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Math as Corpse Pose

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 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, stretching all the way down to my arches. 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-of-math world, I am refreshed and grounded.  When I come face-to-face with madness in the outside-of-math world, for example the multiple readings of Coretta Scott King’s letter by Udall, Warren, Brown, Sanders, Merkley, 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.

 

WIDE-EMU: Writing wants reluctance

I’m preparing for the WIDE-EMU conference in a couple of weeks which has a theme of “What does writing want?”  My colleague and I have chosen to tentatively answer this question with, “Writing wants reluctance.”  For me, I reluctantly write about math (here, on this very blog).  As part of the “Phase II: Respond” pre-conference work, this particular post details some of my reluctance toward the writing-via-math project in which I am engaged.  This post ends with a plea for your input on my actual presentation at WIDE-EMU.

Reluctance 1: Majoring in math.  When I decided last year to enroll at the institution where I teach English and to declare myself a math major, I did not have a very clear rationale for doing so.  If I wanted to learn something new, why not attend a seminar in my own field that I could add to my CV? Why math?  And if it had to be math, why not join a MOOC or audit a class?  The best professional reason I had, as a composition instructor, was that I wanted to better relate to my students by remembering what it felt like to be uncomfortable in a classroom. Humanities classrooms (English, Spanish, history, philosophy) have been my go-to happy places for a long time, so I needed a subject that I had avoided academically.  And I needed to feel the same kind of stress, commitment, and humility as students with a lot (only their entire futures) riding on their coursework.  Enrolling as a degree-seeking Math major is well outside my comfort zone, costs money, and puts my real transcript at risk: three factors that make this a relatively authentic experience.

Reluctance 2: Blogging. The decision to blog about my math journey had a clearer rationale. I frequently ask my students to write publicly, I require that they share drafts, and I offer points for engaging in reflection.  But many of them are as uncomfortable writing about my assignments as I am writing about math:   I don’t know how to write about math.  I don’t know how to relate basic math to the things I do know.  I don’t know who my audience is, what they already know, or what they want to read.   My attempts to make it “meaningful” are kludgy, stilted, and sophomoric, and posting these attempts online has been mortifying.  And I have all of these doubts with every single post, despite the fact that I am an enthusiastic student and am thoroughly enjoying learning basic algebra.  I hit “publish” with reluctance, every single time.  For many of my students, the experience of writing publicly in a composition course probably feels similar.  I’m not sure how to address yet the affective and effective role of reluctance on this writing, but I can feel it at work.  Further down the road, I will work on expressing that more clearly.

Reluctance 3: Asking for help.  I am approaching my few minutes at the front of a room during WIDE-EMU as my chance to give a “classroom presentation” in which I reluctantly-enthusiastically try to explain, in a meaningful and interesting way, a basic mathematical concept on which I have a tenuous grasp and that somehow relates to writing (maybe magnetic reluctance?).  If you have any suggestions, requests, words of encouragement, or cautions, please feel free to comment on this blog post.

PS: I passed my first test of the semester and have almost-a-B in MATH 140 right now.  Hooray!

 

 

Hope springs eternal.

I’m about halfway through Eagleton’s book, Hope Without Optimism.  Optimism, it seems, is a vacuous, ungrounded belief that everything will be ok.  Everything will work out for the best.  It’s an attitude and an outlook.  And when things don’t work out for the best, they have to be quickly recast as actually the best but we didn’t know it right away (the “what doesn’t kill you makes you stronger” kind of thing).  Eagleton is not a fan of optimism.  Neither am I.

Hope, on the other hand, requires a lot of work and for the most part, has very little to do with optimism.  You can be hopeful without being optimistic. You can hope desperately for something, knowing full well that it likely won’t come to pass. And hope requires that we acknowledge that things might not work out for the best.  That doesn’t mean we should quit.  Not at all.  There is a realism and a drive implied with hope that optimism doesn’t require.  Hopeful people hold a certain fidelity to the virtue of hope.  The whole idea is to forge ahead in a hopeful way, despite the presence or lack of optimism.

