How Can I Tell if My Child Has Gaps in Foundational Math Skills?

When parents first contact me, I often hear a similar concern:

“My child is bright, but math is harder for them.”

Sometimes the child cannot seem to keep up with the class or finish homework without a great deal of help.

Sometimes math homework has become a battleground.

A parent may also notice the same kinds of errors appearing again and again on classwork, homework, or tests.

It is easy for a child to begin believing that they are simply “not good at math.”

Parents may wonder whether their child needs more practice, missed an important skill, or is not trying hard enough.

The truth is that these situations can look very similar at first. A child who has just learned something new will make mistakes. A child with a gap in an earlier skill may make mistakes too.

The difference often becomes clearer when we look beyond the final answer and pay attention to how the child is thinking.

Foundational math gaps can be identified and strengthened.

Your child does not have to love math, but “not good at math” does not have to become a permanent part of how they see themselves.

What Is a Foundational Math Skill Gap?

A foundational gap is a skill or concept a student has not yet learned well enough to

support more advanced work.

Math builds over time, and new skills often depend on several earlier skills working together.

The Institute of Education Sciences recommends that math intervention connect new learning to previously learned concepts and provide systematic review so students can strengthen those connections (What Works Clearinghouse).

For example, a student solving a multi-step algebra equation may need to use addition, subtraction, multiplication, division, parentheses, exponents, positive and negative numbers, and inverse operations.

For more information on multi-step problems, you can read this article: Why Does My Child Get Stuck on Multi-Step Math Problems?

They must also understand that an equation stays balanced when the same operation is performed on both sides.

If the student solves the operations out of order, the roadblock may be their understanding of the order of operations.

If they become confused when using inverse operations, they may need a stronger understanding of positive and negative numbers or how operations relate to one another.

If their answer contains a fraction they cannot simplify, they may need more work with factors, multiplication, or division.

The student may appear to be struggling with algebra even though the difficulty began years earlier.

This is one reason that simply repeating the current lesson may not solve the problem. The student may need help strengthening one of the skills underneath it.

Does My Child Need More Practice, or Is There a Deeper Gap?

A child who needs more practice and a child with a foundational gap may initially look alike. Both may hesitate, forget a step, or answer incorrectly.

One clue is how the child responds to a brief reminder.

A student who recently learned a procedure may make an addition or division mistake but correct it quickly when reminded what to do next. The skill is there, but it is not yet automatic.

A child with a deeper gap may still be unsure after the reminder. They may know one procedure but be unable to connect it with an earlier idea. They might complete a problem when it looks exactly like the classroom example, then freeze when the numbers, wording, or layout change.

One mistake does not prove that a child has a skill gap. Instead, look for patterns.

Does the same type of mistake appear across different assignments? Does the child repeatedly forget how to begin? Do reminders help briefly, or does the confusion return as soon as the problem changes?

The goal is not to label every mistake as a gap. The goal is to look for patterns that may explain why math continues to feel harder than it should.

Signs of Foundational Math Gaps Parents May Notice

Some signs appear in a child’s written work. Others appear in the way the child behaves when math begins.

A child may put their head down, find something else to do, or immediately say, “I don’t get it.” They may argue, act defiantly, or turn homework into a fight.

These behaviors do not tell us exactly why the child is struggling. Tiredness, anxiety, confusing directions, attention difficulties, and other factors may also play a part.

Still, repeated avoidance can be a clue that the work feels confusing or overwhelming. If this pattern sounds familiar, you may also want to read why math refusal may be a sign that your child is struggling.

Parents may also notice that their child:

• Relies heavily on finger counting, tally marks, multiplication songs, or a calculator

• Guesses repeatedly until an answer seems right

• Forgets how to begin even after receiving a brief reminder

• Freezes when a familiar skill is presented in a different way

• Repeatedly confuses positive and negative signs

• Makes the same multiplication or division errors across assignments

• Drops decimal points or important signs between steps

• Has difficulty explaining why a procedure works

  
  

These strategies are not automatically bad.

Finger counting, songs, visual tools, and calculators can all provide appropriate support.

The question is whether the child can use and understand the underlying skill when the support is removed or when the problem changes.

A Wrong Answer Does Not Tell the Whole Story

Formal assessments are an important part of my work with students. An assessment helps narrow down what a child can do independently. It can highlight strengths, weaknesses, and patterns that deserve closer attention.

However, a paper or computer assessment cannot always show where or why the child became confused.

A score may show that a student missed several fraction problems, but it may not tell us whether the student misunderstands what fractions represent, struggles to recall multiplication facts, loses track of the steps, rushes through the work, or becomes frustrated and stops trying.

Evidence-based guidance for math intervention recommends using student work and responses to identify misconceptions and adjust instruction, rather than relying only on whether an answer is correct (What Works Clearinghouse).

