What a hiatus. Not long after my last post in October, the election cycle ramped up to such a level of screeching that many of us couldn’t hear ourselves think. And since the election itself, many of us have been struggling just to get out of bed and face the world, much less practice being in and being with the world. And since the inauguration, we’ve been too angry to focus on anything that hasn’t been overtly political or that might smack of self-indulgence in a time of crisis.
But last weekend I managed to pick up and open Manuel Castells’ Networks of Outrage and Hope. And I’m excited again to be on this math journey, even though it has stalled a little. I’m taking MATH 140 for the third time this semester. I dropped it this summer for a lot of good reasons. I took it again in the fall and saw it through all the way to the bitter (BITTER) end when the final exam knocked my barely-passing average down to a D.
So here I am, for, the third time. Things are vaguely familiar, and the repetition of material is replacing my frustration with a sense of calm. Muckelbauer in The Future of Invention talks about the “inventive singularity within repetition itself” (44). He says he is “not so much interested, for example, in getting Plato right,” but rather “in orienting toward the singular rhythms that circulate through his writing” (45). When I think about that, as I struggle to complete literally the same set of problems from the same book for the third time, unaware of everything except my pencil, the calculator, and that smooth, seductive graph paper (I LOVE IT SO MUCH), the repetition does not feel like a waste of time. Far from it. The two-hour block is functioning as a vacuum, as a sensory deprivation tank. Now that I in my third repetition, I can anticipate some quizzes and lectures as smoothly as if we were moving through a daily same-but-different sun salutation sequence. The logarithm as mode of unification, pencil grip as mudra. Trigonometric identities leading to Shavasana. This third-time math class has become a meditative chant through which a hidden rhythm is emerging.
When I am returned to the outside-math world and come face-to-face with (what feels to me like) political madness (for example the multiple readings of Coretta Scott King’s letter by Udall, Warren, Brown, Sanders, Merkley), I think I am able to focus on the emerging rhythm and repetition rather than the cacophony of certain voices and the attempted suppression of certain others. Even in my failure, especially in my failure, this third-time-around math experience is proving to be an especially valuable one when processing the multiple failures of the world around me.
The summer math class ended in disaster, or what I (as a teacher) might have previously called “a teachable moment”: I dropped the class on the last day possible because I tried to build success on the foundation of a Bad Plan.
I ended up with this Bad Plan for Good Reasons. These Good Reasons may sound vaguely like excuses. But they’re not. Totally not. I’m detailing them here because they make me feel good.
After registering for Math Class, I was invited to teach one of my favorite classes during the summer session. How could I NOT teach this class?? I love this class. It grew into two sections. And three concurrent summer classes, whether teaching or taking, is too many.
Then, I was awarded a research grant to visit Ukraine during the fall. A colleague who speaks Ukrainian offered to travel there together, but she was going the week before the summer session. How could I NOT go with a native speaker who could help me translate?? So I flew home the day Math Class started and drove right to campus from the airport, jet-lagged and delirious.
The week after this summer circus began, I was invited to participate in an edited collection directly related to my research. This was great news. How could I NOT agree?? But it included several summer deadlines, lots of intense thinking, and a few wine-infused conversations.
On top of all these Good Reasons, I was facing the Known Obstacles:
Summer classes pack 15 weeks of content into 7 weeks of time.
The class was held from 6:00PM to 10:00PM. PM. The middle of the night.
Math takes me a long time.
Math just really takes me a long time.
Lots of time.
Looking at all this now, it’s obvious that I should have dropped the class right away. My math instructor could see it. He was very kind and after a five-quiz failure streak, he gently suggested that I could consider dropping so that my transcript wasn’t saddled with an F. He suggested that I come by his office to talk about my math goals, because maybe there was a better way for me to achieve whatever it is I’m hoping to achieve. He said I could continue to attend class even after dropping, so that when I did re-enroll into a long semester, I would be as prepared as possible.
Hearing the news that, despite your best efforts, you are very likely to fail is not easy. Delivering the news is worse. But in a world where a single course costs over $1,000 and an F can cause immeasurable problems in a competitive job market, it feels irresponsible not to have this conversation. I’ve discussed Bad Plans with several students over the years because I could see the writing on their walls much more clearly than I could see it on my own. As a chronic Bad Planner, I feel more than a little hypocritical offering others advice on this topic.
