[carlosaguayo]

And I believe it's a problem of the education system. Back in high school they had me solve dozens, if not hundreds, of derivates and integrals, it was not until college that a fantasic teacher had the guts to come up with his own syllabus, threw away all the "traditional" calculus and taught us what was a diffeeential, what were we doing when getting a derivative and an integral, completely changed my mind.

[timr]

"And I believe it's a problem of the education system."

That's just a cop out. We all had teachers and subjects that didn't connect, for whatever reason. Ultimately, the responsibility to learn is personal.

I don't mean to be harsh, but basically every comment on this subthread is someone saying "I was a great math student, but I never understood what radians MEANT until now!" That's crap. If you do 10,000 practice problems and get high marks and still don't understand the concept, you haven't done anything. Good teacher or bad, your job as a student is always, forever, to figure it out on your own.

[InclinedPlane]

The responsibility of a teacher is to instill and assess knowledge. Repetition of busywork does not require a teacher, it only requires a textbook. The purpose of having a teacher in the loop is to ensure that students are actually understanding the material, which is why they are graded. If a student can get through a class without acquiring any degree of competency or basic understanding of fundamentals that's a failure on the teacher's part.

If "teaching" was just a matter of reading and completing exercises then we could replace teachers with scantron machines. Yet college students pay teachers thousands of dollars per course to ensure that they receive more value than that. If they don't get it then they are being mis-served and cheated.

[timr]

So let me summarize your argument: "Teachers cost money. Therefore, if I do not learn the subject matter, it must be because the teacher was ripping me off."

That's an excellent way to externalize personal failure.

A teacher cannot teach a student who doesn't make an effort to learn. Full stop. But it's a symptom of our ever-increasing sense of entitlement that we assume that our role as students is that of the audience for a play. We intend to lie back, and let the education wash over us. If it takes effort to learn, they must not be teaching correctly!

Let me flip around your supposition: if the people in this thread -- all of whom were apparently high-achieving math students -- cannot manage to understand a core principal of elementary trigonometry that is stated clearly in every textbook, the problem is more likely to be with the unwillingness of the students to think independently than the failures of a diverse group of teachers from all over the world to shove the knowledge into their head.

It's far easier to blame the teacher than to do the work of learning.

[aaronem]

> A teacher cannot teach a student who doesn't make an effort to learn.

Quite so. But a poor teacher can do quite a lot to impair a student who does make an effort to learn, and, at least in the public schools of the United States, there is little meaningful incentive for a teacher to be other than poor. Not to say that all US public school teachers are poor, of course; there are at least a few really excellent ones, or were when I was a student. Excellence, though, is anything but a requirement.

I'd also argue that a really good teacher can elicit from her students the sort of effort you describe; I've seen it happen -- indeed, most of my basic facility with the English language, I gained under the tutelage of precisely such a teacher. That's a more complicated proposition, of course, but I start to wonder whether or not it's at the core of the current argument.

It's not hard, or so the US public school system would have us believe, to teach someone enough of a given subject that she can qualify to teach it herself. But is that the essential feature of pedagogy? Or is it instead to lead a class full of students, in such fashion as to overcome the basic distaste, for complex and difficult learning without immediate reward, which is part of the human heritage?

[InclinedPlane]

If a teacher fails to impart understanding and they give the student a passing grade then that's a failure of the teacher. If a teacher is a hard ass but has open office hours and students don't take advantage of them and end up failing then that's a failure of the students as well.

The problem here is that it's so common for students to be able to glide through course after course using rote memorization and a willingness to do busywork without attaining understanding and in so doing not only passing courses but also getting high grades. And that's a failure of student and teacher alike, but it's a failure that the students have been trained for and guided to by the system.

Again, the problem is that schools do not reward or generally even bother assessing learning. And certainly part of the fault for that lies on the student, but given that they are being passed through the system and actively rewarded for not learning I think the bulk of the blame lies on teachers and institutions. If the value of an institutional education is to provide an opportunity for auto-didactism and whether one takes that opportunity or not is not reflected in grades or degrees granted then I have to question the value of such education.

[jackmaney]

"Yet college students pay teachers thousands of dollars per course..."

No. College students pay colleges and universities thousands of dollars per course. There's a difference.

[InclinedPlane]

Exactly. In many subjects it's far easier to concentrate on busywork than on understanding. And rushing through lots of "material" that tests only short term memorization rather than knowledge is a good way for teachers to feel like they are doing a lot more than they actually are. Yet the value of an education 1, 5, 10, or 20 years down the road is always in the fundamental understanding, not the breadth of material covered. Understanding sticks, the details of busywork fades away.

Should an education concentrate on short term knowledge of trivia that fades away rapidly or on long-lasting understanding of fundamental concepts? Is it even remotely reasonable to charge tens of thousands of dollars to students for something that is only temporary?