That is why I combine assessment results with observation and conversation.

As students work, I watch what they do. Are they counting on their fingers? Are they quietly singing a multiplication song? Are they rushing? Do they forget to carry a negative sign or decimal point into the next step?

I encourage students to write down their work and reason aloud as they solve problems.

Explaining their thinking sometimes helps students catch and correct their own mistakes. It also lets me hear how they understand the process. When I notice a consistent pattern, I have a better idea of which skill we need to strengthen.

Assessments help identify patterns. Observations help us understand what those

patterns mean.

How ADHD and Autism Can Affect What Parents See

Foundational gaps can sometimes be harder to recognize in neurodivergent students

because executive-function demands affect how students access and use what they know.

Some students with ADHD may show inconsistent performance.

A child might understand long division one day and seem to have forgotten everything two days later. They may rush, answer impulsively, make errors that look careless, or have difficulty holding information in mind while completing several steps.

Working memory helps students hold and use information while solving a problem.

Research has found that working memory plays an important role in children’s mathematics learning and that working-memory difficulties can contribute to lower math achievement among some children with ADHD (Peng et al.; Kofler et al.; Kofler et al.). This does not mean every child with ADHD will experience the same challenges, but it may help explain why knowing a skill and using it consistently are not always the same thing.

Some autistic students may find it difficult to apply a familiar concept when the wording, layout, or representation changes. Literal or rigid thinking can make an unfamiliar version of a problem feel like an entirely new skill. Vague phrases or figurative language in word problems may create an extra barrier.

Research comparing autistic students with typically developing peers has found that language comprehension and identifying relevant information can affect mathematical word-problem solving (Bae, Chiang, and Hickson, 2015).

A student may also focus closely on one detail or representation without realizing that it is not the most important part of the problem.

Overload can occur when too much information is presented at once. In those moments, a student’s performance may not fully show what they understand.

These are possible patterns, not rules. ADHD and autism affect each student differently.

Parents and teachers should avoid assuming that every error comes from a diagnosis or that inconsistent work means a child is lazy or unmotivated. For a closer look at the many reasons a child may avoid math, read What Triggers Math Avoidance in Children With ADHD?.

How Parents Can Learn More Without Turning Homework Into a Test

When parents notice repeated struggles, they can begin with curiosity. This is especially important with older children, who are also learning to become independent and may not want to feel that they cannot succeed without a parent.

Try asking permission before stepping in:

“Would you like help, or would you like a few minutes to try it first?”

If your child accepts help, invite them to explain their approach. You might ask:

• “Can you show me how you started?”

• “What do you think the problem is asking?”

• “Why did you choose that operation?”

• “Which part feels confusing?”

• “Would you like a hint or an example?”

Show curiosity rather than searching for the mistake.

If your child cannot explain why a process works, model the reasoning calmly.

Asking students to explain, monitor, and reflect on their problem-solving process is also supported by the Institute of Education Sciences’ recommendations for grades 4–8 (What Works Clearinghouse).

Praise the effort to explain, try again, or correct an error instead of focusing only on whether the final answer is right.

Parents who want additional guidance can learn more about scaffolding homework support while building independence.

If math is turning into avoidance or conflict, remember that behavior is communication.

What looks like defiance may be communicating, “I am confused,” “I am overwhelmed,” or “I am afraid I will get it wrong.” Offering support will usually tell you more than becoming angry or pushy.

Low-pressure math games can also help children strengthen number sense and multiplication skills. Play can make practice more engaging and memorable while giving parents another opportunity to notice how their child thinks about numbers.

Work With Your Child’s Teacher

Building a positive relationship with the classroom teacher is one of the best first steps a parent can take. There is no single right time to raise a concern. If you notice falling grades, greater avoidance, repeated mistakes, or growing frustration, it is appropriate to ask for a conversation.

You can wait for a parent-teacher conference, but you do not have to. Ask for a time that works for the teacher, bring a few work samples, and take notes about what you see at home.

Useful questions include:

• “Are you seeing similar struggles in class?”

• “Are these mistakes expected while students are learning this skill?”

• “Does my child understand the concept but need more practice?”

• “Could an earlier skill, such as addition, multiplication, place value, or fractions, be affecting this work?”

• “What support or practice would you recommend?”

• “Would a more focused assessment help us understand where the difficulty begins?”

Parents see how math affects their child at home. Teachers see how the child approaches math in the classroom. When they share what they are noticing, they can often build a clearer picture together.

What Happens After a Gap Is Identified?

When I find a likely gap, I ask questions and gently probe until I find what the student can do successfully. Then we build the next skill from that starting point.

I explain the skill we are working on, model my thinking aloud, and explain why each step matters.

Students deserve to know why we are revisiting a skill, how it connects to their current work, and how it will help them later.

