Math is highly valued and learning math has been given great importance around the world.1 When it comes to learning math, most of you have probably heard of conceptual programs and conceptually based problems. And, the importance of conceptual understanding as a key component of learning math has been emphasized over the years. Before we delve into understanding why conceptual understanding is important, let’s first understand what it means.

What is Conceptual Understanding in Math?

The term “conceptual understanding” refers to a comprehensive and practical grasp of mathematical concepts. Children who understand concepts are aware of more than isolated facts and methods. They comprehend why a mathematical concept is significant and how it can be applied in various situations. They organize their knowledge into a logical structure that allows them to learn new concepts by connecting them to what they already know. Understanding the concepts also helps with retention because facts and methods are easier to remember and apply when learnt through understanding, and may be reconstructed if lost.2

Conceptual understanding entails teaching children not only how to do something but also why they should do it. Through conceptual understanding, children can see the bigger picture that underlies all math topics and exercises, allowing them to think in a fluid way, use their math skills in a variety of contexts, and utilize higher-order thinking skills.3

This was proven true by the research1 conducted by Gao and Bao, whose findings showed that:

Students who were enrolled in concept-based learning environments scored higher than students enrolled in traditional learning environments. In fact, students who learnt conceptually also liked the learning approaches more, with a better grasp of concepts leading to increased understanding and transferability.1

The Importance of Conceptual Understanding in Math for Children

While most people assume that conceptual learning is at the core of higher education and is required in later grades, this is not true. Conceptual learning is a new approach to understanding concepts that focuses on the “why” and the “how.”

For example, many traditional learning environments require children to memorize multiplication tables. When children have learned multiplication tables through repetition and can remember them only by memory, they are bound to get stuck, repeat them over and over, or even panic since they have no resources to help them find the answer.

However, when they are taught through a conceptual foundation for multiplication, they will know that multiplication means repeated addition. So they can understand that 8 x 4 is the same as 8 added three times. Children could then use various strategies that they learn for repeated addition and counting for multiplication, division, and so much more. Eventually, the solution to the multiplication table would come to them automatically without the need for any memorization techniques or supportive strategies.3

Conceptual understanding can also help reduce math anxiety in children and help them become more confident in their math abilities. This holds true even for children who are not generally anxious but can be nervous when it comes to certain kinds of problems. For example, math word problems. Many children might be nervous when they see a complex word problem. But through conceptual understanding, children can draw on the concept to deduce what the word problem means, think logically, and apply what they have understood in an effective manner to solve whatever complex problems they may face.3

When children solve problems based on memorization, they could get stuck without any alternative ideas when they encounter a complex equation or while proving a theory. But when children understand concepts, they are aware that solution strategies may not matter that much while they know how equations work and the smaller things that can be connected together to create the larger idea. With this understanding, they can come up with alternate methods or work on a complex problem in a different way to arrive at a solution. As such, conceptual understanding means knowing both ideas in an interconnected and organized way, as well as how to connect to them.2

According to research, concept-based learning based on an inductive and inquiry-led approach has been shown to improve mathematical proficiency and understanding.1

Developing conceptual understanding in math can benefit children in a variety of ways. This will help children gain confidence in their ability to solve math problems and improve their computational skills, which will benefit them throughout their academic careers as concepts and problems become more complex. So, rather than relying solely on memory aids, children with a strong conceptual foundation learn to think and reason for themselves.

Hope you enjoyed this post and gained some knowledge from it. Please visit BYJU’S FutureSchool blog for more information on math learning.

References:

1. Why Is It Important for My Students to Learn Conceptually? Why Do We Need to Develop Curriculum and Instruction to Include the Conceptual Level? (n.d.).
2. What is Conceptual Understanding? – The Reflective Educator. (n.d.). Retrieved May 20, 2022, from https://davidwees.com/content/what-is-conceptual-understanding/

Conceptual Understanding in Math. (n.d.). Retrieved May 20, 2022, from https://demmelearning.com/conceptual-understanding/