When you’ve understood a subject, there’s a tendency to take parts of the subject for granted. You make more assumptions about how things will work, and why one thing is used versus another. After all, you have spent so much time thinking about the subject that you know it inside and out. This familiarity implies potential sources of confusion don’t even cross your mind because you know how wrong they are. In other words, you start to figure that everyone else probably knows the same amount as you do, so certain things aren’t stated.

As someone who teaches, I struggle with striking the right balance between explaining a concept to a student and giving them the steps to solve a problem (the mechanics). At first glance, it might seem like these two ideas are the same, but a student experiencing difficulties will often need one without the other.

If I ask an adult to tell me what 3-5 is, there’s a good chance that they would tell me the answer is 2 without much thought. This kind of arithmetic is simple to us, since we’ve had to do it over and over again through elementary and secondary education. Even if we haven’t used mathematics in a long time, these questions are straightforward.

Student: What’s the answer to 0/0?