1) Standardized tests, blaaaaaaaaargh
Over the past two months, I’ve been teaching an ISEE math prep course at a tutoring academy, helping students about to enter the sixth grade take a test to place into competitive private schools. Obviously, this brings up certain amounts of angst related to class, race, my notions of the importance of enjoying the summers of your childhood and my absolute disdain for standardized tests.*
I recently found this communitychannel video about how math problems aren’t relevant in real life, which is hilarious but did not make me feel better: “So you remember those crazy math problems they made you solve in school? Yeah, what was that for?”
(I love Natalie, but she’s not kidding about having forgotten how to solve these problems. Check out the problem at 0:26 — her friend would be 0 years old, and her friend’s sister Anna would be -5.)
One of the challenges I had while working with students from high-poverty neighborhoods over the last two years was in drawing the connection between schoolwork and real-life application. But thinking about it now, I realize this isn’t an issue that’s relegated to low-performing schools. I struggled in middle school, not because the material was difficult, but because I felt that all of seventh grade, except for algebra, was a waste of time — the curriculum wasn’t interesting, and the coursework was less challenging than what we’d done in elementary school. I was disconnected from my classes because I wasn’t being asked to think.
Back to standardized tests: I think they’re terrible. The students I worked with over the past two months are pretty advanced in math (they can easily manipulate positive and negative numbers, fractions, decimals, etc.), but they’re becoming intellectually lazy. I commonly asked them to explain how they solve problems, and a lot of the time, they were using guess and check. As a test-taking strategy, this is excellent. As a learning strategy, it’s terrible. My solution, or as close to a solution as I came up with, was to create my own problems for them to solve, mixing concepts and adding unnecessary language so that they had to decipher what information they were looking for and how to solve for it.
The middle school I worked at from 2009 t0 2010, uses connected math, a conceptually interesting approach that pushes students to conceptually understand curriculum by identifying patterns and making discoveries. Why “conceptually interesting”? Because it wasn’t effective. My students didn’t have a strong enough foundation in basic arithmetic to identify patterns, and they were expected to fulfill learning standards that were dependent on previous understanding.
David Bornstein provides great analysis of some of the problems with math education in “A Better Way to Teach Math“:**
Despite the widespread support for “problem-based” or “discovery-based” learning, studies indicate that current teaching approaches underestimate the amount of explicit guidance, “scaffolding” and practice children need to consolidate new concepts. Asking children to make their own discoveries before they solidify the basics is like asking them to compose songs on guitar before they can form a C chord.
The rest of the op-ed is interesting, too, and since you’re following a link, it won’t count against your NYT quota.
Natalie’s video sticks out for me for two reasons: One, I feel complicit in the class-based test disparities. Two, I don’t think it’s true that we don’t encounter crazy math problems or that we don’t need math. As Natalie says, “In real life, people just tell you the answers.” In general, people are comfortable saying they’re bad at math, in a way that most wouldn’t be OK with admitting they were illiterate. It’s a bit frightening, if you ever poll a group of journalists, to see how many struggle with math;*** since accurate holding-truth-to-power bad-assery is contingent on thorough, comprehensive data analysis. Compound poor math reporting with the general public’s shaky math skills and misinterpretation of statistical significance, and think about how easy it becomes for those who do get math to mislead and manipulate.
Leonard Mlodinow’s “The Drunkard’s Walk: How Randomness Rules Our Lives” provides a bunch of interesting examples of how people misinterpret numbers and statistics. (Ironically, it’s as much about the theory of randomness as Alanis Morissette’s “Ironic” is about irony. It’s mostly just random in the meta sense, and it also kind of provides more biographical information about mathematicians than seemed absolutely necessary … or interesting. Wait, here, just read my GoodReads review if you’re still on this parenthetical.)
So my point, I guess, was that standardized tests, are like, the opposite of learning, but that math education in general is flawed, anyway. I find myself using math all the time — mostly for basic computation, which I will concede that calculators do faster — and I also find myself wishing all the time that strong number sense and conceptual understanding of probability was seen as more critically important. But hey, I also think that about literacy, poetry, sustainability and ethics education.
2) Biking is awesome
I always plan to go on bike rides, but the activation energy involved in getting my bike down the stairs and out the front door and two gates often stops me. I went to a Meetup on Wednesday at The Last Bookstore about using the city as a creative canvas, and hearing everyone else talk about biking was a great catalyst. I biked to my friend’s new apartment on Wednesday, and it took about half as long as it would have by bus. I also biked from her place to work the next morning and beat the bus that GoogleMaps suggested. (I had looked it up because I was worried about tutoring students drenched in sweat, but I got there early enough to cool down, anyway.)
I only went about six miles in all, but it was wonderful. I felt completely in control and free from the clutches of LA traffic. LA public transportation is not what I would call reliable, and walking places limits my exploratory radius. I’m also a fan of mixing Metro and biking, at least until I get in better shape. I always forget how freeing biking feels, but getting somewhere using myself as an engine completely changes the way I view the city and my own sense of agency.
3) Cynicism, and our struggles against it
OK, let’s be real. When I started this post as “Three things I’m thinking about,” I was planning on writing about 300 words on each topic, but I got a little carried away with the math part.****
This conversation continued for five more comments. I may digest/analyze them more later, but if you're reading this blog, we're probably Facebook friends, and you can just find it yourself.
