Reflection with respect to the why-axis


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


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.


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.