This approach is consistent with evidence-based recommendations to use clear mathematical language, visual and verbal models, guided practice, feedback, and cumulative review during math intervention (What Works Clearinghouse).

Whenever possible, I use games, engaging practice, or appropriate timed challenges to build accuracy and fluency (sometimes children like the competitiveness of beating their own time).

For example, I worked with a student who struggled when adding fractions with unlike denominators. He could multiply, but his understanding of factors and multiples was not yet strong enough to support the new fraction work.

Finding the least common multiple helps a student identify a common denominator, while understanding factors, including the greatest common factor, helps the student recognize number relationships and simplify fractions.

We discussed what factors and multiples were, why they mattered, and how they appeared in different types of problems. We practiced the missing concept until it became solid. As we worked together, I continued pointing out when he needed the skill and talking through how to use it.

Filling a foundational gap does not mean sending a child backward. It means finding the strongest place to begin moving forward.

You can learn more about how I identify hidden gaps and rebuild skills on my Math Tutoring and Coaching page.

Confidence May Grow Quietly

Some children feel sad or embarrassed when they realize they need to revisit an earlier skill. They may see it as “going backward.” It is important to acknowledge that feeling while helping them understand that strengthening a foundation makes future work easier.

As students become more capable, their confidence often begins to change. They guess less. They become more watchful of their steps. Some begin quietly talking themselves through problems. They catch more of their own mistakes and rely less on an adult to tell them whether every answer is correct.

One of my students used to look at me after solving every problem and ask whether he was right.

As his skills and confidence grew, he stopped looking to me nearly as often. That change was a sign of progress. He was beginning to trust his own thinking.

Confidence does not always appear as a child suddenly saying, “I love math.” Sometimes it appears quietly. They stop guessing.

They begin talking themselves through the steps. They check their own work instead of immediately looking to an adult for approval.

“Not Good at Math” Does Not Have to Be Permanent

Repeated struggles deserve attention, but they do not have to define your child’s future in math.

Your child may never love the subject, and that is okay. They can still develop stronger skills, greater proficiency, and more confidence in their ability to learn.

Begin by watching for consistent patterns rather than isolated mistakes.

Ask your child to explain how they are approaching a problem. Share what you notice with their classroom teacher. You can also use my free grade-level math-readiness checklist to look for skills your child may need before entering the next grade.

If the struggle continues, a focused assessment combined with careful observation may help reveal where the difficulty begins.

Once the missing connection is identified, instruction can begin at a point where your child is successful and move forward from there.

If you are concerned that an unfinished foundational skill is making math harder for your child, contact A to Z Learning Utah to learn how individualized math support can help identify and strengthen the skills underneath the struggle.

Frequently Asked Questions

What are foundational math skills?

Foundational math skills include number sense, place value, addition, subtraction, multiplication, division, fractions, decimals, and an understanding of how operations and numbers relate. More advanced math depends on students being able to use these ideas together.

Does using fingers mean my child has a math gap?

Not necessarily. Finger counting can be a useful strategy. It may be worth looking more closely if an older child depends on it for nearly every calculation, cannot use other strategies, or becomes stuck when the numbers grow larger.

Can a child have good grades and still have foundational gaps?

Yes. Some children memorize procedures, rely on support, or work very hard to maintain their grades. A gap may become more visible when problems become more complex or are presented in an unfamiliar way.

Can foundational math gaps be fixed?

Foundational skills can be strengthened with focused instruction, clear explanations, guided practice, feedback, and review over time (What Works Clearinghouse). The first step is identifying the skill or connection that is causing difficulty.

Should I ask my child’s teacher about math concerns?

Yes. Share specific examples of what you see at home and ask whether the teacher notices similar patterns in class. Parents and teachers often understand the problem more clearly when they compare observations.

About the Author

Alia Zundel is a licensed general education and special education teacher, math interventionist, and parent of neurodivergent children. Through A to Z Learning Utah, she provides online math tutoring for students in grades 4–8, specializing in helping students with ADHD and autism strengthen foundational skills, confidence, and independence.

References and Further Reading

• Institute of Education Sciences, What Works Clearinghouse. Assisting Students Struggling with Mathematics: Intervention in the Elementary Grades.

• Institute of Education Sciences, What Works Clearinghouse. Improving Mathematical Problem Solving in Grades 4 Through 8.

• Kofler, M. J., et al. Working memory and short-term memory deficits in ADHD: A bifactor modeling approach.

• Kofler, M. J., et al. Examining the roles of working memory and trait anxiety on math underachievement in children with ADHD.

• Peng, P., et al. Working memory in children’s math learning and its disruption in dyscalculia.

• Bae, Y. S., Chiang, H. M., and Hickson, L. Mathematical word problem solving ability of children with autism spectrum disorder and their typically developing peers.