Educating For Slavery using Algebra
From December 2008, so lacking in the mellowness of my late years:
Speak all you like about the economic and political ideals of the contemporary school, the education they provide is an education for slaves. Consider this scenario:
You teach algebra to a mixed group of students, some with active minds at least mildly interested in learning algebra but most of them there because the law dictates their obligation. They are there by coercion and so thoroughly has our age accepted the economic necessity for what it calls education that nobody thinks twice about whether children should be coerced to participate in something as inhumane and unnatural as the typical modern classroom.
You may well have just felt a reaction somewhere in the range between personal annoyance and impatience wtih my sweeping generalization. Don’t worry. If you don’t like what I said, just write it off as hyperbole.
On the other hand, you might want to take it at face value and ask if it expresses truth.
Regardless, they are almost all there against their wills and those whose wills are there might well be the worst off. In some situtations, they are merely pleasers and sycophants; the kind of person a system driven by abstract controls cultivates and honors, but whose actual worth to a community is diminished by the meaningless of what the community directs her to do.
So let’s say you teach algebra to this purely hypothtical group of kids. How would you approach it? I’m guessing that in 95% of the cases, the answer is as simple as saying, “I would teach them the text book, lesson by lesson, in sequence.” Ready for some irony? You can do that successfully, but it’s extraordinarily difficult. Here’s my thesis: to teach algebra that way would almost always be teaching your students to think like slaves.
The free mind is the mind that sees into the nature of things. When he reads a sentence like that, his eyes don’t glaze over and complain about it’s obscurity and how it distracts from the immediate needs of the moments. Something within is aroused. That something is whatever is left of the his sense of human dignity, and it is aroused to a very quiet hope that maybe, after all, in spite of the way his human dignity has been abused and belittled by his schooling and his work and his available forms of entertainment and everything about our society, still, maybe there is the possibility of becoming human.
And that possibility is the purpose of education.
So when you teach that algebra class, your immediate goals (getting through the lessons, learning a formula, etc.) can never be allowed to undercut that purpose.
So let’s go back to the classroom. If you were educating them to be and think like free people, how would you teach differently? To think that through, you have to ask this question: How does a free person think? First and obviously to the point of obscurity, the free person is not coerced to think a certain way. He is shown things and then pursues those things that are best with a will.
And that’s the problem. The free person is rather easily tempted, especially if he is blind to noble things. OK, fine. So what are you going to do about that? Poke out his eyes so he isn’t tempted? But if you think it through a little more deeply, the free person is not blind to noble things. Only the person who can see the nature of things, which is always noble, can be free. So the fact that you are teaching students who have slave’s values as well as slaves minds is no reason to rob them of their capacity for freedom.
Your goal is to set them free, and that means giving them eyes to see. This is, in fact, the central reason for studying mathematics as LIBERAL arts. Liberal does not mean left wing, it means the arts of freedom – the arts without which a soul cannot be free. Mathematics gives a person eyes to see.
But only if it is taught in a manner consistent with freedom. Only if it is taught to people as though they were free.
You see the dilemma. You start to teach them like they are free and they are driven amuck by their appetites. They don’t yet see the beauty of algebra with the mind’s eye, so they don’t go after it. They revert back to slavery even if you don’t. How can we set them free?
The short answer is, by teaching them as though they were free and insisting that they guard that freedom while guarding it ourselves. Very confusing. Let me show you in concrete terms by beginning with an ideal class.
Algebra revolves around one principle. By nature, algebra is the application of this one principle to all mathematical reasoning: the law of inverse operations. In simplest terms, this means that algebra is summed up in the single fact that you can do anything you want to one side of an equation as long as you do exactly and precisely the same thing to the other side. Therefore, the goal in algebra is to isolate the variable and the strategy is to do WHATEVER it takes to isolate that variable.
Now, if I’m going to teach my students to be free students of algebra (which is to say, if I’m going to equip them to operate on their own authority in this domain, able to solve their own problems without continually relying on a master, able, in short, to think for themselves), then I need to get them to SEE that principle and internalize it.
Once they get that principle, the next thing is to let them play with it.
Yes, that’s right. Play with it. Play. Chase rabbits. Experiment. Try and fail. Discover things for themselves. Experience “epiphanatic” moments of ecstacy that only can come through this sot of vigorous play.
How do I do that? Use the Socratic mode. Set them a problem and let them go to it. Guide them, offer tips when they want them, caution them about dangerous paths they’re taking, but make sure that they bear the weight of their own freedom. They must do the thinking.
I know. I thought about all those things. Of course, this becomes a big problem because they aren’t all working on the same problem every day. It doesn’t follow our contemporary industrial approach of quasi-efficiency. Did you expect it to? The modern school is an education for slavery. Why would you expect its approaches to work for free people?
The fact that it can’t be done doesn’t mean it shouldn’t be done. It also doesn’t mean we shouldn’t think about it. Nowhere in the world is there a perfect triangle. But we only know that because we know what a perfect triangle is. We have a standard. The modern classroom makes such a big deal out of standards, but they never ask what the perfect math lesson would look like. They just administer the math lesson of the text book publisher. That’s not how free people learn math. Let your dignity as a teacher come alive and offer some resistence. Please. For the children’s sake.
Back to the classroom. Given the opportunity, this is what I wish a teacher could do. During the first two weeks of school, set problems for the students and let them have at it. Divide them in groups if it helps, but make sure every single kid has a problem he has to solve using his own resources under your guidance. Don’t over-guide. Just tell them where they have to get (set the goal) and tell them the one rule (you can do anything you want to this side as long as you do it to this one). Give them some simple problems to start with that will reveal the principle and build their confidence. Then set them increasingly challenging problems. For two weeks. And don’t discipline them during this time except for the moral element. In other words, let them show as much interest in math as they want to show.
At the end of two weeks, divide the class into two groups. The first group (it might only be one person) will be the kids who spent their time trying to figure things out. Whether they did it well or not is irrelevent. All you care about is if they tried pretty hard and sustained their effort.
The other group will consist of the kids who couldn’t handle it. Some were the teacher pleasers who couldn’t let go of your approval as the driving force of their activities and became angry when you wouldn’t mother them and were utterly lost when you didn’t have some external validation of their accomplishments or some grade by which they could be affirmed. Some were the disinterested. But these are the kids who did not show any indications of interior life in relation to math.
Now you will teach each of them in separate groups using different means. The first group is your free class. They will continue to study as they have been.
The second group is your slave class. They can use the text book.
I guarantee you that after three months the free students will have deeply learned and been transformed by their encounter with algebra. And I guarantee that they will have learned everything the slave class will learn over the course of the year. The difference will be that they will have truly learned it while the slaves will have forgotten almost all of it by the end of summer.
What I am proposing is, of course, impossible. It’s more of a prayer than a serious proposal. I have no expectation that an American school would care so much about freedom that it would take on the risk of a lower SAT score and I have even less expectation that the parents will put up with it. But that’s the thing about having the mind of a slave. It can’t see so it doesn’t believe. Common sense would reveal that the free approach would lead to better SAT scores, but we have such enslaved minds that we fear the power of a mind set free. We fear education that is not strictly regulated and controlled by experts.
The free man ought not to learn any study slavishly. Forced labour performed by the body don’t make the body any worse, but no forced study abides in a soul.
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