It’s really interesting to study Mathematics through YouTube. The lecturers are compelled to make their lectures good, because the best lectures win the most views- and we click the videos with the most views, so there’s an element of natural selection at play. The good videos get all the hits, the rest don’t.

A good lecture for beginners focuses on accessibility over accuracy. The lecturer has to present his ideas in a way that makes it stick, that makes it easy for the novice to understand what’s going on.

What happens, I’m noticing, is that they simplify. They use scaffolding. (My girlfriend hates that word.) They take the trouble to make sure you understand, instead of presenting you with the information and assuming that you do.

Every teacher- or anybody explaining any idea- has to make a trade-off between accuracy and accessibility. We choose accessibility when we tell children that electrons of an atom orbit the nucleus like the planets orbit the sun. It’s not accurate. The truth is a little more complex. (Or at least, what we think it is.) But the original model stays, at the foundation level. Because it’s accessible.

Experts tend to underestimate the complexity of their own expertise. Teachers who’ve been teaching the same subject for years tend to forget that bombarding students with detail and information from the get go tends to alienate them from the topic.

When you choose accuracy over accessibility, you aren’t really making a trade-off- because there is no value in inaccessible accuracy. The students will struggle to grasp what you’re saying. The accuracy is wasted on them- even counter-productive, because it throws them off the trail.

YouTube was still in its infancy when I was in Junior College; but I swear that the lectures available on the internet now are vastly superior to what you’re going to be getting in school.

I plan to support this hypothesis (I cannot prove it by myself, because there are all sorts of other factors that come into play, like my new-found motivation to study) by using the internet to study for my A-Levels.

You can follow my academic YouTube journey here.