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How to Teach Maths using Concrete, Pictorial and Abstract Method

How to Use the Concrete, Pictorial, and Abstract Method When Teaching Math to Your Child

Teaching maths to young children can sometimes feel overwhelming, but using the Concrete, Pictorial, and Abstract (CPA) method can make the process easier and more effective. This method, widely used in early childhood education, breaks down learning into three stages, helping children develop a deeper understanding of mathematical concepts. By using hands-on activities, visual aids, and abstract thinking, parents can guide their child’s mathematical journey in a fun and engaging way. Here’s how to incorporate each stage of the CPA method into your child’s learning.

Concrete Stage: Hands-On Learning

The first step in the CPA method is to make maths as tangible as possible. At this stage, children interact with real objects, which helps them develop a concrete understanding of mathematical concepts.

How to apply

Use Everyday Objects: Start with familiar objects like toys, fruits, blocks, or even coins. These physical items help children grasp basic maths ideas such as counting, addition, subtraction, and grouping. For example, you can use 5 apples to teach the concept of “5,” and then remove 2 apples to show subtraction.

Manipulatives: Use maths manipulatives like counters, beads, or building blocks to represent numbers and solve problems. For instance, when teaching addition, you can physically move blocks or counters to demonstrate how numbers combine.

By allowing your child to touch and manipulate objects, they make connections between numbers and real-world experiences, which forms the foundation for abstract thinking.

Pictorial Stage: Visualising Math Concepts

Once your child is comfortable with the concrete stage, it’s time to introduce visuals and images that represent the mathematical concepts. In the pictorial stage, children begin to associate numbers with pictures, helping bridge the gap between hands-on learning and abstract reasoning.

How to apply

Once your child is comfortable with the concrete stage, it’s time to introduce visuals and images that represent the mathematical concepts. In the pictorial stage, children begin to associate numbers with pictures, helping bridge the gap between hands-on learning and abstract reasoning.

  • Drawings and Diagrams: Use simple drawings, diagrams, or charts to represent maths problems. For example, if you are teaching addition, you can draw 3 apples and 2 apples to show the sum of 3 + 2.

  • Flashcards or Number Lines: Use number lines or flashcards to help your child visualise addition, subtraction, or counting. These visuals help children understand how numbers relate to one another.

  • Stories and Illustrations: Create maths-related stories with pictures, where your child can count or solve simple maths problems through the storyline. For example, “Sarah has 3 toy cars, and her friend gives her 2 more. How many toy cars does she have now?”


At this stage, the visual representation of numbers helps solidify the connection between concrete objects and abstract concepts, making the transition to more abstract thinking smoother.

Abstract Stage: Thinking in Symbols and Numbers

In the final stage of the CPA method, children move from hands-on experiences and visual aids to working with symbols and numbers. This stage involves thinking abstractly and using mathematical symbols (such as numbers and operations) without the need for physical objects or pictures.

How to apply

  • Use Numbers and Symbols: Start writing out simple equations, such as 3 + 2 = 5, and encourage your child to solve them using their knowledge from the concrete and pictorial stages. They should now be able to perform the maths in their minds or on paper.

  • Introduce Word Problems: Begin using word problems that require abstract thinking. For example, “If Sarah has 3 toy cars and her friend gives her 2 more, how many does she have?” Ask your child to solve the problem without using objects or pictures.

  • Mental Maths: Encourage your child to solve maths problems mentally, using their understanding of numbers and operations. This helps them strengthen their abstract reasoning skills.


At this stage, your child should be able to solve problems using mathematical symbols and perform operations without needing visual aids or physical objects. This is the culmination of the CPA method, where their understanding of maths becomes more flexible and efficient.

Why the CPA Method Works

The Concrete, Pictorial, and Abstract method works because it provides children with a gradual, step-by-step approach to understanding maths. It starts with hands-on learning to build a solid foundation, then moves to visual representations to help children make connections, and finally transitions to abstract thinking, where they can perform mathematical operations independently.

By following the CPA method, you allow your child to build their maths skills at their own pace, ensuring a strong conceptual understanding before they move on to more complex topics.

Conclusion

Teaching maths to your child using the Concrete, Pictorial, and Abstract method is an effective way to ensure they develop a strong, deep understanding of mathematical concepts. By starting with hands-on activities, moving to visual representations, and finally transitioning to abstract thinking, you’re giving your child the tools they need to become confident and capable in maths. With time, patience, and practice, you’ll see your child not only understand but also enjoy learning maths.

References

Adams, C. (2016). The concrete-pictorial-abstract approach to teaching mathematics: A brief overview. Early Childhood Education Journal, 44(1), 23-32.
https://doi.org/10.1007/s10643-015-0771-2

Bishop, A. J. (2017). Teaching and learning elementary mathematics: Connecting the concrete, pictorial, and abstract stages. Springer.
https://doi.org/10.1007/978-3-319-55970-4

Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2014). Elementary and middle school mathematics: Teaching developmentally (9th ed.). Pearson Education.

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