Learning Through Connections

As I am now teaching more at home than at school, I have developed my own methodology. I have yet to give it a name, but it essentially revolves around random walks through knowledge landscapes.

It really makes no difference which "ology" I bump into, so long as it can answer a question. If you rewind history, you can end up with the illusion that you are standing at some important station, on the way to the future. But if you start from the past and move forwards, you see how many extrinsic factors come into play that make the future less than predictable.

One of my favourite TV series as a kid was Connections, by James Burke. Perhaps more than the Horizon series, that took one topic at a time, here was a guy who thought like I did, pulling in a bewildering array of ingredients to produce some signature dishes. It is not just a history of inventions, but a history of the relationship between random events and feedback - the application of human intelligence to what would otherwise be mere accidents.

For example, why didn't the Greeks or Romans build steam engines? They had the ideas and the tech - see this amusing counterfactual.

All you really need is one starting question followed by a lot of "how" and "why" questions to push the network of ideas in different directions. How far you can go depends purely on your interests. If you are using this with a child student, then it also depends on their age and motivation. Even a young child will quickly learn to "ask the right questions."

One of the most annoying things that teachers (and parents) say is:
"You don't need to know that!"
"Well, I asked the question precisely because I do want to know!"
"Oh, it's way too complicated."
This usually means that they don't know - and can't be bothered to look it up with you.

Firstly, don't fall for this appeal to ignorance, but also know at what point to stop - to realise at what point you really are asking a very complex question that requires a whole language to understand the answer.

A simple example. There are plenty of popular books on quantum mechanics so that any bright student can get some ideas as to how it operates. But, to truly understand it will require months of mathematics just to comprehend the formalism. Without knowing the language it becomes difficult to even articulate good questions - never mind understanding the answers.

This doesn't mean you should stop asking, but it means looking around at the landscape you find yourself in and seeing what you need to carry on your journey. Sometimes (indeed, often) it is more mathematics, but sometimes it is a lack of physical tools such as a laboratory, a workshop or a supply of chemicals - even a library.

So, if you reach a point in your studies where it looks like you can't go any further, this is not a cause to be disheartened but a message that you need to become familiar with a new landscape of knowledge.

The internet is filled with both a wealth of knowledge and a morass of opinionated garbage. Being able to tell the difference is important. Being able to teach the difference is doubly so.