How to understand something backwards: teach!

The process of learning something involves starting with simplest topics and building on them.

When teaching, the process is reversed. You aim to have taught the student up to some advanced topic. But to get to that point, you have to know what the prerequisites are.

But it’s more thoroughly backwards than that implies. In some certificate, such as a mathematics undergraduate degree, each module has prerequisite modules. But so do the smallest of progressions of knowledge. To know how to add three numbers together, you must first know how to add two.

While that seems obvious and insignificant at improving one’s own understanding, consider how many times you have been asked a question about a topic you understand advanced concepts – but have been unable to explain simple questions, like “But why?”

“But why”. You have failed to explain the reasoning – the prerequisites to a conclusion. You have forgotten all about the “why”, because you have for a long time only practiced the “how”, and progressively expanded upon it.

So by teaching,  you are re-learning the “why”. You are literally learning it backwards – for the first time!

So to learn something backwards, teach. Reminding ourselves of the “why” opens doorways to new understandings. It gives us greater confidence, greater certainty, greater agility of mind.

However, we could simply always ask ourselves “why” – and sometimes that’s wise to do – so why teach? Students have the advantage on the mentor. They know when the “why” is an assumption, a prerequisite, unintuitive, or perhaps just wrong.