Why Can Children Answer So Fast, Yet Not Truly Understand Math?
A Reflection
When Fast Is Mistaken for Smart
Not long ago, we received a report about children at another school who were still struggling with something very basic: numbers in the range of 24 to 42. The difficulty lay at the most fundamental level, their sense of what those numbers actually mean. These children could memorize. They could follow a procedure. But when asked to explain why 27 + 15 = 42, or why 36 can be broken into 30 and 6, they stopped. They simply did not know what to say.
And this is where we want to ask a question we feel must be asked honestly. When those children see the numbers 24 and 42, do they truly grasp how much 24 is, how much 42 is? Have they ever touched that amount, held twenty-four real objects in their hands, arranged them, seen them with their own eyes? Have they ever felt that forty-two is four groups of ten and two ones, something they can pick up, move around, and count one by one? Numbers are symbols. They stand for something real, something that can be experienced through the senses. And it is truly a shame when our children spend all their time with the symbols alone, writing them, memorizing them, operating on them on paper, without ever knowing what those symbols represent. It is like a child who memorizes every word in a dictionary but has never seen, touched, or experienced the things those words name.
This phenomenon is a symptom of a learning culture we have normalized for a long time: math as a race to answer fastest. We see it everywhere. In tutoring centers that promise “5-second tricks.” In YouTube and TikTok videos showing young children rattling off multiplication answers at machine speed, met with applause. In classrooms where success is measured by how many problems a child gets right and how many minutes it takes. The child looks smart. The child looks capable. But does the child understand?
A Misguided Direction for Math Education
Let us be honest with ourselves. When we feel proud watching a child answer 7 × 8 = 56 in two seconds, what are we actually celebrating? We are celebrating memory. We are celebrating reflex. Calculators have been doing that since the 1970s. The phone in our pocket does it right now. If the entire purpose of math education is to produce numerical answers as quickly as possible, then we are training children to become slow, anxious versions of a machine. And that, with all due respect, is mechanical training. It is far from education.
What is even more troubling is that when children are only trained to answer, they never learn to ask. They never feel that 42 is forty-two, four groups of ten and two ones, something real and tangible. They never build number sense, the quantitative intuition that underpins everything in mathematics that comes later. So we should not be surprised when, in grade 4, 5, or 6, the child who was “so good at fast mental math” suddenly hits a wall with fractions, ratios, or word problems. The foundation all along was memorized procedures. And memorized procedures have an expiration date.
What Is the Real Purpose of Math Education?
This is a question we rarely ask, yet it should be the very first question before we choose a method, a curriculum, or a tutoring program. Mathematics, at its core, is a way of thinking. It lives in a territory far wider than numbers. Math education aims to build several fundamental things in a child.
First, it builds the ability to think in a structured way. Mathematics teaches that every big problem can be broken down into small, logical steps. A child who understands why we add the ones first and then the tens is learning the principle of decomposition, a thinking skill they will use for a lifetime, in any field.
Second, it trains reasoning and shifts the habit of guessing. “If I add 3 here, what happens there?” “Does my answer make sense?” These are habits of critical thinking that can only grow through a gradual process of understanding, through exploration and reflection. Drilling 100 quick-answer problems per page will never produce them.
Third, it nurtures sensitivity to patterns and relationships. Mathematics is the language of patterns. The sequence 3, 6, 9, 12 tells a story about consistent growth. A child who sees the pattern can predict, generalize, and eventually think abstractly.
Fourth, it builds intellectual resilience. The process of understanding a concept step by step (trying, getting it wrong, trying again, and finally having that “click” moment) teaches a child that temporary confusion is a natural part of learning. This is the opposite of the “answer fast or you’re stupid” culture we unknowingly instill.
Fifth, it develops a logical language for communication. Mathematics trains children to express their thoughts with precision. “Greater than,” “equal to,” “if… then…” are the foundations of clear argumentation, a skill that reaches far beyond the math classroom.
If these five things are not happening in a classroom or at a child’s study desk, then what is taking place is arithmetic drill, and nothing more. And arithmetic drill without understanding is a building without a foundation.
Mathematics as a Way of Thinking
Philosophically, there are two broad views of mathematics that shape how we teach it. The first view, which dominates in practice, treats mathematics as a calculating tool. Its goal is to produce correct answers. Its method: repetitive practice, memorize formulas, master tricks. Success is measured by speed and accuracy. The second view, the one that should underpin education, treats mathematics as a way of understanding the world. Its goal is to build logical, spatial, and quantitative thinking structures within the child. Its method: exploration, hands-on manipulation, discussion, reflection, and step-by-step understanding. Success is measured by depth of understanding and the ability to transfer knowledge.
