Why Can My Child Get Maths Answers Right But Still Not Understand Why?

Worksheets build calculation speed, but correct answers don't always mean your child understands the maths. Learn how to foster true conceptual understanding.

Quick Answer: Worksheets and fact practice are useful for building calculation speed, but correct answers alone do not always show conceptual understanding. Asking children to explain relationships, compare quantities, and use visual models can help reveal how they are actually thinking about maths.

It is a common puzzle for parents: your child can quickly fill out a worksheet of addition problems, but when asked a slightly different question—or asked to explain their work—they freeze.

This happens because there is a difference between procedural fluency (knowing the steps to get an answer) and conceptual understanding (knowing why those steps work). Both are important, but when practice relies entirely on memorisation, children can miss the underlying mathematical relationships.

The Equals Sign: A Balance, Not a Command

One of the best examples of this is how children understand the equals sign. Educational research, such as the work by McNeil (2008), shows that traditional arithmetic practice often leads children to believe that the equals sign just means "calculate the answer."

When they encounter a problem like 4 + 3 = 5 + ?, many children will simply write '7' or '12', because they do not conceptually understand mathematical equivalence—the idea that the equals sign represents a balance between two quantities. Rittle-Johnson et al. (2001) demonstrate that children need opportunities to develop this conceptual understanding alongside their procedural skills.

5 Practical Ways to Build Conceptual Understanding

You do not need to throw away the flashcards, but you can supplement them with activities that encourage mathematical reasoning:

• Ask "How Do You Know?": After they get an answer right, ask them to explain their thinking. Being able to explain the "why" is a strong indicator of conceptual understanding.
• Show Both Sides: Give them equivalence problems like 4 + 3 = 5 + ?. Ask them what they would need to do to keep both sides balanced.
• Build a Real Balance: Use physical objects like blocks or Lego to demonstrate that numbers represent real quantities that can be compared and balanced.
• Find Another Way: Ask them, "Can you solve 8 + 6 in a different way?" (e.g., "I know 8 + 2 is 10, and 4 more makes 14"). Flexibility shows deep understanding, similar to the part-whole thinking we encourage in Number Bonds.
• Let the Mistake Teach: Instead of immediately correcting an error, ask, "What changed?" or "What could you try differently?" (Learn more about how to handle mistakes productively).

"Weight Balance": Seeing Mathematics

At BornFab, our primary mission is to provide an educational learning platform for children aged 6–11. We believe that visualising mathematics is one of the most powerful ways to build conceptual understanding.

Weight Balance is an entertaining educational game designed to give children opportunities to reason about equality, quantity, and mathematical relationships through visual problems. By presenting numbers as weights on a balance scale, children are encouraged to think about equivalence naturally and visually, rather than just memorising rules.

Sources & Further Reading

• McNeil, N. M. (2008). Limitations to teaching children 2 + 2 = 4: Typical arithmetic problems can hinder learning of mathematical equivalence. Child Development, 79(5), 1524-1537.
• Rittle-Johnson, B., Siegler, R. S., & Alibali, M. W. (2001). Developing conceptual understanding and procedural skill in mathematics: An iterative process. Journal of Educational Psychology, 93(2), 346.

Frequently Asked Questions

Are maths worksheets bad for children?

No, worksheets are not inherently bad. They are useful tools for building procedural fluency and calculation speed. However, they should be balanced with activities that require children to explain their reasoning so they don't just memorize rules without understanding them.

What is conceptual understanding in maths?

Conceptual understanding means knowing the 'why' behind the maths. It is the ability to see relationships between numbers, understand concepts like equivalence, and solve problems flexibly rather than just following a memorized set of steps.

Why can my child get the right answer but struggle to explain it?

This usually means they have strong procedural memory but are still developing their conceptual understanding. They know the steps to get the answer, but haven't fully grasped the underlying mathematical logic yet.

How can I help my child understand maths instead of memorising it?

Use physical objects like blocks to represent quantities visually. Ask them to explain how they arrived at an answer, and encourage them to find more than one way to solve a simple problem.