Lifting the Curse of Mathematics

In his article "Ending the Curse of Remedial Math", David Kirp describes a CUNY program to teach low performing students the math skills they need to be eligible for course work at the associates degree level. That is, he describes a program to teach remedial math. This seems a funny way to end something. Isn't the way to end the curse of remedial math to end remedial math?

Everybody agrees remedial math is a problem. Remedial courses are the great choke point in increasing college access. More students are getting in to higher ed to get the careers they need to make a decent living. These new students are, in general, people with weak K-12 achievement: Many of them are people who would not have been considered qualified for college in the past (even an AA program in community college). So to get them the degrees they need to get jobs, we first need to get them qualified to get in to the programs they need to get the degrees they need to get jobs. The way we get them qualified is by giving them "remedial" courses-- courses to teach them the skills they failed to learn the first time in high school. The problem is that students have already shown they have trouble mastering these skills, because they failed to learn them the first time in high school.  So, what do we do? We work harder. We devote more resources to teaching these classes. And we make (or count on) the students to work harder too. Maybe they goofed-off in high school, but now they are mature 20-yr-olds and they can buckle down and get it done. Some do, but many don't. 

The curse of remedial math is that many students fail to pass the remedial classes, and those who fail are doubly screwed. They have wasted time and money, and all they get in return is confirmation that they can't do any more than a high school degree. College is just too high a bar for these guys to clear. We know this because we set the bar somewhat lower (not a college class, just a remedial class) and they still can't clear it. 

So, what can we do to lift this curse? There are a few options. The simplest and cruelest is to follow the Silicon Valley start-up mantra: Fail early. Figure out who can't cut it in college early on and steer those folks away. A slightly less cruel way of putting this is that we should develop some screening tests to decide who has a good shot at clearing the bar before we set people the task of doing so. If you fail the test, then we tell you, "come back when you are ready."

A second strategy, embodied by the program Kirp describes, is to give kids a boost. Help them up over that first remedial bar and then hope they will do OK. There are couple of obvious problems with this approach, but one big positive. The positive is that it lets us keep believing it is possible for everyone to go to college: Everybody can have access to the goodies higher ed provides. There is a second, generally unstated, clause to this benefit statement. Everybody can have access to the goodies higher ed provides...and we don't need to change higher ed much at all. That is, we can keep college the way it has always been and just increase the number who get through. I'm a university professor and I like this idea. I like what I do, and don't want to change.

Now to the problems. Again, one is obvious: It is difficult and expensive to get everyone through remedial classes. Maybe there is a silver bullet out there, but the history of educational innovations does not provide a lot of reason to hope we will hit on a solution that will really change things for a large number of people. This is a hard problem. But this is just a technical problem. Give education researchers enough money and they’ll solve it.

There's a second kind of problem that is more fundamental, baked in to the idea of helping people through remedial classes. Which is, if people need this much help getting through the remedial classes, are they really ready for the more advanced coursework? How you think about this problem really determines your attitude toward remediation (or it ought to). How you think about this problem also largely turns on what you think students need to know to succeed in higher ed.

Kirp starts his piece with an in-class question asked of the remedial students, "Can you simplify this square root?”  The right answer to this question is, "Who the fuck cares?" How much effort is it worth to learn how to simplify square roots? Let's say we can get lower performing students to learn this skill. Will this ability really prepare them for college-level work? Probably not. There are very few things people will do in school or in life where they really need to know how to simplify square roots. Put another way, there are very few majors or careers where not knowing how to simplify square roots is a disqualification. So, why make these kids learn this?

There are 3 reasons, and two of them are bad, and one is pretty bad. 

Bad reason number 1: There are actually plenty of majors and careers where you have to do things like simplify square roots. True, but are people who struggle through remedial math really going to pursue those careers? How many? Is it right to make everyone learn this? This is a bad reason because it is only relevant for a small number of cases. I don’t know how many of these degrees really require much math at all. Certainly not all of them.

Bad reason number 2: People need to be mathematically literate to be responsible citizens and successful adults. I agree with this, but what does it mean to be mathematically literate? Kirp mentions 3 kinds of math content in the article, simplifying square roots, understanding negative numbers, and dealing with decimals. Of these, only the last is clearly a skill that you need to survive in the modern world. Negative numbers don’t come up that often, and when they do, it’s probably because you’ve made a mistake*. Anybody who has helped a kid through high school knows that there is very little about the curriculum that is focused on everyday mathematical literacy. It would be great to have classes that really made people comfortable solving quantitative problems and understanding mathematics as a modeling technique. If such classes exist, they are not in high school or remedial math: Algebra is not mathematical literacy.  Reasonable people can disagree on this, and I won’t demand you be reasonable and agree with me here. But, I think you do need to agree with me that there is no particular reason why algebra has to come first, why you have to get “algebraically literate” in order to get an associates degree. So you get an AA degree and you are not mathematically literate. Is that worse that being mathematically illiterate and not having an AA degree? Even if a major does require some math (you need to know about proportions for a “Culinary Arts” degree?), why do you have to take a GENERAL course in algebra (chefs don’t square roots, but they do cube them, heh heh), and why should it be a prerequisite?

Pretty bad reason. I think this is really the crux of the matter: People think sitting through an algebra class trains good habits of mind that prepare students to learn in other classes. I had a Math professor tell me that I needed to add an algebra prerequisite to my statistical thinking course because students would be so much more “mature” after taking algebra. This is the old 19th century view of education: You make people learn difficult pointless stuff (like Latin) and then they will be able to learn anything. This is a pretty bad reason because it is nonsense: Learning math doesn’t make you smarter. But it’s only pretty bad because it would be great to teach people how to learn. What struggling students need to learn (IMHO) is how to be better students.

And now we come to the third strategy for lifting the curse (I know my numbering is hard to follow, but you’ve passed algebra so you should be OK).  What if instead of teaching people remedial math, we taught them “remedial study skills”? Give them some classes where we can scaffold good study habits etc. As far as I can tell from Kirp’s description, this is just what’s going on in the remedial math program he describes. The innovation here is that students need extra support to learn how to learn. I wonder how much better such programs would work if students were learning something they actually cared about and were motivated to learn. Something that’s not math.

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*I’m assuming “understanding negative numbers” means more than knowing the difference between owing money and being owed money. I expect most people understand this even before taking algebra.