“Why does my child need to play with blocks to learn maths?”

It’s a question many parents ask when they first encounter the unique teaching style behind Singapore Math. The answer lies in one powerful framework: the CPA Approach, which stands for Concrete → Pictorial → Abstract.

This isn’t just another teaching trend — it’s the secret sauce that has helped Singaporean students excel in maths worldwide.

What is the CPA Approach?

The CPA Approach is a learning journey with three essential stages. Instead of jumping straight into numbers and symbols, children build a strong foundation by first experiencing maths in hands-on, meaningful ways.

Let’s unpack what each stage means.

Concrete Stage: Learning with Real Objects

Think of the concrete stage as “learning by touching.” Children start by using physical objects like:

• Counting blocks

• Beads

• Coins

• Straws

• Everyday items at home (buttons, Lego bricks, etc.)

For example:

• To learn addition, a child physically groups 2 red counters and 3 blue counters and counts them all together to see that 2 + 3 = 5.

• To explore fractions, they might cut a pizza into equal slices to see what “half” really means.

Why it matters: Children are naturally tactile and visual learners. Concrete materials help them “see” numbers in action and understand what mathematical operations actually do.

Pictorial Stage: Drawing It Out

Once kids are comfortable handling objects, they move to the pictorial stage — drawing pictures to represent maths ideas. Instead of physical counters, they draw:

• Circles

• Rectangles

• Lines

• Bar models

For example:

• Instead of moving blocks around, they might draw 2 circles and then 3 more to show 2 + 3 = 5.

• For problem sums, they draw bar models to show relationships between quantities.

The famous bar model method is part of this pictorial stage, helping children visualise even tricky concepts like ratios or fractions.

Why it matters: Pictures help bridge the gap between hands-on learning and pure numbers. It’s like training wheels for abstract thinking.

Abstract Stage: Working with Numbers and Symbols

Finally, children reach the abstract stage, where they work directly with numbers, symbols, and equations — the maths as adults know it.

Instead of blocks or drawings, they write:

• 2 + 3 = 5

• ½ × ¾ = ?

By this stage, they understand what the numbers mean because they’ve:

1. Touched it (Concrete)

2. Seen it (Pictorial)

Why it matters: When kids jump straight to abstract numbers without the earlier stages, maths becomes mysterious and scary. CPA makes abstract concepts meaningful and logical.

Why CPA Works

✅ Prevents rote memorisation — kids understand, not just remember

✅ Builds confidence — no fear of new concepts

✅ Helps solve complex problems — especially word problems and bar models

✅ Supports all learning styles — tactile, visual, and logical

It’s especially powerful for:

• Addition and subtraction

• Fractions and decimals

• Multiplication and division

• Problem sums

How Parents Can Support CPA at Home

✨ Use real-life examples:

• Count coins while shopping

• Share snacks into equal parts

• Measure ingredients for baking

✨ Encourage drawing:

• Bar models for word problems

• Simple pictures to explain sums

✨ Don’t rush to symbols:

If your child seems confused, go back a step. Use objects or drawings before returning to numbers.

✨ Ask questions:

• “Can you show me with blocks?”

• “Can you draw what you’re thinking?”

A Simple Example of CPA in Action

Problem: 7 – 3 = ?

• Concrete: Place 7 counters on the table. Remove 3. Count how many remain.

• Pictorial: Draw 7 circles. Cross out 3. Count what’s left.

• Abstract: Write 7 – 3 = 4.

This simple progression ensures your child truly understands subtraction, not just the steps.

Final Thoughts

Singapore’s success in mathematics didn’t happen by chance. The CPA Approach has helped countless students understand, visualise, and master maths concepts from the inside out.

So the next time you see your child playing with blocks or drawing bars instead of scribbling equations, smile — it means they’re building the foundation for mathematical thinking that will serve them for life.

Because in Singapore Math, understanding always comes before solving.