I’ve begun MATH 140 for the second time.  So far, the material is familiar and I am passing, but I’m certainly not “acing” this course the way I expected–given that his is my second time through.  And, of course, life is again getting in the way in all kinds of wonderful and insidious ways.

However: I will remain hopeful.  Not optimistic.  But unflaggingly hopeful.

Dropping like a hot potato (or: This was a Bad Plan.)

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.

Trigonomotastic

After a two month hiatus from learning anything new, the summer session careened into view.  MATH 140: Introductory Mathematical Analysis started over two weeks ago, and only just now, today, do I have time to take a breath.  Initial observation: summer class timelines are not to be taken lightly.

This is the course in which we finish up the algebra begun in MATH 120, and we start trigonometry.  How did I not know that trigonometry was just Super Fantastic Geometry?  I vaguely remember enjoying geometry in high school, although my only concrete memory is the gift of a pencil that said, “A logarithm is an exponent.”

IMG_20160713_131948In trigonometry, we’re learning how to calculate the speed of airplanes, the velocity of tsunami waves, and the ascent of hot air balloons.  We can also calculate a ship’s bearings and a satellite’s orbit.  Of course, algebra is simmering under the surface of it all: even if I get the concept and pick the right formula, I can’t complete the calculation without stupid PEDMAS poking me in the eye again.*  But the ability to look at a triangle on the page and see movement and change in the physical world is powerful.  I am in love.

The ability to see movement and change through language is powerful too, and it’s one reason I was an English major from the get-go.  These days, I write a lot of things without knowing my words’ trajectories once launched.  This blog is one of those things.  Many of my social media posts are these things, too.  Someone blocked me last week because of a comment I made related to #BlackLivesMatter and the Dallas sniper.  Now that I’m blocked, I can’t access the comment to delete or amend it, I can’t respond, and I can’t see what anyone else has written.  That ship has sailed, and in which direction I have no idea.

Who knows what other trajectories my writing has taken or what kind of change I have effected, I hope more often for better than for worse.  But in just two short weeks of trigonometry, this power pops all over again, clearly and consistently. I am excited to have been reminded that it is sometimes possible to see a large chunk of the world on a relatively small piece of paper.

*Look! I just tried to express a relationship between algebra and trigonometry, which I couldn’t have done six months ago.  Related: I still don’t know what calculus means.

Reflection with respect to the why-axis

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When drawing functions on a graph, adding a little negative sign in just the right place will make the lines flip sideways or vertically: this is called “reflecting with respect to the y-axis” (or the x-axis). Similarly, this little algebra class has flipped some of my directions and perspectives.

Mercifully, the semester has ended.  People keep asking me (because I keep bringing it up) why I took a math class.  Originally, I wanted to better understand some of my favorite theorists and writers.  While that’s still true, I don’t know now if it’s entirely true.  I’m not at all sure why I’m doing this.  With all the time I spent on this course, wouldn’t I have been smarter to do something overtly career-related?  Maybe.  Probably.  I don’t know.

In January, I planned to work ahead so I could linger over important concepts and make astounding connections.  But that never happened.  It was all I could do to keep up with the basics. I had too much else going on.  Everyone does.  A writing student wrote something similar in his reflection on my English course.  In fact, he described it as “crushing.” I empathize, but I also disagree:  a particular course is not crushing.  It’s just one variable within a larger societal structure designed to present “crushed” as our natural state of being.  (In other words: If my course hadn’t crushed him, something else would have.)  Same goes for math. And even when a course is pared down to make room for lingering, students (including myself) will likely absorb that extra time into other, more tangible and measurable commitments.

Despite the difficulty in assessing a good linger, I nonetheless believe in its value.  A thoughtful reflection can far outweigh the more easily quantified skills.  And so here’s mine:

From the perspective of teaching and student-ing:  Doing math problems together in class is super helpful.  Sitting on the back row is, generally, the bad idea I always knew it was.  Offering to help a student during office hours has huge impact, even if the student never actually comes to office hours. Test anxiety is real, and “eating a good breakfast” doesn’t help.  Grading math tests seems to be as labor-intensive as grading essays.