At SJMES, we choose the second view. Computational fluency still matters, and we still practice it. But we position it as a natural byproduct of understanding, as fruit that grows from a sturdy tree of comprehension. A child who understands why 24 + 18 = 42 (because 20 + 10 = 30, then 4 + 8 = 12, then 30 + 12 = 42) has a system. And that system can be applied to 347 + 285, to fractions, to algebra, to whatever comes next. A child who merely memorizes that 24 + 18 = 42 will run out of memory the moment the numbers get bigger.
Why “Speed” Content on Social Media Distorts Our Perception
We need to talk honestly about this. Videos of children answering math problems at extraordinary speed on TikTok, YouTube, or Instagram Reels are designed for one thing: the viewer’s emotional reaction. Amazement. Pride. “Wow, a child that young can already do that!” Appreciating a child is a wonderful thing. The problem arises when this kind of content redefines what parents and the wider public consider “good math learning.”
Suddenly, a child who needs 20 seconds to answer but can explain the process is seen as less bright than a child who answers in 2 seconds but cannot explain why. Suddenly, parents feel anxious and rush to find tutoring programs that promise “fast methods,” without pausing to ask: fast at understanding, or fast at answering? The two are very different. And the difference only becomes visible three, four, five years later, when problems can no longer be solved with a single trick and instead require layered reasoning.
We are open to technology and social media. What we ask of parents is a simple request: let depth of understanding be the standard of competence, and do not let virality replace it. Your child is a growing human being. Their thinking process cannot and need not be cut into 15 seconds.
SJMES Always Starts from There
At SJMES (Saint Joseph Montessori Elementary School), our approach to mathematics always starts from there. From concrete experience. From objects that can be held. From quantities that can be seen and felt. From understanding built layer by layer before a symbol is ever written down.
The first principle we hold is that concept comes before procedure. A child touches, draws, manipulates, and feels a concept before being asked to write it down as a formula. When we introduce 24 + 18, we begin with questions: “What does 24 mean? What does 18 mean? What happens when we put them together?” Only then do we move to how to write it down. A child needs to know what they are working with before they learn how to write it.
The second principle is that the process is valued equally with the answer. In our classrooms, a child who writes an incorrect answer but shows a sound line of reasoning receives the same appreciation as a child who gets the right answer. Because that line of reasoning is the mathematics. The final answer is just the dot at the end of the line.
The third principle concerns fluency. We do train fluency, of course. But the fluency we pursue is fluency born of understanding. A child who truly understands will become fast on their own. A child who is only fast without understanding will be fragile the moment the context changes. We choose to build meaningful slowness today, for the sake of sturdy speed tomorrow.
The fourth principle is making room for confusion, mistakes, and trying again. We welcome confusion as part of the process, because that is where real learning happens, in the space between “I don’t know yet” and “oh, now I get it.” A child who is never allowed to be confused will never experience the joy of truly understanding.
The fifth principle is communication. Children naturally narrate and discuss. When older children communicate with younger ones, they exchange ideas, challenge each other’s thinking, and build arguments together. This process strengthens understanding and the courage to think, and it makes mathematics a living social experience rather than a silent interaction between a child and a sheet of paper.
And the most fundamental point of all: because what we are training is a way of thinking, a completed worksheet is not the measure. A sheet full of correct checkmarks does not necessarily mean a mind is at work. Conversely, a sheet covered in scribbles, attempts, and one or two errors that the child has corrected on their own often signals understanding that is growing in a healthy way.
We write this in a spirit of sharing. We write this because we see children, in our school and beyond it, whose thinking potential lies buried under piles of practice problems they never truly understood.
If your child needs more time than their friend to arrive at an answer, it may well be a sign that they are building a deeper understanding. And that is an investment of tremendous value.
If you feel tempted to enroll your child in a “speed math” program because of a viral video, we ask just one thing: ask yourself first, will my child learn to understand, or will they only learn to memorize, or simply become mechanical?
True mathematics grows patiently. It is built stone by stone, concept by concept, with curiosity and with the willingness to walk slowly so that every step is firmly placed. And a child built that way will have a foundation that no problem, however complex, can shake in the years to come.
Antonius Widitrianto
Posted on 12 August 2026