Sorry for the lack of a proper first post or anything like it. I guess I’ve set this up just for comments that are too long to fit nicely in comments sections.
This is a reply to
In some ways, this is also a reflection on
and maybe also
For most of my students, education is not for anything. They are not for anything. They are too far behind. The cognitive abilities they needed to be born with, or to attain by age five, or ten, or fifteen, they never have quite gotten. They are unnecessary. They will always be unnecessary.
To be useful today and tomorrow, you need to be able to perform a task that cannot be automated. Better yet, you might create something that can then be reproduced cheaply and automatically. Either that or you need to luck into a job that dozens of essentially unemployed people are equally willing and able to do. (Connections help.)
To be above automation, you have to be able to come up with ideas, and you have to be able to get a reasonably accurate sense of whether your ideas will work or not. My best students can do this, and, as far as I can tell, they seem a little better at it at the end of the semester than at the beginning. My average student cannot.
Every semester, one or two of the many very confused students summon up enough courage to visit my office and ask me to take the time to explain carefully what, for example, linear independence means. We read the definition carefully. We read all the definitions of the words in the definition. They try to understand it. By the time they understand the last word, they have forgotten the first word. Well, actually, we have the book open or wrote the definition on the board, so they know what the first word is, but they have no idea what it means. They go back and work to understand the first word and forget about the last words, or any of the words in the middle. Forget about trying to see what any of the words have to do with each other.
At this point, it’s been an hour, and I can see the smoke coming out of their ears. I suggest coming back and trying again tomorrow or the day after, which they do. I try starting with examples this time. They understand that the facts we deduce about the example and can verify them. They look at the definition and forget everything about the example. They look back at the example, forget all the conclusions we made about it, and forget the definition. Never mind about trying to make any kind of connection between the example and definition beyond a vague feeling that they must have something to do with each other, since I talked about them at the same time. On the next exam, when I ask for an example of linear independence, they produce this one with some garbled nonsensical explanation. I feel obliged to give them a decent amount of partial credit.
They thank me for my time. They appreciate what I am trying to help them do. If this isn’t their first course where they’ve been asked to do something other than memorize facts or procedures, they’ve been through this before. If this is their first such course, and sadly quite frequently this is the first such course for a senior, they see that trying to work with ideas is new to them and understand why learning to work with ideas is important.
They ask if it was this hard for me. I’m not a very convincing liar since I can’t very well make up stories of spending hours every week in my professors’ offices semester after semester. Besides, they see the best two or three students in the class waltz into my office, ask a quick cryptic question, get a short cryptic answer in reply, and waltz off with a perfect idea of what to do. Sometimes they ask me to explain the cryptic question and reply, and I’ve already told you what happens if I try to explain.
More than anything else, they learn they are just not good enough. They have thought more intensely for two or three hours then they ever have in their lives. If they’ve just barely managed to get linear independence, they see no way to get the next concept, or any concept, on their own or in a reasonable amount of time. Maybe they might keep trying a few more times. It makes no difference. They never quite get it, and they work hard to get their C for learning to be an okay imitation of Wolfram Alpha, or sometimes a B for learning to be a good imitation of Wolfram Alpha.
To talk about something a little more directly useful than a conceptual understanding of Linear Algebra, I should mention that I recently taught Algorithms. A few students could handle it. Most students will never be able to look at a description of an algorithm or a piece of a program and understand what it is doing and how and why it works. They program by copying snippets of code from the Internet and trying random modifications until it passes the tests it is supposed to pass. Unfortunately, India graduates 10,000 programmers a year, all capable of doing that (and many capable of doing more) for less than half an American salary. For that matter, code generators can pretty much do that now too. If they talk their way into a programming job, they don’t last very long.
You might think they are just not good at math or at computer science. Occasionally I look at a transcript just out of curiosity. Almost always it’s filled with C’s and B’s in challenging classes, A’s in the classes that seem not to demand any grappling with ideas, and maybe D or two when they made the mistake of trying a class that absolutely demanded it.
Don’t get me wrong; I get some slackers, and some very smart slackers too. They also have B and C averages, and they are also frustrating, but for different reasons.
So maybe I have a second answer to the question of what education is for. For half my students, it’s for them to come to understand that they just do not have any of the talents needed to be useful, and to understand how and why their abilities are inadequate. To echo Calvin, the role of education is to teach them to praise society for its justice in condemning them to damnation. Even better, they can teach their friends and family who never even made it to college in the first place to praise society for their damnation.
This is absolutely borne out by employment outcomes. Our B and C students mostly graduate and end up working odd jobs, at best becoming shift managers for fast food. They might try, and mostly fail at, selling cars or insurance. They do better at keeping full time employment than most non-graduates, but you would expect that just from their willingness to work hard.
Hopefully, they believe God loves them and finds them useful, whether they put it in those words or not. Hopefully they have family and friends (and professors) who love them and find them useful, even when society finds them, and all their family and friends, unnecessary. Thankfully, I haven’t yet had a student who decided that their best option was a bullet to the head or an overdose of oxycontin, though I expect some of them will be voting for Trump purely out of nihilism.