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Why Some Children Are Good at Numbers but Struggle With Geometry?
September 8, 2026
Why do some children struggle with geometry even when they are good at maths?
Many students are comfortable with numbers. They can add, subtract, multiply and divide with confidence. They may be quick with calculations and perfectly comfortable solving numerical problems.
But put a geometry diagram in front of them, and suddenly things feel different.
They look at the lines.
They look at the angles.
They look at the numbers.
And they don’t know where to begin.
So, why do children struggle with geometry?
The answer isn’t always that they don’t understand mathematics. Sometimes, the challenge lies in something less obvious: how they see and interpret mathematical information.
And this brings us to an important mathematical skill: spatial thinking.
What is spatial thinking?
Spatial thinking is our ability to understand where things are, how they relate to each other, and how they may look when we move, rotate, combine or transform them.
Think about what happens when a child is asked to:
- imagine a shape being rotated,
- identify a pattern in a diagram,
- understand how two shapes fit together,
- visualise a three-dimensional object,
- understand position on a number line,
- or work out how different parts of a diagram are related.
None of these tasks is simply about calculation.
They require the child to see relationships.
And mathematics is full of relationships.
This is one reason why mathematical thinking involves much more than getting the right answer quickly.
As we discussed in our article on building mathematical thinking and confidence in children, strong mathematical thinking involves being able to approach unfamiliar problems, try different approaches, notice patterns and reason through a problem.
Spatial thinking can be part of that process.
Why does geometry feel different?
Consider a simple angle problem.
A child may know:
Angles on a straight line add up to 180°.
The rule is not the problem.
But when several lines and angles appear in a diagram, the child first has to decide:
Which angles are related?
They have to identify the relevant lines.
They have to recognise the relationship between the angles.
They may need to mentally extend a line.
They may need to ignore information that isn’t relevant.
Only after that can they apply the mathematical rule.
So there are actually two different things happening.
Knowing the mathematics.
And seeing where the mathematics applies.
A child can be strong at the first and still need more practice with the second.
Spatial thinking is not just a geometry skill
This is where things get particularly interesting.
Spatial thinking doesn’t stop at geometry.
It appears in many areas of mathematics.
Fractions
A fraction describes a relationship between a part and a whole.
A child who sees three-fourths as three equal parts out of four is connecting a symbolic representation with a visual or conceptual one.
Measurement
Length, area and volume all involve space.
A child may memorise a formula for the area of a rectangle, but understanding why the formula works involves understanding the relationship between length, width and the space inside the rectangle.
Number lines
A number line is spatial.
Numbers have positions.
Distances between numbers matter.
Moving to the right or left represents a change.
Patterns
Patterns aren’t always numerical.
They can be visual as well.
A child may need to identify what changes, what stays constant and what comes next.
Problem-solving
Sometimes the best way to understand a mathematical problem is to draw it.
A diagram can turn an abstract situation into something the child can reason about.
This is particularly relevant when children begin encountering the kind of unfamiliar, reasoning-based questions that appear in Olympiad mathematics.
Our Math Olympiad preparation guide discusses why Olympiad mathematics is different from simply knowing school methods: children need to reason, solve unfamiliar problems and decide how to approach a question.
Spatial thinking can be one part of that toolkit.
What does research say?
The connection between spatial skills and mathematics has been studied for years.
A 2022 meta-analysis looked at 45 studies and found a moderate positive relationship between spatial skills and mathematical performance.
More recently, a 2026 meta-analysis examined 62 studies, 68 independent samples and 14,356 participants.
It found a moderate relationship between spatial reasoning and mathematical ability.
The researchers also found particularly strong relationships involving spatial visualisation and spatial orientation. The association was stronger for areas such as geometry and logical reasoning than for arithmetic.
These findings do not mean that every child who struggles with geometry has weak spatial skills.
Nor do they mean that spatial training automatically makes a child better at mathematics.
But they do highlight something worth paying attention to:
Mathematical ability is not only about manipulating numbers.
So, what can parents do?
The good news is that spatial thinking doesn’t have to be taught through complicated activities.
It can be incorporated naturally into everyday mathematics.
