Reading vs Speaking
How being a choral musician is like being a mathematics graduate student
I’m sitting in my shared office at University of New Mexico writing this rather than working on two imminent assignments or studying for my upcoming midterm exams. Life as a graduate student here in Albuquerque has been rather oppressive at times. I’ve had a professor outright tell me to switch to an easier class on two separate occasions (which would ruin my standing as a graduate student and lose me my teaching assistantship aka funding aka job). I’ve been swamped with various assignments. To put it simply, the work requirements are far harder than I expected, and I went in knowing it would be quite hard.
It is only just now, in the middle of the sixth week while I was waiting for a bus, that I realized what has been so challenging. You see, it’s not just that there’s a lot of work—something which is already an overbearing obstacle because of my ADHD—but that the work is difficult in a way that it wasn’t before in my undergraduate courses. Clearly, a graduate program should be more rigorous and challenging than an undergraduate course. Yet, my experience is more than it just being challenging, it’s an entirely different sort of problem to overcome.
The challenge arises from the difference between reading and speaking. I can sit in lecture and (mostly) comprehend what my professor is saying to me and writing on the chalkboard. I can spend time reading the textbook and get the point or the reasoning or the logic of a problem. But, when it comes time to do an assignment—to answer a question—I often find myself at a loss for where to start. I know how to read; I don’t know how to speak.
My classes have taught me the words, the symbols, and the definitions. I can read the theorems and know what they’re saying, but I don’t know why they’re saying or how they’re saying. It is well and good for me to memorize Cayley’s Theorem, but if I don’t know how it can be used or why it was created, how can I be expected to use it myself? How can I use a theorem or a definition to answer a question?
This brings me to my rather absurd analogy. Being a choral musician is like being a mathematics graduate student. In what way? What am I specifically getting at here? Well, I want you to imagine yourself in a choir. Maybe you’ve never done that before, but it’s not too complicated. You stand (or maybe sit) with a group of people with a director in front. You have a piece of music in front of you with its arcane scribbles and sep-a-rat-ed lines of text spanning along them. You can read the music notation; you can even sing it. You’re given a pitch and, once cued by the director, you start to sing the piece. You’re not perfect, but it’s passable for the rehearsal. You can both read and sing (speak) the text on the page. Perhaps you even have an understanding about the deeper intentions and meanings of the lyrics.
But then, you finish that piece and the director tells you to bring out a different one. It’s in a language you do not know—let’s just say German. You’ve been informed how to read the text on the page and pronounce it when you sing. Your pronunciation is even passable to a native German speaker (though they tell you your accent is clearly northern). You have even written in a word-for-word or phrase-by-phrase translation of the text. You know what it means both literally and literarily—the translation and the interpretation.
And then, you travel to Germany. You’ve spent plenty of time on this piece of German music. You even have a few words memorized. But, can you speak German? Were you actually taught anything at all about how to ask for a restroom, or how to say “please and thank you?” Did your experience in choir provide you with any actual useful experience in speaking the German language? Sure, you now know the rules to say a phrase in German out loud, but if you do not have the text in front of you, can you say anything beyond what you memorized? Can you form new sentences and answer questions when after the concert the German audience comes up to converse with you?
My experience so far in my mathematics program has been akin to this. No one teaches me how to speak anything in mathematics. My lectures focus on the vocabulary and the theorems, but not the use of them beyond the ever-building foundation of bricks used to reach higher and more complex concepts.
I am not struggling with the work simply because it is hard, but because I do not know where or how to start; I do not know where or how to start because nobody teaches me where or how.
Perhaps the onus is on me—perhaps the great tradition of higher academia is that one must learn to speak simply by reading. I am the one to blame. I should try harder. I should work more, work longer. I should spend less time writing blog posts and more time reading textbooks and answering questions. I should inexplicably see the obvious reasons or approach to answering a problem. The fussy things aren’t all that fussy if I actually think about it.
I reject that last paragraph. I know for certain that my undergraduate professors rejected that idea, at least to some extent. One can still derive a proof and understanding for themselves if first given an outline or told which theorems will be useful. One can speak an incredibly wide variety of unique sentences if first told the sentence starts with “I am.”
I am not struggling with the work simply because it is hard, but because I do not know where or how to start; I do not know where or how to start because nobody teaches me where or how. Nobody teaches me where or how because it is hard, and they do not know where or how to start.
In my experiences both as a student and instructor, helping students to understand where or how to start without just giving them the answer or a direct set of instructions is not an easy task. It takes careful prodding and direct questioning of the student. Oftentimes, a technique which works for one student will not work for another. There is no one solution, but I find that my courses do not seem to even try. There is no attempt whatsoever. Speaking is left as an exercise to the reader.