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# Understanding Terminology

I wrote about how getting traction in the beginning of our studies in school can really affect our trajectory. I want to take this a step further today and talk about a specific example that alienates many students: terminology.

This issue is most persistent in mathematics, where definitions and theorems abound. It’s as if everything has a special name and meaning for it. To make matters even more confusing, the experts have decided to make shortcuts and give all these terms symbols to describe them. Now, the student has to learn – not one – but two sets of vocabularies to understand what is being discussed. And if I’m being honest, that’s only in the good-case scenario. More often, we find concepts that have multiple terms for them, and I’ve seen students quickly disengage from it all.

It’s great to have descriptors for all mathematical ideas, but we are often teaching them to students just for the sake of teaching them. Just as I’ve never been in a language class that painstakingly goes over words that have a bunch of synonyms, this isn’t particularly useful in class. Worse, getting tested on this sort of thing is nonsense, since one should be able to get by with only one name for an object. Sure, it can make for smoother conversations while exchanging mathematical ideas, but that knowledge and retention comes from familiarity, from actual usage. I know this because a lot of useless mathematical “facts” have long since departed from my memory since we never use them anymore. I remember doing step functions in secondary school (where the function was essentially a series of horizontal lines of the same size and would “jump” to a new new function value after a certain interval). I remember the notion of the step function, but it has been about four years since then and I don’t remember looking at this kind of function once. Maybe it’s because I’m in physics and mathematics and not in some different program, but the time spent on that function wasn’t useful at all. In the same sense, students aren’t learning the terminology because there is such little use for it.

The solution I propose is simple. If we really want to keep all these terms in mathematics education, we need to use the terms while discussing with students. Furthermore, we need them to practice using the terms. It’s not enough to just give a bunch of definitions and expect students to understand what they mean. Make them familiar with the terms, not just something that was copied once into a notebook and then forgotten about except for on a test.