Raising empowered girls: 3 – The girl who fell in love with the question

There is a particular kind of moment that teachers live for. It does not happen during a test. It does not happen when a child gets the right answer. It happens when a child gets an answer, looks at it, and then asks: but why does that work?

That question, small and instinctive and entirely self-generated, is the sound of a mind catching fire. It is the moment a child stops performing maths and starts doing it. And it is the moment, in our experience, that separates a girl who can do maths from a girl who loves it.

This piece is about how to nurture that moment. How to build the conditions at home and at school in which your daughter does not just learn to calculate but learns to derive, to question, to explore and to delight. How to stretch her without pressuring her. How to grow her without forcing her. And why spontaneity, that most unscheduled and ungovernable of qualities, might be one of the most powerful mathematical tools she will ever develop.

“We are not trying to raise girls who always have the right answer. We are trying to raise girls who push to uncover many different answers to the same question. Nowhere is this truer than in mathematics.”

What Maths Fluency Actually Means

Ask most parents what it means for their daughter to be good at maths and the answer will involve speed, accuracy and confidence with numbers. These things matter. But they are not fluency. They are more like fluency’s prerequisites, the scales a pianist must practise before she can play.

True mathematical fluency is something richer. It is the ability to move flexibly between different ways of seeing and solving a problem. To recognise patterns and ask why they exist. To hold a mathematical idea in the mind, turn it over, approach it from a different angle and understand it rather than simply execute it.

A child who has learned only to follow procedures has a single blade. She will cut through anything that matches the procedure and come to a standstill the moment it does not. A child who has developed genuine fluency has the whole compass. She can approach the problem from the north when the south does not work. She has range.

Deriving rather than memorising is at the heart of this. When a child derives a mathematical fact rather than simply remembering it, she builds something that memorisation cannot: understanding. She knows not just that seven eights are fifty-six but why multiplication works the way it does. Not just that the angles in a triangle sum to one hundred and eighty degrees but what that means and where it comes from. This understanding is durable. It transfers. It gives her something to reach for when she encounters a problem she has never seen before.

This is why we do not simply drill facts at our school and then move on. We linger. We ask: does that make sense? Could you show me another way? What would happen if we changed this? The lingering is not inefficiency. It is where the real learning lives.

The Greenhouse, Not the Hothouse

There is a distinction worth drawing clearly, because it matters enormously for how you support your daughter at home.

A hothouse forces growth. It raises the temperature artificially, pushes plants beyond their natural pace and produces results that often look impressive until you move them outside, where they struggle to survive without the heat that created them. A hothouse child can perform under exam conditions. She is less sure of herself in the open air of genuine challenge. The real world, in plein air.

A greenhouse is different. It creates optimal conditions: the right warmth, the right light, the right amount of challenge and the right amount of rest. It does not force. It enables. The growth it produces is real growth, rooted growth, the kind that travels with the plant wherever it goes.

“High performance and gentleness are not opposites. The greenhouse understands this. The hothouse has forgotten it.”

In mathematical terms, this distinction looks like the following. A hothouse approach gives a child more content before she has genuinely understood the content she has. More procedures, harder problems, faster pace. The results can look like progress. But understanding has been skipped in the rush, and understanding, in mathematics, is the only thing that compounds.

A greenhouse approach gives a child more depth before it gives her more content. It asks her to understand what she knows more completely, to explore its edges and its connections, to find it surprising and to find it beautiful, before moving on. The pace looks slower from the outside. The understanding being built is far more powerful.

This is what we mean when we talk about depth of learning. Not doing harder sums earlier. Doing the sums you are doing more deeply, more flexibly and with more genuine comprehension of why they work. Exactly what is required to be successful at GCSE and beyond.

What Depth Looks Like on a Tuesday Morning

In our Year 3 classroom last term, a group of eight-year-olds were working with multiplication. The lesson was not about drilling the times tables. It was about understanding what multiplication actually is.

The teacher put a single question on the board: what is the link between four times twelve and eight times six? She did not tell them the answer. She asked them to find out, and to explain why.

What followed was twenty minutes of genuine mathematical thinking. Children drew arrays. They built models with counters. They argued. One girl said: they have to be the same because you are counting the same things, you are just looking at them differently. Another said: but how do you know they are the same things? They look different. And then something happened that the teacher described later as one of her favourite moments of the year: the first girl paused, thought, and said quietly, I need to think about that more.

She did not have the right answer… yet. But she had something more valuable: a real question. A question she had generated herself, from her own thinking, that she genuinely wanted to resolve. That is the moment mathematics becomes something more than a subject. It becomes a way of thinking.

Depth of learning looks like this. It looks like confusion that is productive rather than distressing. It looks like questions that nobody has prompted. It looks like a child who comes to a standstill, not because she has failed but because she has noticed something she does not yet understand and wants to. These are our Superstar Mathletes!

The Ideas Compass in the Maths Classroom

Everything we have written about The Ideas Compass, about the habit of asking what else could I try, applies with particular force in mathematics. Mathematics is, at its heart, a subject about finding paths. There is almost always more than one route to an answer. The child who knows only one route is vulnerable. The child who has developed a compass full of approaches is not.

