It’s been a busy summer for me, and I’m just getting into the swing of the school year. Some of my readers may recall that last year, for some strange reason, I decided to send myself back to school to acquire the math knowledge I never managed to master as a young adult. It’s been a struggle, but I haven’t given up yet, probably for three reasons: first, I’m a non-traditional (old) student, so I have a lot of experience being a student as well as a teacher; second, I have more patience than I did as a young person; and third, I have a lingering professional interest in how students learn. It occurred to me today, after a particularly frustrating experience which involved a trigonometry test and my concomitant inability to answer what seemed to be the most basic questions, that one thing math teachers could do is something we writing teachers have been doing for quite a few years now: asking our students to submit journals on their learning experiences. I actually think this is a somewhat brilliant idea, so, to test it out, I decided to try it out here, on my blog. So from here on out, I guess I should consider this my first entry in my math learning log.
But before I get started, a brief warning. I am horrifically bad at keeping journals. I am probably even worse at journaling than I am at math, and that’s saying a lot. From the outset, I warn any reader of this math learning log that there will huge lacunae here, because I often start a journal and then completely forget about it. Nevertheless, I am going to forge ahead with this journaling idea, because one of the reasons I started this whole math learning process in the first place was to see what happened when a person of normal intelligence but sparse math knowledge attempts to learn enough math to get to calculus. Is such a progression–from basic College Algebra to Calculus I–possible? Today, after my test this morning, I have serious doubts. But I have to set those doubts and my growing frustration aside, and remember to regard myself not as a frustrated and humbled learner who knows she should have been able to do better on this test, but as a subject in an experiment. In a sense, I’m like that scientist in a black-and-white film who decides to test out a vaccine, or an antivenom, on himself. I need to maintain a sense of calm detachment, even while knowing that the results of this test could be disastrous. And, getting back to the journaling idea, documenting my journey through writing may well be more instructive than documenting it through grades.
For the moment, I will not mention my other reason for taking math courses–the existential, ideological, philosophical, or, if you like, the religious reason for this foray into mathemaltical studies. However, I write about it here.
Now, on to the subject at hand: the trig test on basic functions. I thought I had mastered about 2/3 of the concepts for this test, but I was wrong. Even those concepts I felt sure of slipped away from me as I began the test, in exactly the same way the memory of a dream evaporates upon our waking. By the end of the test, working frantically against the clock (and I have to add here that although I’ve always been a relatively fast test-taker, today I worked up to the last second), I was both frustrated and ashamed. Yet, to be fair, my poor performance (I do expect to pass the test, but only because of partial credit and because I wrote down everything I thought that could be pertinent to each problem), is due neither to laziness nor to disinterest. I had to miss four classes because I was taking care of my grandson in a different city (okay, so that was a delightful experience, and I wouldn’t have missed it for the world, to be honest). I did go to the tutoring center when I got back, but after an hour or so there, I deluded myself into thinking that I actually understood what had been covered. I also watched about three hours total of various YouTube videos (Khan Academy, Organic Chemistry Tutor, Dennis Davis’s series) about the trig concepts covered, but in the end, I think they might have hurt me, making me think I understood things when I really didn’t.
The frustration is real. At my age (62), learning something new can be unfamiliar, and it’s easy to see why this is so. We oldsters found out what we are good at and what we like long ago, and we have kept doing those things for decades, getting better and better at them through the years. We tend to forget how hard it is to learn, how much energy and commitment it takes, and most of all, how very frustrating and embarrassing it can be. In other words, learning something new from scratch, without any context to fit things into, is not only intellectually challenging but also emotionally draining. I suspect young people learn more easily not only because they are quicker and more resilient, but also because they don’t know any better. Because they don’t know yet what it feels like to have actually mastered something, not mastering or “getting” concepts doesn’t produce as much cognitive dissonance in them as it does in us oldsters.
Whatever my grade on the test this morning, and I don’t expect it to be good, I have to say that I don’t think studying more would have helped me, because I know I wasn’t studying the right things in the right ways. (That’s probably where that missed week of classes hurt me.) And although I was incredibly frustrated when I turned in the test, I feel less so now, a couple of hours later, because I realize that I don’t have to pass this class to obtain knowledge from it. In fact, I know I can take the class over next semester whatever grade I get this time, and that doing so is no great dishonor or waste of time. I have the luxury of taking my time with this, and although that’s really hard to remember when I’m in the throes of studying and test-taking, it’s the way all learning, in a perfect world, should be.