instructional conditions they are experiencing.

If a student isn’t learning, we should ask:
What can we change?
Maybe the set is too large.
Maybe there aren’t enough repetitions.
Maybe the student needs more explicit modeling.
Maybe the cues need to be stronger.
Maybe they’re ready for fewer cues.
Maybe they’re ready for timing.
Maybe they’re not.
Maybe they need more spaced practice.
Maybe they need more interleaving.

The answer is not the same for every student.

And that’s exactly why effective math intervention cannot be reduced to simply choosing a worksheet, a flashcard deck, or a timed test.

What Effective Math Fact Practice Really Looks Like

By the end of this conversation, a bigger picture emerges.

Building math fact fluency is not about giving students more problems.

It’s about giving them the right practice at the right time.

Students need opportunities to:
🔴Learn accurately.
🟠Receive immediate feedback.
🟡Practice in appropriately sized sets.
🟢Retrieve information independently.
🔵Gradually reduce instructional cues.
🟣Build fluency before being pushed to more complex applications.
⚫Practice skills over time through spaced and interleaved practice.
⚪Receive instruction that changes based on their individual response.

And perhaps most importantly, they need adults who are willing to look beyond the question:

“Can this child learn math facts?”

and instead ask:
“Under what conditions does this child learn best?”

That shift changes everything.

Because when we stop treating a student’s current performance as a fixed limit and start treating it as information, struggling becomes something we can investigate.

We can test.
We can adjust.
We can try again.

And we can give students more opportunities to surprise us.
 

What Comes Next

Building math fact fluency is not about memorization for memorization’s sake.

It’s about giving students the automatic access to foundational skills that allows them to do more with mathematics.

And as Dr. Poncy emphasizes, the path to that fluency is not one-size-fits-all. It requires careful assessment, intentional practice, and continual adjustment based on what the student actually does.

Because the most effective intervention isn’t the one we believe should work.

It’s the one that helps this student learn.

You can learn more about Dr. Brian Poncy’s Facts on Fire resources and access the free materials discussed in this episode through his website.

Check out our other episodes of Unlocking Dyscalculia here: