How children learn mathematics in primary school – beyond the right answer

As a primary school teacher, one of the questions I hear most often in class, during maths lessons, is simple, but very profound: “Miss, is this correct?” Not “why is it like this?”, but “is it correct?”

And from here, in fact, begins the conversation about how children learn mathematics.

When “correct” becomes more important than “understanding”

In primary school, especially in the first years, I constantly notice one thing: children very quickly associate mathematics with the idea of a correct answer. They want to know if they did it right, if they ticked it correctly, if they reached the result.

It is natural. But in this process a risk appears: attention moves from thinking to result.

The difference between knowing and understanding

I remember a moment in class, when we were working with large numbers. One of my students read without hesitation a six-digit number – correctly, quickly, confidently.

But when I asked him: “Why is it written like this? How do you know the value of each digit?”, there was a pause. He knew how to read the number, but he could not yet explain the structure behind it.

And then the difference between knowing and understanding becomes very clear.

This difference is also important for parents, especially in a context where learning is changing. In order for learning to be consolidated in the long term, understanding is needed. That is why I always explain to parents that speed of solving, for example, is not always a sign that the student has truly understood mathematics.

How a maths lesson works

At Avenor, in classroom practice we look less at the “final answer” and more at the process: how the child thinks, how they explain, how they check their ideas. Because, in reality, children will not only need correct calculations. They will need to understand, to make decisions, and to apply reasoning in new contexts.

That is why lessons do not always start with the “rule”. Many times they start with a question:

“Why did people need numbers?”

“How would the world look without a common system of measurement?”

Such questions give children the opportunity to talk, to ask questions, and to compare answers. In this process, they can discover, for example, old numbering systems and can reach by themselves the conclusion of why these are necessary.

Only afterwards do we formalise and state the rule.

In this way, mathematics is no longer perceived as abstract, but becomes concrete and logical – because students understand where and why it is useful in real life.

When mathematics becomes useful in decision-making

Another example I often use in class is a module that children love: a “space mission”.

Students receive a situation: they have limited resources and must decide how to use them in order to complete a mission.

There is no single correct solution. There is estimation, calculation, argumentation and decision-making.

I remember a child saying: “We can complete one more leg of the journey, but we no longer have enough fuel for the return trip.”

At that moment, mathematics was no longer an abstract exercise to solve in a notebook. Mathematics had become a decision, with real consequences.

The teacher’s role: less “how to do it”, more “how do you think”

For me, as a teacher at Avenor, these moments are the most important – when I see how children start to build their own way of thinking: they ask, they explain, they make mistakes, they come back, they try again.

Here comes the role of the teacher – not to say “this is how it is done”, but to guide through the right questions, which lead to understanding and, later on, to the acquisition of concepts that would otherwise remain too abstract for a 7- or 9-year-old child.

What happens when children make mistakes

I am happy every time a mistake appears.

Because mistakes are essential in the learning process. We do not correct them by simply saying “it is wrong”, but we use them as a starting point:

“How did you think?”

“What would you change?”

“Is there another way?”

These questions help us, as teachers, understand the thinking behind the mistake and, at the same time, help children clarify their thinking and avoid repeating the same errors.As a primary school teacher, one of the questions I hear most often in class, during maths lessons, is simple, but very profound: “Miss, is this correct?” Not “why is it like this?”, but “is it correct?”

And from here, in fact, begins the conversation about how children learn mathematics.

When “correct” becomes more important than “understanding”

In primary school, especially in the first years, I constantly notice one thing: children very quickly associate mathematics with the idea of a correct answer. They want to know if they did it right, if they ticked it correctly, if they reached the result.

It is natural. But in this process a risk appears: attention moves from thinking to result.

The difference between knowing and understanding

I remember a moment in class, when we were working with large numbers. One of my students read without hesitation a six-digit number – correctly, quickly, confidently.

But when I asked him: “Why is it written like this? How do you know the value of each digit?”, there was a pause. He knew how to read the number, but he could not yet explain the structure behind it.

And then the difference between knowing and understanding becomes very clear.

This difference is also important for parents, especially in a context where learning is changing. In order for learning to be consolidated in the long term, understanding is needed. That is why I always explain to parents that speed of solving, for example, is not always a sign that the student has truly understood mathematics.

What a maths lesson looks like

At Avenor, in classroom practice we look less at the “final answer” and more at the process: how the child thinks, how they explain, how they check their ideas. Because, in reality, children will not only need correct calculations. They will need to understand, to make decisions, and to apply reasoning in new contexts.

That is why lessons do not always start with the “rule”. Many times they start with a question:

“Why did people need numbers?”

“How would the world look without a common system of measurement?”

Such questions give children the opportunity to talk, to ask questions, and to compare answers. In this process, they can discover, for example, old numbering systems and can reach by themselves the conclusion of why these are necessary.

Only afterwards do we formalise and state the rule.

In this way, mathematics is no longer perceived as abstract, but becomes concrete and logical – because students understand where and why it is useful in real life.

When mathematics becomes useful in decision-making

Another example I often use in class is a module that children love: a “space mission”.

Students receive a situation: they have limited resources and must decide how to use them in order to complete a mission.

There is no single correct solution. There is estimation, calculation, argumentation and decision-making.

I remember a child saying: “We can complete one more leg of the journey, but we no longer have enough fuel for the return trip.”

At that moment, mathematics was no longer an abstract exercise to solve in a notebook. Mathematics had become a decision, with real consequences.

The teacher’s role: less “how to do it”, more “how do you think”

For me, as a teacher at Avenor, these moments are the most important – when I see how children start to build their own way of thinking: they ask, they explain, they make mistakes, they come back, they try again.

Here comes the role of the teacher – not to say “this is how it is done”, but to guide through the right questions, which lead to understanding and, later on, to the acquisition of concepts that would otherwise remain too abstract for a 7- or 9-year-old child.

What happens when children make mistakes

I am happy every time a mistake appears.

Because mistakes are essential in the learning process. We do not correct them by simply saying “it is wrong”, but we use them as a starting point:

“How did you think?”

“What would you change?”

“Is there another way?”

These questions help us, as teachers, understand the thinking behind the mistake and, at the same time, help children clarify their thinking and avoid repeating the same errors.

We invite you to read the full article on the Despre Copii platform.

Avenor actively contributes to the conversation about education in Romania by promoting best practices and collaborating with relevant editorial partners in the field of education. We aim to bring greater clarity and perspective to the dialogue between schools and parents, supporting informed and responsible decisions regarding children’s educational journeys. We invite you to stay connected to the latest articles published in the Avenor x DESPRECOPII section, a space dedicated to reflection and continuous learning for both parents and teachers.