When your daughter comes to a standstill with a maths problem at home, the instinct is often to show her the method. To point to the path she has missed. This is understandable and sometimes necessary. But before you do, try the compass approach. Ask her: what do you know about this problem? What have you already tried? Is there a simpler version of this problem you could solve first? Could you draw it? Could you make it smaller? What do you know to be true?

These questions do not give her the answer. They give her directions. They model the habit of generating multiple approaches, which is exactly what genuine mathematical thinking requires. Over time, she begins to ask these questions herself. The compass becomes internal. And an internal compass, in mathematics as in life, is something nobody can take from her.

The Power of Spontaneity

Here is something that formal mathematics education can accidentally squeeze out of a child: the pure, unscheduled joy of noticing something mathematical in the world and wanting to understand it.

A young child is spontaneously mathematical. She lines things up by size. She notices patterns in tiles. She counts steps and compares distances and wonders, without being asked, whether the longer route takes more steps or fewer. She is doing mathematics all the time, not because she has been told to, but because mathematical thinking is a natural human instinct when it has not been schooled out of us.

“Spontaneity in mathematics is not the absence of rigour. It is rigour that has become so natural it no longer needs to be imposed from outside.”

What formal education can do, if it is not careful, is replace this spontaneous curiosity with performed compliance. The child learns that mathematics happens at a desk, with a pencil, when an adult says so. She learns that there is a method and that her job is to execute it. The aliveness that she brought to mathematics naturally begins to narrow into something more cautious and more dependent on external direction.

The greenhouse approach actively works against this. It creates space for mathematical spontaneity: for the detour, the tangent, the question that nobody planned for. It treats the child who notices something unexpected not as a distraction but as the whole point.

Cultivating Spontaneity at Home

You do not need to be a mathematician to nurture mathematical spontaneity in your daughter. You need only to be curious alongside her and to take her questions seriously when they arise.

Notice mathematics in ordinary life. The angle of a slide in the park. The pattern on a bathroom floor. The way a pizza is divided. The ratio of orange juice to water in a squash. Not as lessons. As genuine curiosity. Look at that. I wonder why that works that way.

Let her be wrong without anxiety. Spontaneous mathematical thinking involves a great deal of being wrong. A child who fears being wrong will not think spontaneously. She will wait to be shown. Create a home where a wrong guess is interesting, not embarrassing. What made you think that? Let us find out together.

Ask unanswerable questions together. Some of the best mathematical conversations begin with questions that neither of you can answer immediately. How many steps would it take to walk to school if you were a cat? If we doubled everything in this room, what would change? These questions are not solvable in sixty seconds. They require imagination, estimation and genuine thinking. They are also, quietly, mathematically rich.

Resist the rush to the answer. When your daughter is working something out, the most powerful thing you can often do is wait. Let her sit with the uncertainty. Let her try something and see what happens. The moment you supply the answer, the thinking stops. The moment she finds it herself, something is built that will not be forgotten.

Celebrate the question more than the answer. This is perhaps the single most important shift a parent can make. When your daughter asks why, resist the instinct to simply tell her. Say instead: that is a brilliant question. What do you think? Then think together. A daughter who learns that her questions are celebrated will keep asking them. A daughter who learns that questions are just the slow route to being told the answer will stop.

Stretching Without Straining

There is one more thing worth saying plainly, because it is the thing parents worry about most.

You want your daughter to be stretched. You want her to be challenged, to grow, to work at the edge of what she can do. These are right and good instincts. But there is a version of stretching that strains rather than strengthens, and it is worth knowing the difference.

Stretching that strengthens happens at what educators call the ‘edge of understanding’: the place where a child is working just beyond what she can do comfortably, with enough support that she does not fall but enough challenge that she cannot coast. This is the greenhouse. The warmth is real. The growth is real. And crucially, the child herself often does not experience this as pressure. She experiences it as engagement.

Straining happens when the challenge outpaces the understanding beneath it. When a child is given harder content before she has genuinely grasped the content she has. When speed and correctness are prioritised over comprehension. When she learns that the point of mathematics is performance rather than understanding. This is the hothouse. It can produce short-term results. It produces long-term fragility.

The question to ask, both at school and at home, is not: is she doing hard enough work? It is: does she have a deep understanding of what she is doing? Does she have questions? Does she find it interesting? Is she reaching for the compass or waiting to be shown the path?

“A girl who finds mathematics genuinely interesting is a girl who will always keep going. That interest is not a nice extra. It is the engine.”

A Note on Love

We have talked a great deal in this piece about depth, fluency and spontaneity. But underneath all of it is something simpler: we want your daughter to love mathematics. Not to tolerate it. Not to be adequate at it. To find it genuinely, lastingly, surprising.

This is not a naive hope. Mathematical love is not a personality trait that some children are born with and others are not. It is something that grows in the right conditions. It grows when questions are celebrated. When being wrong is interesting. When depth is valued over speed. When a child is given room to notice, to wonder and to derive rather than simply to remember and repeat.

It grows, in other words, in exactly the conditions we are trying to build together: at school, at home, and in the conversations between the two. It grows when the adults around her believe that she has more than one answer inside her, and are patient and curious enough to help her find them all.

That is the greenhouse. That is the compass. That is the girl we are growing together.

Gillian Panton, Head of Junior School

Sydenham & Dulwich Girls  ·  Parent Thought Series: Learning & Mathematics