From the perspective of learning:  THIS WAS SO HARD.  It was a lot of trial-and-error, repetition, and memorization.  I’m not advanced enough yet to understand the whys, the causes, or the “meaning” in most of what we learned, and that made it even harder to commit a formula or process to memory.  Note to self: You felt the same way when you were learning to knit and could only make square things.  Eventually, you did knit a sock. Be patient.

From the perspective of math:  With only the very tippiest tip of the iceberg under my belt, I see now that basic math is not the tight narrative I was expecting.  I knew the advanced stuff would be hairy and imaginary and unpredictable, but I was naively expecting to find a solid foundation in this basic algebra class–I guess because the last time I tried to learn algebra was in high school where ideas are often presented as immutable Truths.  Instead, I see math has the same bunch of tiny little truths with which postmodernism has littered the humanities.  I should have known: it’s always turtles all the way down.  Not to be overly dramatic, but this is causing some existential angst to flare up. Note to self: Take a breath.  The world isn’t any less stable than it was this time last year.

What’s next:  I have passed MATH 120a: Algebraic Methods somewhere between the skin of my teeth and the hair on my chinny-chin-chin. In the upcoming summer session, I’m taking MATH 140: Introductory Mathematical Analysis.  Despite the awesome course title, I think it’s really just Algebra II since we’re using the same book as 120a.  My (likely faulty) expectation is that 140 won’t be as difficult: I won’t have to do so much legwork to get caught up, and the math classroom won’t feel so unfamiliar.  However, it’s 15 weeks of material done in 7 weeks.  So we’ll see.  I’ll check in here during the first week of July.

All equalities are not created equal

DiagramSentence2

Diagramming sentences: “pretty” equals “predicate adjective.”

I love diagramming sentences.  When learning grammar, it’s a great alternative to the traditional way of labeling and describing parts of speech and sentence structure.  But the trouble with diagramming, as many in my life have been quick to point out, is that you can diagram a grammatically incorrect sentence.  And so for that reason, it is a flawed teaching tool.  I suppose.  Just because you put a slash in front of a word and call it an “adjective,” that does  not make it equal to an adjective.

In my parallel-universe-math-class, we are learning how to solve linear equations, which means finding the point(s) at which various lines intersect on a graph.  The intersection is the solution.  If there is no intersection, there is no solution.  If you graph the lines, you can see there is no intersection.  But if you’re working with formulas to find the solution, you end up with an inequality–for example, “0 = 26”–that you then call “false.”  Everyone knows that 0 does not equal 26, and just because you put an equal sign in between two numbers does not make them equal.

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Solving a linear equation with substitution: “0” does not equal “26.”

I feel especially sensitive to this because this semester it has taken me (is still taking me) so long to understand how to solve equations, and I frequently end up with mathematical gibberish.  The assumption that I can look at “0 = 26” and “know” that it is false is, itself, flawed.

What do you do when you meet someone who doesn’t share the foundational knowledge that lets them know when something is or is not equal to something else?  And related, what do you do when that someone does not want to acknowledge that they have created a false equality?  And in these general terms, can we then go from diagramming –> to linear equations –> to hashtags and pithy memes?  How do you explain to someone that #BlackLivesMatter does not equal #AllLivesMatter, despite the structural similarity and the simple swapping of adjectives? How do you explain that gender neutral bathrooms do not equal the rape of your daughter? That religious freedom laws do not equal nondiscrimination laws?

Here’s where I end up:

  • In the grammar world, inequality can be a reason not to use a teaching tool, but this is because many grammarians acknowledge that not everyone recognizes inequalities when we see them.
  • In the math world, inequality can be just one of many outcomes, and it is a way to learn something about the problem at hand. “No solution” means something.
  • In the real world, how can we reconcile these two approaches when it comes to inequality in our communities?  There seems to be no (easy) solution.