Thursday, March 15, 2012
The End of the Education System
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.
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I've thought very similarly when I'm in a certain mood. But then I remember that I didn't like math until I took calculus. Calculus tied together all the stuff I'd learned throughout school into a cohesive whole. Calculus helps us analyze real world occurrences and we need algebra and geometry to do calculus. So yes, a lot of students won't need algebra in the future and they don't want to learn it now. But playing scales on an instrument is just awful and that's what they make you do for years when you're learning to play the violin, but once you're ready, playing a real piece of music feels miraculous. I feel like a big part of my job is persuading, cajoling, motivating and enticing kids to continue with math because once they have the basic tools and they finally learn to apply those tools to analyzing the world around them, they won't ever think math is useless again. There are very few students I think who would naturally be interested in math even if they were good at it. But can anyone truly like something before the even know what it is? So our job is to show them what it is, how beautiful it is, and how with work and dedication they can bend it to work for them- just like music.
ReplyDeleteOn the other hand- I totally agree that students should be allowed to pursue other options. If they're interested in becoming mechanics or carpenters they'll need one kind of math, if they're interested in pursuing accounting, banking or business, they'll need another kind of math. If they're interested in being scientists, engineers or teachers, they'll need a more traditional college prep math experience. If we asked kids to keep pursuing math, but we gave them options for types of math they'd like to study that will help them prepare for careers they're interested in- wouldn't we have more success getting kids engaged?
Although tomorrow I may feel totally differently and agree with you whole-heartedly. The above is what I think when I'm in an optimistic mood to convince myself that what I'm doing is worth the 80 hour work weeks.
I agree that math seems to make a lot more sense once you get to calculus. I wonder why we don't teach derivatives much sooner. I recall someone telling me that in some programs the students are introduced to them in 8th grade.
ReplyDeleteIn any case, it is interesting that we have a system that is designed to lead up to calculus when a large number of students never get there. It seems that completing Algebra II has been the standard for being "college ready", but does that make sense if to some degree Algebra II is really just calc prep?