What is CPA Approach?

And how parents can use it at home?

If your child struggles with math, the issue might not be ability—but how the subject is taught. One of the most effective and research-backed instructional strategies is the CPA approach—short for Concrete–Pictorial–Abstract. This method builds deep understanding step by step, making math more accessible for every learner.

What Does CPA Stand For?

1. Concrete – Learning by Doing

Students begin with physical objects to understand math ideas. For example:

• To learn 5 + 2, they use 5 red counters and 2 blue counters, then combine them and count 7.

• To understand multiplication, they might use arrays of LEGO blocks to visualize '3 groups of 4'.

2. Pictorial – Drawing What They See

After hands-on experience, students draw pictures or diagrams:

• For 5 + 2, they might draw 5 apples and 2 apples.

• For fractions, a circle divided into equal parts helps visualize ¾ as “3 out of 4 parts shaded.”

3. Abstract – Using Numbers and Symbols

The final stage involves traditional math notation:

• 5 + 2 = 7

• ¾ × 8 = 6

Because students have experienced the concept physically and visually, the symbols now make sense.

What Does the Research Say?

The CPA model is rooted in Jerome Bruner’s (1966) theory of enactive, iconic, and symbolic representation. Bruner argued that children learn best by progressing from doing (Concrete), seeing (Pictorial), to symbolizing (Abstract).

Key research support includes:- Carbonneau, Marley & Selig (2013): A meta-analysis found that using manipulatives significantly improves math achievement.- Boaler (2016): Emphasized visual learning and flexible thinking in her book 'Mathematical Mindsets'.- OECD (2015 PISA Results): Countries like Singapore using CPA perform consistently at the top in global math scores.- Baroody (1989): Supported visual and hands-on strategies as key to number sense.

Why CPA Works

Builds conceptual understanding, not just procedural knowledge.- Bridges the gap between real life and abstract math.- Supports diverse learners: visual, kinesthetic, or ELL students.- Encourages reasoning and problem-solving.

Real-Life Examples

Math Topic	Concrete	Pictorial and Abstract
Addition	Combine buttons	Draw circles, then write 4 + 3 = 7
Fractions	Slice a pizza	Color a pie chart, then write 1/2 + 1/4 = 3/4
Division	Share 12 beans among 4 plates	Draw 4 groups with 3 dots each, then write 12 ÷ 4 = 3
Area	Tile squares on a table	Grid drawing, then write Area = l × w

How Can Parents Use CPA at Home?

Concrete: Use items like coins, spoons, cereal.- Pictorial: Encourage drawing math ideas.- Abstract: Move to symbols when confident.

Example activity: Show “4 groups of 3” with LEGO bricks, draw it, then write 4 × 3 = 12.

Final Thoughts

The CPA approach helps children make sense of math—not fear it. It turns abstract symbols into something meaningful. Whether your child is just learning to count or exploring fractions, CPA provides a research-proven way to build confidence and real understanding.

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See also