How do I use the Concrete-Pictorial-Abstract (CPA) approach in the classroom?

Have you ever been in the middle of teaching a math lesson and noticed your students look like this?

A man looks confused as he counts on his fingers and math equations float through the air.

Math can be stressful for students and teachers...but it doesn't have to be!

Two girls are sitting at a table in the library. They look up from their books and high five.

Use the Concrete, Pictorial, Abstract (CPA) approach to help students build a deep understanding of math concepts and develop problem-solving skills.

Concrete Stage

What is it?

the "doing" stage
students model math problems using concrete objects

Example:

laying out two mittens and adding three more mittens to find the sum
cutting a watermelon into twelve pieces to model twelfths

Concrete representations are bestfor:

when students are learning a new concept

A man slices a watermellon into ten parts.

Pictorial Stage

What is it?

the "seeing" stage
students model math problems by drawing

Example:

drawing two mittens and drawing out three more mittens to find the sum
drawing a picture of a watermelon and dividing it into twelve pieces to model twelfths

Pictorial representations are bestfor:

concepts that don't have a concrete representation (like negative numbers)
when students show mastery of concrete representations

Abstract Stage

What is it?

the "symbolic" stage
students model math problems using symbols like +, -, x, ÷, =

Examples:

writing the equation:2 + 3 = 5
using the equation:1 ÷ 2 = 1/2

Abstract models are bestfor:

concepts that don't have a concrete representation (like negative numbers)
when students show mastery of concrete and pictorial representations

A Simpson holds a note pad that reads 3-2=1. The caption reads, 'Numbers are fun.'

Why use the CPA Approach?

Ben Stiller points with his finger as the caption reads, 'Let me hit you with some knowledge.'

The CPA approach is beneficial because:

students achieve a deeper understanding of math concepts instead of using memorization
teachers can scaffold abstract math concepts to make them more accessible
students and teachers can go between stages as needed
it can be used with students in both primary and secondary school
you can use any of the models alongside each other to provide multiple representations of class material or to double-check student knowledge

Quiz

Mrs. Ramirez just began a multiplication unit with her class. Her students have minimal experience with multiplication. She wants to show her students how to solve 3 x 10. Which of the following methods would be most useful in introducing this concept?

using counters to show 3 rows of 10

laying out 3 sticks of 10 blocks

drawing 3 rows of 10

writing out the equation 3 x 10 = 30

Did you know?

The CPA approach was created by Jerome Bruner and is widely used in math instruction in Singapore (structural-learning.com, "Concrete Pictorial Abstract Approaches in the Classroom").

Take Action

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Are you ready to use the CPA approach in your classroom?

Think about your math curriculum. Can you use the CPA approach to introduce a new topic?

Check out these related Bytes: What is the difference between formative and summative assessments? and 5 effective co-teaching models

Take a look at resources for using the CPA approach to teach addition, subtraction, multiplication, and division at the bottom of this article.

How do I use the Concrete-Pictorial-Abstract (CPA) approach in the classroom?

Have you ever been in the middle of teaching a math lesson and noticed your students look like this?

Concrete Stage

Concrete representations are bestfor:

Pictorial Stage

Pictorial representations are bestfor:

Abstract Stage

Abstract models are bestfor:

Why use the CPA Approach?

The CPA approach is beneficial because:

Quiz

Did you know?

Take Action

Are you ready to use the CPA approach in your classroom?

This Byte has been authored by

Lauren O'Neill