For example, differentiation by itself is just pushing symbols around according to some arbitrary-seeming rules. It's not until I did physics that its purpose made sense. I studied calculus for years, and it never "clicked" for me, and I forgot most of it promptly. Then in just a semester of physics where I was applying it in the context of complicated problems, it suddenly felt like second-nature. I had to basically re-learn all of it from scratch, but with the context of my physics problems it was so easy!

I've had similar experiences teaching programming to junior staff. Anything you talk about in isolation goes in one ear and out the other. They have to encounter the problem in something larger that they are solving for the solution to make sense and motivate them to learn.

An example is string-escaping. E.g.: how do you represent the quote symbol in a quoted string? This seems trivial, but it trips up everyone when they are getting started. I mean literally everyone. So okay, I make sure to cover it in like... lesson #1 or #2 because string literals are everywhere, and escaping is common. Every single time, the people that sat through that lesson will ask me a week later to help me fix as program that has a literal like 'O'Brian' in it, and they can't figure out why it's broken. But once I show them that they should have used 'O''Brian' or 'O\'Brian', it all makes sense to them and they memorise the technique.