In mathematics, there’s a sense of play that must be achieved if one wants to really understand what is going on in mathematics. Contrary to what people might think, this sense of play and “just getting” mathematics is not some sort of genetic feature (or at the very least, not only genetic). It’s the result of immersing oneself in mathematics and freely playing with the concepts. After a long time, this play translates into what people call “intuition”.

One of the classic methods of teaching I’ve witnessed in a science classroom is the “finish the sentence” method. Essentially, it involves the teacher saying a sentence and trailing off at the end while raising their voice in order to make it sound like a question, which prompts the students to answer. In and of itself, this isn’t a bad strategy. It engages students and makes them participate in a class discussion instead of having a teacher lecture the entire class time.

When you have a lot of homework, it’s awfully tempting to just look up the answers. After all, you’re only doing it because you want to get other homework done, right? And if you take the time to read through the solutions, it’s good enough. You aren’t just copying down answers. You’re following the work that is done.

One of the incorrect assumptions I’ve long made is about teaching. Basically, I would get excited by the prospect of teaching some sort of concept to another person, and so I would work very hard on the presentation. However, there would inevitably come a moment when I’d realize that I wasn’t actually an expert in what I was talking about, so I would decide to stop the project.