Instead of immediately giving a child the formula, try asking:
“What do you see?”
Instead of solving a geometry problem for them, ask:
“Which angles do you think are connected?”
Instead of telling them what to draw, ask:
“Can you draw what the question is describing?”
Other simple approaches include:
- asking children to draw a diagram before solving a word problem;
- using blocks or objects to explore shapes;
- asking them to imagine a shape being rotated;
- using number lines;
- comparing different representations of the same idea;
- asking children to estimate before calculating;
- asking “How do you know?” rather than only “What is the answer?”
These small changes can encourage children to explain and visualise their thinking rather than simply perform a procedure.
This is also why the quality of questions matters
There is an important connection here with mathematical confidence.
A child who is given question after question where the method is obvious may become very good at recognising familiar patterns.
That is useful.
Fluency matters.
Accuracy matters.
Practice matters.
But mathematics also requires flexibility.
What happens when the question doesn’t look familiar?
What happens when there is no obvious formula?
What happens when the child needs to decide what to do first?
This is where carefully designed questions become important.
As we wrote in How to Build Math Confidence and Mathematical Thinking in Children, a child may be perfectly comfortable solving familiar questions but become unsure when faced with something that requires them to figure out the approach themselves.
Geometry provides many opportunities for exactly this kind of thinking.
Don’t ask only, “Can they solve it?”
When a child gets a geometry question wrong, it is tempting to immediately look at the final answer.
But there may be a better question to ask:
“Where did the thinking break down?”
Did the child:
- misunderstand the diagram?
- miss a relationship?
- apply the wrong rule?
- struggle to visualise the situation?
- rush?
- misunderstand the question?
- know the concept but not know how to begin?
These are very different problems.
And they need very different kinds of practice.
This is similar to what we discussed in our article on why children make careless mistakes in maths.
An incorrect answer doesn’t always tell us what the child doesn’t know.
Sometimes, we need to look at how they arrived there.
Mathematics is more than numbers
Perhaps this is the biggest idea worth taking away.
When we think of a child who is “good at maths”, we often imagine a child who calculates quickly.
But mathematical ability is broader than that.
A strong mathematical thinker can:
notice
visualise
connect
reason
estimate
question
try
change strategy
and explain.
Sometimes that thinking happens with numbers.
Sometimes it happens with symbols.
Sometimes it happens with words.
And sometimes, it happens through a diagram.
So, why do some children struggle with geometry?
There isn’t one answer.
Every child is different.
But if a child is comfortable with numerical calculations and repeatedly struggles when mathematics becomes visual, it may be useful to look beyond whether they have memorised the required formula.
Ask instead:
Can they see the relationships?
Can they interpret the diagram?
Can they visualise what is happening?
Can they move between a picture and a mathematical idea?
Because sometimes the problem isn’t that the mathematics is too difficult.
The child may simply need another way to see the mathematics.
The goal is not just to get the answer
At Simplified Mathematics, we believe mathematics is more than getting through a set of questions.
Our Math Olympiad quizzes and practice resources are designed around conceptual understanding, problem-solving, reasoning, speed and accuracy—not simply memorising procedures.
And that distinction matters.
Because the goal isn’t to create children who can solve only the questions they have seen before.
The goal is to help children become more comfortable with questions that make them stop and think:
“How do I figure this out?”
Sometimes that thinking starts with a number.
Sometimes it starts with a pattern.
And sometimes—
it starts with being able to see.
Want to strengthen mathematical thinking?
Explore Simplified Mathematics’ Math Olympiad quizzes and practice resources, designed for Grades 4–6 with chapter-wise practice, different difficulty levels and detailed explanations.
You can also explore our Maths blogs for more articles on mathematical thinking, problem-solving, confidence and Olympiad preparation.
Research
Atit, K., Power, J. R., Pigott, T., et al. (2022). Examining the relations between spatial skills and mathematical performance: A meta-analysis. Psychonomic Bulletin & Review, 29, 699–720. Research paper
Lu, H., Fan, Z., Leung, F. K. S., et al. (2026). How is spatial reasoning associated with mathematical ability? Evidence based on a meta-analysis. Learning and Individual Differences, 125, 102838. Research paper
