Thursday, March 15, 2012
What is the end of the education system (as in the goal, not the apocalypse)? From what I can tell, it is to ensure that every child in America is ready for college after graduating from high school. For math teachers, that means that as a minimum they need to know the curriculum up to and including Algebra II.
The public education system is the most progressive institution in America. By that I mean it is an effort by the government to achieve an obviously desirable social goal. The problem is that progressive goals are often based on a simplistic view of reality, and they have unintended consequences. I am coming to the view that the education system is based on some major misconceptions: first, it is a good thing for every American child to achieve the same education; second, that it is possible for every American child to be given the same level of education.
One of the things that makes me question the whole system is the difficulty of teaching mathematics through problem solving. The main obstacle is that a lot of students simply aren't interested in learning. It is possible to give students a worksheet full of similar problems, tell them how to do it, and then make them work for an hour. It is not possible to force students to engage in problem solving for any extended period of time if they don't want to do it.
School is mandatory. Students are forced to attend, and they are forced to take math when they get there. Thus, many of them are there against their will. A few of them decide that even if they don't want to be there they might as well take advantage of the opportunities that exist. Others protest. You can make me sit here, they say, but you can't make me think. And they are right. We can't make them think. And if they don't think, they won't really learn. Sure, they will be exposed to a variety of mathematical techniques and they will acquire some familiarity with a variety algorithms. But I think that the knowledge they gain is next to useless. They won't be able to apply it because that would involve understanding, which requires thinking, which they refuse to do (at least some of them do).
The truth is that students may not know what is good for them, and they may be better off for having been forced to learn. Unfortunately, the government doesn't really know what is good for them, either. Is it really necessary for everyone to understand complex numbers? I think not. Most students would probably be better off learning some specific skill in some kind of apprenticeship.
High school is the result of flawed assumptions about what people need to know to be useful to society. The assumptions are flawed because they are the result of a political process instead of a "market" interaction between supply and demand. No group of experts (and especially not state legislatures or school boards) is expert enough to understand a complex economy and know what skills are actually useful. If we could know, the answer certainly wouldn't be that everyone ought to learn the same skills.
There is no demand for the kind of education we are giving aside from political demand. Students don't want to learn what we are teaching. The economy doesn't demand that they know what we are teaching. Students often ask when they will ever use what we expect them to learn and for the most part the answer is never. If they were actually interested in what we were learning they could make a career out of it (and a highly lucrative one). But if they aren't interested they will never achieve the level of mastery required for the knowledge to be useful.
This perspective is a bit troubling for a public school teacher. I basically don't believe in the whole premise of the institution that employs me. I don't think every student needs to learn geometry or algebra to be successful, and I think it is nearly impossible to teach anything useful to students who don't want to be there.
The thing is, I like teaching math, and I like working with teenagers. But I am pretty disillusioned about teaching math to teenagers who don't want to learn math.