In any case, I was also going to write something about the struggle between cynicism and idealism, the search for meaning and everything else that I write about on this blog and elsewhere, always.
The LA Times ran an article last week about the use of facial recognition software in advertising, and I was most disturbed by the kicker (I’m literally rehashing the image, sorry), a quote from a 27-year-old who describes himself as “hyper social”: “It’s not that scary. … I always get upset at new Facebook privacy settings, and then I get over it.” Umm, just read the image.
I also just finished reading “Up, Simba,” David Foster Wallace’s article about John McCain’s 2000 primary campaign, in which, inter alia, he discusses how deep political cynicism among young people helps incumbents:
“[T]he lower the overall turnout, the more the Establishment voters’ ballots actually count. Which fact then in turn … helps explain why even though our elected representatives are always wringing their hands and making concerned noises about low voter turnouts, nothing substantive ever gets done to make politics less ugly or depressing or to actually induce more people to vote: our elected representatives are incumbents, and low turnouts favor incumbents for the same reason soft money does.”
Speaking of DFW, NYT Magazine blames poorly done “post-ironic sincerity” on him, sort of; the problem is that his writing style, part of his appeal, is also infectious (see this blog, for one):
And if, even from Wallace, the aw-shucks, I-could-be-wrong-here, I’m-just-a-supersincere-regular-guy-who-happens-to-have-written-a-book-on-infinity approach grates, it is vastly more exasperating in the hands of lesser thinkers. In the Internet era, Wallace’s moves have been adopted and further slackerized by a legion of opinion-mongers who not only lack his quick mind but seem not to have mastered the idea that to make an argument, you must, amid all the tap-dancing and hedging, actually lodge an argument.
The problem is that people adapt DFW’s approach of not explicitly making arguments without simultaneously undermining them as a way to say outrageous things and pretend that the hedging makes them somehow less culpable. (See also Jon Stewart criticizing the ways in which TV networks abuse the question mark.)
DFW was not unaware of what he was doing; Maud Newton, in the NYT Magazine article, quotes Keith Gessen, who “applauds Wallace for ‘trying, at last, to destroy’ the oppositions between ‘irony and sincerity, self-consciousness and artifice.'” Read “Up, Simba,” and it’s painfully clear that Wallace is aware of how deep cynicism, posturing, awareness of cynicism and further posturing, paranoia about posturing and insincerity are all ruining everyone’s belief in everything, or something.
But Wallace also urges voters to get beyond their cynicism, or at least to acknowledge their complicity and the inescapability of the system:
“Let’s pause here one second for a quick Rolling Stone PSA. Assuming you are demographically a Young Voter, it is again worth a moment of your valuable time to consider the implications. … If you are bored and disgusted and don’t bother to vote, you are in effect voting for the entrenched Establishments of the two major parties, who please rest assured are not dumb, and who are keenly aware that it is in their interests to keep you disgusted and bored and cynical and to give you every possible psychological reason to stay at home doing one-hitters and watching MTV on primary day. By all means stay home if you want, but don’t bullshit yourself that you’re not voting. In reality, there is no such thing as not voting: you either vote by voting, or you vote by staying home and tacitly doubling the value of some Diehard’s vote.”
OK, fine, so I guess I wasn’t done with the post and, also, that the three things are somewhat related. It upsets me when my students shut down instead of trying to figure out a problem, because it reflects years of being conditioned not to expect to think. I really like Michael Gerson’s phrase “the soft bigotry of low expectations” (if not the reasons behind the coining of the phrase) — it makes a lot of sense in the context of education and learning outcomes. On a broader scale, too, our cynical acceptance of low expectations allows the perpetuation of systems of oppression and eroding personal rights. Inaction always supports the existing power structures.
“If you are neutral in situations of injustice, you have chosen the side of the oppressor. If an elephant has its foot on the tail of a mouse and you say that you are neutral, the mouse will not appreciate your neutrality.” — Bishop Desmond Tutu
You should leave me comments. Do I need to end posts with questions so people will reply?
* I should note that I hate standardized tests in a conceptual sense, for their purported ability to measure anything more than how well an individual can prepare for that test. As a nerd, I kind of enjoyed taking standardized tests in school,^ the same way I enjoyed math competitions, Odyssey of the Mind, and the WordMasters challenge. Once I hit middle school, though, the tests became much less interesting, and I became conceptually aware that they were taking away from instruction time.
^ Cf. this morning, when I woke up at my friends’ apartment and everyone else was asleep or at work. The only books they’ve unpacked were pop lit, a GRE prep book and a GMAT math review book. I went for the GMAT first, but got bored after taking a few chapter tests. I tried reading the GRE prep book, but it seemed kind of silly, since I’ve already taken the GRE. (This is also why I try not to go anywhere without my own books.)
** Article search deconstruction: I had the sense this article was somewhere in my gmail archive, but I realized that there were probably a ton of similarly tagged e-mails. I then tried to search for the opening quote about people being OK with announcing they’re bad at math, but realized that wasn’t specific enough either. Then I remembered the sentence “Is that a good day or a bad day?” (in his example about adding and subtracting integers). Third search result.
*** Of course, an informal poll of just a roomful of journalists wouldn’t give you a very reliable statistic. But since you’d be working with a roomful of journalists, you could probably get away with it by throwing out a bunch of percentages and interjecting “standard deviation” a few times.
**** (Pun intended, always).