If you were talking to a friend about the drive you made this morning, you might tell them something along the lines of, “I drove from my place to hear in about an hour, going east for the entire time.” Your friend, who knows where you live and has a rough idea of the route to get to where you both are, understands implicitly that you don’t really mean that you went and drove in one direction only for the entire hour. After all, you first had to exit the property of wherever you were parked, then you probably had to navigate through the neighbourhood of where you live, before finally getting onto a highway or a direct route to your destination. It’s only at that point that you actually began going east. Before then, you may have driven in all directions, for varying amounts of time.

Teachers are usually regarded as people who are experts at their subject. They may not be literal experts (such as those who teach scientific courses), but they have usually enough experience to make them experts. This expertise is usually forged through many years of teaching and working with students.

When I do nearly any assignment for homework, I’ll make a rough copy of my work before writing the copy that I will hand in. I do it for a practical reason: while it may take extra time to write my work twice, the truth is that I often take a lot of detours on my first try tackling a problem. I go down dead-ends, make little mistakes here and there that need to be corrected, and generally do a lot of messy work. Once I get the correct answer, I can tidy all my work up in order to make my final copy as concise as possible.

When I work with younger students in subjects like mathematics or physics, it doesn’t take much to impress them with my ability to quickly see through a problem and calculate things that would take them minutes. Just like any other student at my level, we often skip the use of calculators because it’s easier to just focus on the work we are doing and do the arithmetic in our head. The most prominent example of this, however, is in algebra.