I do know, though, that failure for a Bad Planner is relative. Did I fail to meet the requirements of the course? You betcha. But look at all the other things I got done while I was fretting about failing math. Many of us do our best work when we’re looking at it peripherally. And that means the risk of failing whatever we’re looking at head-on.
The fall semester starts next week, and I’m again enrolled in MATH 140. Have I learned anything from this summer’s teachable moment? Debatable. I am again over-committed in a dozen other ways. And I am again underestimating the time commitment. Because technically, I’ve already taken this class once. And this time, it’s in the morning. And I have 15 whole weeks. So I’m pretty confident that this semester will be a success. It just might not be a success when it comes to math.
We had our first test this week. The last question was a word problem about the amount of pollution in the air based on the speed of the wind. Somehow, I ended up with a negative wind speed. Which I know is illogical and impossible (unless I completely misunderstood the LIGO announcement this week). But the math that I had worked out to arrive at the negative wind speed looked pretty much right to me. And so, knowing that my answer was absolutely wrong, I wrote it down anyway. Something is always better than nothing.
It is only this week dawning on me that I might actually fail this course, which has put me into a very fast five-stages-of-grief tailspin. At the peak of my frustration, I told a friend that I was doing everything I knew how to do, and it wasn’t enough. She said:
“Did you visit your professor during office hours?” No.
“Did you seek out tutoring?” No.
“Did you find other books to explain the same problem differently?” No.
She pointed out that I was not, in fact, doing everything I knew how to do. Fellow math students have also suggested that I sit in the tutoring center while doing homework and that I ask around for links to YouTube videos of people working through the steps for given problems.
Honestly? I HATE THESE IDEAS. I believed learning math wouldn’t require as much collaboration as learning to write seems to require. And honestly, the idea of doing math in a vacuum appeals to me. I’m not sure why, when I know how powerful collaboration can be. For some reason, I want to be inside a black hole with math, where nothing IS something. Or something like that. Maybe my answer to this test question was me trying to tell myself as much. Except I don’t know enough math to have ever orchestrated the negative wind speed answer on purpose.
This week, I need to reassess my goals with this math business. If this project is going to last longer than a semester, I suppose I need a better plan. Working in a black hole, as much as I like the idea of it, isn’t going to get me very far.
We have begun working with quadratic equations. I am failing this miserably, but I think I have discovered the root of the problem: the Order of Operations. This is the fundamental set of rules that dictates 5 + 6 x 2 equals 17 and not 22. I realized last week that when overwhelmed by an equation, I start with the parts that look easy (so I do all the addition first, for example). The Order of Operations says no, no, no, you can’t do it that way, and it makes my answers non-negotiably wrong.
Until today, I believed that basic math skills were grounded in axioms (self-evident propositions) and theorems (things capable of being proved). But in studying up on the Order of Operations, I found that it is a convention. Granted, it’s a widely accepted, super duper important one. But at its heart, a convention is simply “an agreement or covenant between parties.” In other words, I’m failing math because of a spit and a handshake.
If a convention is simply an ongoing agreement to a set of (arbitrary) rules, then the Order of Operations is just math’s grammar, a study of “the relations of words in the sentence, and with the rules for employing these in accordance with established usage.” My field of writing and composition has largely abandoned the right/wrong binary of grammar in favor of multiple grammars representing marginalized voices. My biased impression is that basic math has, conversely, tightened its grip on this binary.*
Math and writing used to have multiplicity more in common. In Hidden Harmonies: The Lives and Times of the Pythagorean Theorem, I read that Babylonian scribes may have “thought of values differently arrived at the way we think of variant spellings: there is no ideal that ‘color’ or ‘colour’ better realizes” (36). And the authors then write that the algebraic Babylonian culture “was founded on recipes, which are always modified by locality and detail” (41).
I have to tell you, I love the idea that my test answer isn’t wrong–it is simply my shiraz to math’s syrah. Come on, Aunt Sally. Let’s carve out a little space for my particular dialect of quadratic equation. We can discuss further over a glass of wine.
*This might be because so much of the homework is done online with inflexible, automated grading systems. The computer is a harsh mistress.