High school graduation the supposed skill certification and high school graduation the social ritual have become inextricably intertwined in our culture. So it's no surprise that people are up in arms and saying things like, "These kids ought to be able to graduate." I even agree with them, but not in the way they think: I don't think high school graduation is most useful when it's a certificate of attendance. But I do think that if you don't know enough or can't do enough to meet graduation requirements, you should be getting feedback to that effect. The idea that you would have passed all your classes and yet not know the things they feel you should know at that point seems like something has gone wrong, and I doubt that there would be this much uproar if we were talking about kids who hadn't passed their classes--for whatever reason, we are culturally on board with the idea that if you fail math, you don't graduate. But these kids are failing at learning math, and they're not failing math, and that, to me, is a big problem. Sure, we're not talking about students who are passionately committed to mathematics here; not every student is or should be. But we are talking about students whose best indications on whether they know an acceptable level of math for a high school student is that they do, and those best indications are, apparently, wrong.
I'm sure there are people who are totally okay with a math test but not with this math test. But that's not what we hear every time this issue comes around. It starts to boil down to, "But math is hard! You don't really need math! And it's hard!" And at that point, well, what do you really need from a high school education? What can't you work around? There's not a heck of a lot, on the level they're talking about here. If having to calculate the area of a room from its dimensions is too much to ask of high school graduates, I'm starting to think that the people constructing these arguments are, in fact, arguing for a high school diplomat to be a certificate of attendance, a verification of age.
One of the things we are not willing to say in this discussion is that people who can't do math are missing out. They're missing out on ways of protecting themselves, sure, on a measure of independence that comes from being able to do some rough calculations yourself. But they're also missing out on something wonderful. Something beautiful. I know I'm talking to some of you about yourselves, and yes, I'm sorry: you're missing out. That dimension of understanding is worth cultivating. It is worth having. Some of you can't do math the way a person who is completely tone-deaf from birth can't learn to identify a piece of music upon hearing it, but the vast majority of you who can't do math are more like someone who doesn't know any songs because no one ever taught you any. It doesn't make you a worse person. It doesn't make you an unintelligent person. But it's still a damned shame to induce disabilities in people who don't have them to begin with.
I believe that math-related learning disabilities are real. I absolutely do. I do not believe that irremediable math-related learning disabilities are as prevalent as people who were taught math very, very badly, often by people who did not themselves know how to do math.
I don't really know what to do about that. Saying, "Yes, fine, go on ahead and get out of here; it's not like we have any real preparation to teach you math from here anyway," seems practical in the short-term but distinctly suboptimal in the long-term. It treats the problem as one of what to tell the students--yes, you are a high school graduate, or no, you are not--rather than what to do to fix a system that "should have" done something but did not.
It allows us to keep on with math education the way we have been. And on the one hand, we sort of have to. And on the other hand, we sort of can't.