The case against algebra II
There’s an interesting debate described in this essay, Wrong Answer: the case against Algebra II, by Nicholson Baker (hat tip Nicholas Evangelos) around the requirement of algebra II to go to college. I’ll do my best to summarize the positions briefly. I’m making some of the pro-side up since it wasn’t well-articulated in the article.
On the pro-algebra side, we have the argument that learning algebra II promotes abstract thinking. It’s the first time you go from thinking about ratios of integers to ratios of polynomial functions, and where you consider the geometric properties of these generalized fractions. It is a convenient litmus test for even more abstraction: sure, it’s kind of abstract, but on the other hand you can also for the most part draw pictures of what’s going on, to keep things concrete. In that sense you might see it as a launching pad for the world of truly abstract geometric concepts.
Plus, doing well in algebra II is a signal for doing well in college and in later life. Plus, if we remove it as a requirement we might as well admit we’re dumbing down college: we’re giving the message that you can be a college graduate even if you can’t do math beyond adding fractions. And if that’s what college means, why have college? What happened to standards? And how is this preparing our young people to be competitive on a national or international scale?
On the anti-algebra side, we see a lot of empathy for struggling and suffering students. We see that raising so-called standards only gives them more suffering but no more understanding or clarity. And although we’re not sure if that’s because the subject is taught badly or because the subject is inherently unappealing or unattainable, it’s clear that wishful thinking won’t close this gap.
Plus, of course doing well in algebra II is a signal for doing well in college, it’s a freaking prerequisite for going to college. We might as well have embroidery as a prerequisite and then be impressed by all the beautiful piano stool covers that result. Finally, the standards aren’t going up just because we’re training a new generation in how to game a standardized test in an abstract rote-memorization skill of formulas and rules. It’s more like learning student’s capacity for drudgery.
OK, so now I’m going to make comments.
While it’s certainly true that, in the best of situations, the content of algebra II promotes abstract and logical thinking, it’s easy for me to believe, based on my very small experience in the matter that, it’s much more often taught poorly, and the students are expected to memorize formulas and rules. This makes it easier to test but doesn’t add to anyone’s love for math, including people who actually love math.
Speaking of my experience, it’s an important issue. Keep in mind that asking the population of mathematicians what they think of removing a high school class is asking for trouble. This is a group of people who pretty much across the board didn’t have any problems whatsoever with the class in question and sailed through it, possibly with a teacher dedicated to teaching honors students. They likely can’t remember much about their experience, and if they can it probably wasn’t bad.
Plus, removing a math requirement, any math requirement, will seem to a mathematician like an indictment of their field as not as important as it used to be to the world, which is always a bad thing. In other words, even if someone’s job isn’t directly on the line with this issue of algebra II, which it undoubtedly is for thousands of math teachers and college teachers, then even so it’s got a slippery slope feel, and pretty soon we’re going to have math departments shrinking over this.
In other words, it shouldn’t surprised anyone that we have defensive and unsympathetic mathematicians on one side who cannot understand the arguments of the empathizers on the other hand.
Of course, it’s always a difficult decision to remove a requirement. It’s much easier to make the case for a new one than to take one away, except of course for the students who have to work for the ensuing credentials.
And another thing, not so long ago we’d hear people say that women don’t need education at all, or that peasants don’t need to know how to read. Saying that a basic math course should become and elective kind of smells like that too if you want to get histrionic about things.
For myself, I’m willing to get rid of all of it, all the math classes ever taught, at least as a thought experiment, and then put shit back that we think actually adds value. So I still think we all need to know our multiplication tables and basic arithmetic, and even basic algebra so we can deal with an unknown or two. But from then on it’s all up in the air. Abstract reasoning is great, but it can be done in context just as well as in geometry class.
And, coming as I now do from data science, I don’t see why statistics is never taught in high school (at least in mine it wasn’t, please correct me if I’m wrong). It seems pretty clear we can chuck trigonometry out the window, and focus on getting the average high school student up to the point of scientific literacy that she can read a paper in a medical journal and understand what the experiment was and what the results mean. Or at the very least be able to read media reports of the studies and have some sense of statistical significance. That’d be a pretty cool goal, to get people to be able to read the newspaper.
So sure, get rid of algebra II, but don’t stop there. Think about what is actually useful and interesting and mathematical and see if we can’t improve things beyond just removing one crappy class.