I will talk mostly of mathematics at the high school level, since that is what I taught. The standardized tests for mathematics required my students to memorize vast numbers of equations and mechanical techniques in order to regurgitate them upon the standardized tests. If my students performed poorly on the standardized tests, the state came down on the district. The district came down on the principal. The principal came down on me. Shit flows downhill. When the state instituted promotion testing things got even worse. For example, students could not be promoted out of 10th grade unless they passed a standardized test of algebra problems -- all of which were basically about how to perform various mechanical operations upon recognizing that a problem was of type X.
The problem is that memorizing vast numbers of equations and mechanical techniques is not mathematics. It is what standardized tests measure, but it is not what algebra is.
Algebra is, in the end, a method for modeling problems using mathematical equations. If you are incapable of understanding the concept of a "variable" as a stand-in for any changable item in a real-world problem, you are not in possession of any mathematical knowledge. You are merely a trained monkey, who has undergone obedience training in order to convince you that knowledge consists of rote memorization of things handed down by Big Brother rather than something developed by human beings using a very small set of assumptions plus a lot of logic and reason.
The hilarious thing is that while my students tended to do poorly on standardized tests, they always did well at the "Math Olympiads" and similar competitions, because they understood *mathematics*, and thus were capable of devising means of solving the problems they encountered, rather than being restricted to a set of memorized techniques to be regurgitated for the set of standardized tests. The problem they had with standardized tests was primarily one of time -- they approached each problem as a unique and individual question to approach using logic and reason. But logic and reason take time. And usually they only got through with maybe 1/4th of the problems before they ran out of time. Thus one of the things I tried to do, at standardized test time, was spend some time on test-taking strategies. But it was hard to de-program kids who had learned to approach mathematics as an intellectual question and instead force them to view mathematics as a set of rote-memorized equations and techniques to be regurgitated upon demand upon the standardized test.
In the end, modern education appears to be designed to be incompatible with the use of logic and reason to approach problems. If a teacher attempts to teach his or her students to use logic and reason, the students will perform poorly on standardized tests, because it will be hard to put them back into the mindset of viewing mathematics as a set of fixed-in-stone facts and techniques to be regurgitated upon the test. Since the whole *point* of mathematics is the use of logic and reason to model and solve problems, this has rather dire consequences for our children's education. But, alas, many ignorant people, having never encountered any mathematics, believe that the rote monkey training you received in school is in fact "mathematics", and that "if it was good enough for me, it is good enough for my children" -- ignoring the fact that you received no mathematics education at all.
Which, of course, is the point. Mathematics is the use of logic and reason to create models of potential universes (albeit the mathematical systems most commonly used were created to try to model our *own* universe, mathematics itself has no such restriction). Knowledge of mathematics (as vs. the rote mechanical crap taught in schools) would interfere with our rulers' ability to bypass logic and reason and drill down direct to the inner monkey of the jumped-up hairless ape that is the human animal. And if politicians had to actually present logical and reasonable policy proposals rather than simply hoot and howl and fling feces at one another... why, someone intelligent might actually get elected. Oh the horror!
- Badtux the Mathematical Penguin
You have just presented the reasons that No Child Left Behind, with its emphasis on standardized testing, is a big failure (along with its being under-funded).
ReplyDeleteYou have also made me confused. My conservative friends have told me that it was tenure that ruined education. In other words, they claim that the problem with education is teachers and you claim it is technique. One of my friends gets very eloquent about it. He's a pump salesman. You were (and maybe still are) a teacher.
I have to go with the pump salesman on this one. You don't actually go to teachers to learn something about education. That isn't the conservative way. You go to someone who has no clue about the issue. It's the only thing agood conservative can do.
Having "different universes" is just liberal propoganda.
ReplyDeleteKeep 'em stupid, keep 'em pliant.
ReplyDeleteGood point, Mr. Frog. If I want to do something like, say, improve medical care in the United States, I shouldn't listen to doctors (who say the current health insurance system is a nightmare). I should instead listen to self-proclaimed experts who tell me why the doctors are full of ****. And if I need heart surgery, well, I don't know why we're paying these guys to learn all that stuff about medicine anyhow. Anybody could do it just by picking up a copy of 'Heart Surgery for Dummies' at the bookstore, so why should I pay $100K for heart surgery?! Better yet, let's bring in some undocumented Mexicans to do the heart surgery (hey, it works for lawn care!), now *that* would reduce the price of medical care!
ReplyDeleteBut of course education is different from medicine because, just like everybody has survived going to the doctor's office and thus is a medical expert, everybody has survived going to the teacher's classroom and thus is an education expert. Alrighty then!
- Badtux the Former Teacher Penguin
Great post, Bad Tux. The whole standardized testing thing drives me up a wall. William Butler Yeats pointed out, "Education is not filling a bucket, but lighting a fire." Thank goodness you were able to light a few math fires before you went on to other things.
ReplyDelete