Categories: GSI Online Library, Teaching Effectiveness Award Essays
By Sterling Saint Rain, Mathematics
Teaching Effectiveness Award Essay, 2025
Odds are that you can relate to the experience of staring at a math assignment and having absolutely no clue where to start. Perhaps you’ve even participated in the decades-old tradition of exclaiming, “It’s all Greek to me!” In my view, there’s truth to this phrase in more ways than one. From my experience as a graduate student instructor for calculus, it’s precisely the notation—often Greek letters—that instills students with the intense and debilitating feeling known as math anxiety. To remedy this, my approach is to treat notation like a language with a common-sense grammar system; one initially built together, then translated to make the formerly strange and unfamiliar notation feel natural.
Just as in math homework, solving a problem comes only after understanding what the problem is in the first place. In my case, the problem was students’ diminishing confidence and capacity for approaching exercises as the semester wore on. To better understand the origins of this problem, I worked step by step with students in discussion sections, review sessions, and office hours to identify where their understanding would break down. Invariably, this breakdown would involve some form of mathematical notation. Whether it was exponents, limits, summations, or the notorious “…”’s of a sequence, nearly every time I sat down with a student one-on-one to identify what they struggled with the most, the issue would involve a failure to translate the notation we mathematicians use to express a concept into the concept itself.
The most insidious aspect of this issue is how notational comprehension issues would impact students’ confidence in the course as we progressed. Notation in mathematics has a habit of stacking on top of itself, meaning that students who struggled earlier in the semester, or even in an earlier course, would be stricken with nervousness and discomfort as they see their familiar rivals imbued with painful relevance to current topics. This issue threatens to cascade into later courses, especially those that are proof-based where precision in mathematical language is crucial for students’ understanding.
The strategy I implemented to remedy this issue was to invite my students to think about how they would communicate the concepts behind the notation, then I would show how the notation mathematicians use is just as effective when given an appropriate translation. For example, the concept expressed by limit notation is that we are “approaching” some possibly infinite value. So, I discuss with the class how we might communicate this idea, then afterward I reveal how we can translate our usual notation grammatically as a question: “What happens (lim) to my function (f(x)) as we (x) approach () a value (c)?” Having put this concept in their own words beforehand, students come to appreciate the efficiency and naturality of our standard notation. A similar exercise works to motivate summation notation, integrals, algebraic rules, and more. This process has made a significant difference in my students’ confidence as measured by their course evaluations, their feedback during our discussion sections, and the relief they express during our review sessions. Treating notation like grammar in the language of mathematics, I help my students discover that it doesn’t have to “all be Greek” to them: it’s just plain English in disguise.