(And what parents need to know about the CPA method)

A decade ago, Singapore maths was all the rage in our UK schools and with good reason. When global maths rankings are released, the same regions appear at the top:
Singapore, Shanghai, Hong Kong, Japan, South Korea all following the CPA method.

Children are not doing more maths or learning faster, they are learning maths differently, which is in alignment with their natural development.

As a teacher who visits different schools, sadly I don’t see this methods used as much these days in schools.

What makes Singapore Maths so powerful is not worksheets or pressure. It’s the way concepts are built so that understanding comes before memorisation.

What is Singapore Maths?

Singapore Maths is a mastery-based approach that focuses on:

• Fewer topics taught each year

• Concepts being explored more deeply

• Progression happening only after understanding is secure

In contrast, Western systems in my professional opinion:

• Cover too many topics too quickly

• Move on regardless of mastery

• Prioritise curriculum coverage over conceptual security

The result?

In the East instead of rushing through content, children stay with a concept until it makes sense. In the West, children, move on whether it makes sense or not. Eastern students therefore build strong foundations that support later complexity. Western students often develop gaps that compound over time.

Naturally, children in the East love maths and are renowned for being very good at it.

Their approach reduces:

• Cognitive overload

• Maths anxiety

• Guessing and rote learning

It increases:

• Confidence

• Flexibility

• Long-term retention

So how does Singapore Maths work and How can parents support their children’s learning at home using this method instead? The CPA approach

CPA stands for:

Concrete → Pictorial → Abstract

This sequence mirrors how the brain actually learns.

1. Concrete means hands-on understanding

Children begin by physically manipulating objects:

• Counters

• Cubes

• Beads

• Numicon-style resources

At this stage, maths is not symbolic. It’s experienced. It’s practical. Young children literally feel the maths.

But what does that mean?

It means they don’t learn numbers 1-10. They feel the numbers.

1 is one jump

2 is 2 claps

3 is collecting 3 toys

It’s about associating the numbers to themselves. How many hands do they have? How may fingers do they have etc. They become the numbers.

Why this matters:

• It reduces fear

• Anchors meaning

• Builds real number sense

Children don’t just hear that 7 + 5 = 12.
They see and feel why.

Concrete learning means they are physically immersed in the learning.

Once they understand what numbers are physically, they move to the next phase.

2. Pictorial – Now this is where most western schools start

This is the visual representations:

• Seeing the patterns

• Reading the text

• Using pictures

• Using paper

• Bar models

• Number bonds

• Part–whole diagrams

This is where Singapore Maths is especially distinctive.

The pictorial stage is about problem solving:

• Seeing relationships visible

• Drawing the answer

• This helps children organise thinking

This is why Singapore-trained children are so strong at word problems—because they can see the structure, not just the numbers.

3. Abstract (Symbols make sense)

Only once the physical and visual understanding is secure do children move onto:

• Numbers

• Symbols

• Algorithms

At this point children are able to work things out in their heads – what we refer to as mental maths:

• Symbols like + = x now simplify their knowledge and make things easier to write down.

• Procedures are logical, not random

• Children know why methods work

This is where many systems begin. Whereas this is where Singapore Maths ends.

Why this makes maths feel “easy”

When children:

• Understand how numbers work they can manipulate them memorising concepts more easily

• When concepts are built step by step, there is a natural flow

• Children don’t feel rushed and confused

Maths stops feeling like a test of intelligence and starts feeling like a solvable puzzle.

What parents need to know (and unlearn)

1. Confusion is not failure

If your child is drawing, using cubes, or talking through a problem, they are learning—even if it looks slower.

Once they understand the pictorial stage, ask them is there a way we can do the maths quicker? That’s when abstract representations make more sense.

For example: I want to solve the following problem: I have 20 seeds and need to plant them in my garden. If I plant them in rows, how many seeds will I plant in each row?

Concrete: put the seeds physically in different arrays.

Pictorial: draw the seeds in arrays

Abstract: 1x20, 20x1, 2x10, 10x2, 5x4, 5x4

2. Don’t rush to “the shortcut method”

Don’t jump to the abstract if they can’t see the concrete

Ask instead:

• “Can you show me how you see it?”

• “What does this part represent?”

3. The pictures matter

Bar models and diagrams are not a crutch. They are a bridge.

Strong visual thinkers become strong abstract thinkers.

4. Mastery means depth, not speed

Revisiting the same concept is a feature—not a flaw.

Why this matters beyond primary school

Children taught through CPA:

• Are more resilient problem-solvers

• Transfer skills across topics

• Are less likely to develop maths anxiety

• Perform better on unfamiliar problems

They don’t just learn maths.
They learn how to think mathematically.

Singapore Maths works because it respects how children learn.

When we slow down, make learning visible, and build understanding from the ground up, maths becomes something children can trust themselves with.

And that changes everything.