CPA Approach

Overview

Concrete Pictorial Abstract (CPA) is a three step instructional approach that has been found to be highly effective in teaching math concepts. The CPA method involves using actual objects for children to learn mathematics. They then progress to using pictorial representations of the object, and ultimately, abstract symbols.

The first step is called the concrete stage. It is known as the “doing” stage and involves physically manipulating objects to solve a math problem. It brings concepts to life by allowing children to handle physical objects themselves.

The pictorial (semi-concrete) stage is the next step. It is known as the “seeing” stage and involves using images to represent objects to solve a math problem. Building or drawing a model makes it easier for children to grasp concepts they traditionally find more difficult, such as fractions, as it helps them visualize the problem and make it more accessible.

The final step in this approach is called the abstract stage. It is known as the “symbolic” stage and involves using only numbers and symbols to solve a math problem. Once a child has demonstrated that they have a solid understanding of the ‘concrete’ and ‘pictorial’ representations of the problem, the teacher can introduce the more ‘abstract’ concept, such as mathematical symbols.

Children are introduced to the concept at a symbolic level, using only numbers, notation, and mathematical symbols, for example +, –, x, / to indicate addition, multiplication, or division.

CPA is a gradual systematic approach. Each stage builds on to the previous stage and therefore must be taught in sequence.

This style of learning can be found in our resources Everyday Mathematics and Big Ideas

Benefits

• Provides students with a structured way to learn math concepts
• Students are able to build a better connection when moving through the levels of understanding from concrete to abstract
• Makes learning accessible to all learners (including those with math learning disabilities)
• Taught explicitly using a multi-sensory approach
• Follows Universal Design for Learning guidelines
• Research has proven that this method is effective
• Able to use across grade levels, from early elementary through high school
• Aligned with NCTM standards
• Helps students learn concepts before learning rules
• Can be used in small groups or entire class