Math Challenge

Your child absolutely needs to learn the why behind the what

One of the strongest indicators of a healthy dose of curiosity in a child is the frequency with which the child asks why.

Why is the sky blue?

Why do things fall down and not up?

Why do the angles of a triangle sum to 180?

Why does the Pythagoras Theorem work?

For a parent, it is important to understand how powerful this why-framework of thinking is for a child’s overall mental development and long-term success.

Unfortunately, our education system emphasises upon the “what”, but not upon the “why”. We will take a simple example from mathematics teaching to illustrate this.

Consider a triangle with base b and height h:

Do you remember what the formula for the area of this triangle is? Some of you may remember that the formula involves the base and the height of the triangle. Well, the exact formula is A = 1/2 x b x h. And this is what is taught to children as well. Nothing wrong with this – except the fact that why this formula works is never discussed!

The teacher will say – kids, this is the formula for the area of the triangle; now memorise it so that we can do a few problems. Covering the “what” and ignoring the “why” is what generally happens in math classes, and is most probably happening with your own child as well.

What do you think are the consequences of such an approach?

• The child will get disengaged. Having offered no “why” behind the “what”, the child will start to lean towards a rote-learning rather than a conceptual-learning approach.
• The child will begin facing more difficulty in learning – because memorising seemingly disconnected facts and formulas is not easy without any underlying coherent framework. If the child is not good at rote-learning or memorisation, the child’s performance in tests will start to suffer.
• Most importantly, the child’s natural curiosity will start to go down. By repeatedly being exposed to situations where only the “what” matters and the “why” is totally ignored, the child’s curiosity will be killed in a systematic manner. This will have an impact not just on the child’s academic performance, but will severely affect the child’s overall mental ability.

The tragic reality is that the impact of such a learning experience in childhood manifests many years later – when the child will face situations where the “what” is secondary and the “why” is all important – and the child will struggle.

This is coupled with something even more dangerous – in schools, children are taught the “what” and are also tested on only the “what” – thus, many children keep scoring well on school exams without building any fundamental understanding, and everything seems hunky-dory. Everyone is happy, because “at least the child is scoring well on school tests”.

Here’s a real story from our experience.

Aditi* scored an A+ on her class 10th board exams, including a 100% score on her math final exam. However, and shockingly, her fundamentals were entirely missing. She could tell you the statement (the “what”) of each and every theorem from her grade-10 textbook, but she would struggle to justify even one of those theorems (the “why”). Not surprisingly, her parents, her teachers and Aditi herself had no clue about this gap.

When she moved to grade-11, Aditi suddenly found that rote-learning was no longer effective, because the complexity of the subjects she was studying had gone up significantly. As time passed on, she started lagging in her studies, further demotivating her (because she had always performed so well on school exams). No amount of tuition classes or coaching helped her, because she had no conceptual foundation at all. By the end of grade-12, she was on the verge of clinical depression. Although she managed to obtain a decent score on her grade-12 board exams, she had been scarred for life, and had lost all self-confidence.

This is a very common story. We inflict upon our children, years of a deeply flawed system of learning, and then put them in hyper-competitive environments, expecting them to excel. When they don’t – we blame them. We say – probably the child was not good enough.

Let us be clear – in such tragic scenarios, the child is the only one who cannot be blamed. The real culprit is the system – the combination of the school, the teachers, the tuition and the parents.

With the system’s almost blinding focus on the “what” and “good marks”, the truly important aspect of learning gets completely ignored. In Aditi’s case, the situation would have been dramatically different if only the system had built in Aditi the ability to ask why.

Parents have the best of intentions for their children. But, it’s also their obligation to be aware of how their children are really learning – are they only being made to do the “what”, or are they being exposed to the “why” behind the “what”. This simple difference can totally transform a child’s life. Trust us – we have seen it firsthand!

By the way, remember the area of the triangle question we asked above. Let’s see why the formula works. Complete the rectangle on the triangle’s base, with the same height as the triangle, as shown below:

It’s easy to see that the left part of the triangle has an area half that of the left rectangle R1, while the right part of the triangle has an area half that of the right rectangle R2. Thus, the total area of the triangle is half the total area of the rectangle. But – what’s the total area of the rectangle? b x h of course – that’s something we learn very early on. The triangle’s area is therefore 1/2 x b x h.

Amazing, isn’t it? Do you think a child will ever forget a beautiful piece of mathematical reasoning like this? We don’t think so! Because this is the “why”, from which the “what” follows automatically.

*Name changed

Remember this why-vs-what approach the next time to sit down with your child to discuss anything!

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Manan Khurma

Manan is the founder, lead program designer and CEO of Cuemath. He is a graduate from IIT Delhi and is also an acclaimed mathematics author with Pearson and McGraw Hill. His mission is to make every child in India love math the way he does.