Some kids have an excellent memory. Memorizing and reciting math facts seems like a walk in the park for them, but ask “How many rows of 6 chairs do we need for 24 kids?” and they hesitate.
At Mathnasium, we assess students’ math skills every day, and this is one of the most common challenges we see. Memorizing facts is one thing. Understanding how numbers work and how to use them flexibly is something else entirely. That’s where we focus.
Our seasoned math tutors share five strategies parents can use to help their child shift from quick recall to true understanding.
Mathematical thinking is the ability to make sense of numbers by reasoning through problems and recognizing underlying patterns. It involves asking questions, drawing connections, and understanding how and why different strategies work.
Instead of focusing only on correct answers, mathematical thinkers explore the relationships between ideas and approach problems with curiosity and flexibility.
This differs from rote learning, where learning occurs through repetition.
Consider this problem: “What’s 25 × 4?”
A student who relies on rote learning may answer quickly “100” because they’ve memorized the fact. But if you ask how they got it, they may simply say, “I just remember it.”
A mathematical thinker might reach the same answer but in a different way. They could say, “I know 25 times 2 is 50, and 50 times 2 is 100.” Or, “Four quarters make a dollar, so 25 times 4 is 100.” Their approach shows pattern recognition, flexible thinking, and a clear grasp of how numbers relate.
So why does this difference matter?
According to the National Council of Teachers of Mathematics (NCTM), students who are encouraged to reason, justify their thinking, and explore multiple solution paths develop deeper, more lasting understanding.
At Mathnasium, we also find that when students learn to reason through problems and try different ways of solving them, they remember more and feel more confident, especially as math gets tougher in later grades.
Mathematical thinking means making sense of problems, exploring ideas, and connecting concepts, not just recalling answers.
There are numerous studies on the impact of mathematical thinking on children's development, from cognitive to academic. We would highlight:
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We often get questions from parents about what they can do outside of school to support math skill development. What we’ve found is that the most effective approaches are usually simple, practical, and easy to weave into everyday family routines.
Here are five strategies we suggest for fostering mathematical thinking at home.
Imagine your child solves 12 ÷ 3 = 4 and quickly writes the answer. Instead of moving on, pause and ask: “How do you know it’s 4?”
They might draw three groups of four, count them out with blocks, or explain that 3 × 4 equals 12. Each of these responses goes beyond memorization by linking the numbers to reasoning.
Younger children (ages 5–7) might simply line up objects and count, while older ones (8–12) may explain the relationship between multiplication and division.
When children learn to justify their answers, they strengthen their ability to reason, organize their thoughts, and explain ideas clearly.
Praise the process by saying things like, “I like how you explained that,” or “That’s a smart way of checking.”
Gradually, these small prompts build a habit of thinking mathematically, not just answering quickly.
Abstract numbers often click when children can see what they represent. Instead of just saying “two-thirds is bigger than one-half,” show it. Pour water into two glasses of the same size. Fill one halfway, and the other with two-thirds. Ask, “Which has more?” and let your child compare.
You can do the same with multiplication or division. For 18 ÷ 6, place 18 buttons on the table and ask your child to sort them into groups of 6. Suddenly, division is no longer a rule to memorize but a picture they can describe.
Encourage your child to sketch or build whenever a problem feels tricky. Household objects or even fingers are enough.
Habits like these help them move from memorizing procedures to recognizing patterns and relationships.
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Our tutors often hear students ask questions like, “When will I use this?” or “Why does this matter?” What we’ve seen work, and what we strongly recommend to parents, is showing math in action to answer those questions.
You might ask your child to estimate the grocery bill, plan how many slices are needed for pizza night, or figure out how much time is left before bedtime.
If your student is older, planning a family outing with a set budget can be a powerful way to show how math problem-solving applies in real life.
Games turn practice into something children genuinely enjoy. Whether it’s a card game, rolling dice to create number challenges, or hands-on activities that involve counting and patterns, play invites kids to use math without realizing they’re “doing math.”
These activities build number sense, sharpen logical thinking, and encourage strategy, all in a relaxed setting.
When you make math part of playtime, you show your child that problem-solving can be fun and rewarding, not just something reserved for worksheets.
Math games turn practice into play and help children strengthen number sense and reasoning in a relaxed way.
Every error holds insight. Imagine your child is solving 3 + 5 × 2. They might add first (3 + 5 = 8) and then multiply (8 × 2 = 16). Their answer makes sense given their logic, but it shows a misunderstanding of order of operations.
Instead of saying, “That’s wrong,” ask, “Can you explain the steps you took?” Then show how multiplying before adding changes the result. By comparing both paths, your child learns why the order matters.
This approach reflects a growth mindset: mistakes aren’t proof that they “can’t do math,” but evidence that their brain is stretching. When children see errors as chances to refine their reasoning, they build resilience and confidence—qualities that matter as much as the correct answer itself.
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Building a true understanding of math is most effective when it begins early. While habits that encourage this start at home, families often find that busy schedules make it hard to work consistently with their children.
When that happens, Mathnasium is a trusted partner, chosen by over a million parents, to help students grow into confident math thinkers.
At the core of our learning centers is the Mathnasium Method™, a proprietary teaching approach proven not only to help students excel in math but also to transform how they think and feel about the subject.
Our approach consists of:
Personalized learning plans: Each student begins with a diagnostic assessment that pinpoints strengths and gaps. From there, we create a learning plan tailored to their needs.
Teaching for understanding: We use natural language and Socratic questioning to draw out what students know, how they reason, and where support is needed. Instruction combines mental, verbal, visual, tactile, and written techniques to adapt to how each student learns best.
Caring and supportive tutors: Our tutors are skilled not just in math but also in guiding students with patience, encouragement, and the right level of challenge.
Independent critical thinking and problem-solving: Beyond correct answers, we focus on the “why” and “how” behind each one. Students learn to reason independently and productively struggle through challenges, which are skills that build true self-reliance.
Singular focus on math: With thousands of pages of curriculum powered by the Mathnasium Method™, we specialize in math and go deep into how students learn and retain it.
And the results speak for themselves:
94% of parents report improved skills and understanding.
93% report a more positive attitude toward math.
90% of students see better grades.
With over 1,000 centers nationwide, Mathnasium is close to home for many families. For those in and near La Jolla, CA, Mathnasium of La Jolla has a dedicated team and years of experience in transforming students’ relationships with math.
One parent described their experience this way:
If your child is looking to catch up, keep up, or get ahead in math, schedule a free diagnostic assessment at Mathnasium of La Jolla. We’ll take it from there and help them grow into independent math thinkers, session by session.
📅 Schedule a Free Diagnostic Assessment at Mathnasium of La Jolla
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(858) 291-8186
