The first time a teacher teaches something, the teacher learns. The second time a teacher teaches something, the students learn. After that nobody learns!
I think the reverse is more accurate. When learning something study as if you have to explain it to someone else. If you can explain it to someone who doesn't have a lot of knowledge in the particular subject you are studying then you really know it. The converse is definitely not true though.
I was bored to tears in high school and college. If I taught like I was teaching myself, the majority of the class would be left behind and we'd all fail.
No thanks.
The real moral here is to empathize with students and then teach.
I teach mathematics at a community college. I definitely don't teach like I'm the student. A large majority of my students don't like mathematics and don't want to be in the class. If I taught like I was the students only a few people would pass. Few of my students have the desire to know, to learn that I had as a student.
I think his advice best applies to a group of students who care about learning and want to learn. It doesn't apply to those who don't possess these qualities.
Out of curiosity, if this is the case, why should more than a few people in the class pass? Do you believe that shoving the material down these unwilling students' throats in such a way that they are able to pass results in a higher portion of them gaining and retaining the knowledge than would have otherwise? To me it sounds like very few in this class are interested in or successful at learning your material, so what is the definition of "passing" a class?
It's a very good question to ask what it means to pass a class. It's also a difficult one to answer but I'll try.
More than a few people should pass because that's what the Board of Regents, the college president, the Governor, the Legislature, and society at large want and they pay my salary. This isn't a flippant statement. In my state one of the Board of Regents wants my pay to be dependent upon how many people pass my class. Every year the president of the college sends a report to the Department of Mathematics and asks what we are doing to improve the passing rate.
The state wants three things,
1. we must accept anyone who applies
2. we should pass almost everyone who takes our classes
3. everyone who passes should 'know' the material
You can have any two of these things but not all three. I have a lot of pressure from the administration and so my perception of what skills it takes to pass has been a decreasing function for the past 10 years.
Almost all of my colleagues give point based on things that a well trained chimp can do. They give points for attendance. They give points for turning in homework. (The homework doesn't have to be correct to get the points.) My colleagues try their hardest to give students enough points so that they can reach the magical 70% thresh hold. Some have lowered this magical thresh hold to 60%.
What it means to pass a class is a level of achievement that most people in the class can reasonably achieve. It has nothing to do with knowledge, skills, or anything that really matters in terms of learning. Will 70% of the students pass with this grading scheme, with these assignments, with this level of work and effort? If the answer is yes then you've got a good idea of what it means to pass a class.
This has bad, long term consequences for society writ large. I'm aware of this and I try the best I can to reach as many students as possible.
I definitely don't teach my students as if I was in the audience. I'm an outlier in terms of mathematical talent and interest. It would be insane for me to teach as if I was in the class.
My personal opinion is this goes back to the same mentality that gives everybody a trophy for playing soccer. We are trained from first grade that you just need to show up to succeed. Almost every experience from kindergarten to a high school diploma emphasizes that.
Can't let it stop with college or a job, now can we?
I love teaching a room full of interested, motivated people. It's too bad I can't become a teacher to do that. :(
It seems like the meat of the course and how you grade it are somewhat orthogonal. Have you ever tried teaching it for real, however you think the semester would best be spent, then just curve/inflate/whatever the grades to get the desired distribution at the end?
They are orthogonal to a large degree. What you say happens quite frequently. Mostly, I'm teaching to 3 or 4 students. That's how many are interested on average.
You might like the dy/dan blog http://blog.mrmeyer.com His focus is on elementry/high school but I think his approach would also make college-level classes much more interesting.
I've seen both of those. I have incorporated some of their suggestions into my classes. Some of their techniques don't fit my personality.
The way I learn mathematics is suited only for a small percentage of the population. As an example, I have little use for diagrams. I don't think in terms of geometry but in terms of abstract definitions. I don't need a diagram to conceptualize and understand that pi is the ratio of the circumference of a circle to its diameter. Even with diagrams most of my students don't understand what this means.
Meyer's enthusiasm is contagious and I appreciate that about him. It's exceptional, in fact. It's also not duplicable by most teachers. He's found a style that works for him. It doesn't work for everyone though.
One of his methods involves watching videos of water pouring out of a container and experimentally verifying whether or not his calculations make sense. For me, this is a great big yawn. I could not bear watching such a thing in a class as a student.
The real problem in education, as I see it, is that schools do a terrible job of matching student personality with teacher personality. I believe that solving this problem would significantly increase retention and learning.
It's hard to fit a teaching method to a personality that isn't predisposed to such a method. It just doesn't work. The human interaction dynamic of such a class is a mess.
This advice should be taken with a grain of salt. It all comes down to the level of the instructor vs the level of the students.
If i taught like i were the student, most students would be left far behind probably trying to figure out how i got from point a to b.
With that said, on occasion (during advanced courses) i can really go all the way with the students and challenge them and sometimes even myself, it's a rare synergy between the student and teacher.
In any situation teaching is an act - it all about enthusiasm - even when its the most boring subject , you need to make the students feel excited about learning it.
"That the stupid pupils were these! I explained once—they did not get it. I explained second time—they still did not get it. I explained third time—I myself got it, but they did not!"
The biggest mistake in teaching is not providing enough context.
So often teaching (or documentation) devolves into mere description. As if detailing every part of an automobile is a good way of teaching how one works. The human brain is a wondrous thing, so even with such a horrible method of teaching eventually smart people will pick things up. But it's a very inefficient and error prone method.
The right way to teach is to start with an abstract, low-fidelity model and then build upon that. Once students have a good mastery of the model then you can delve down into fine-grained specifics (how each component works, for example) and only then can you evolve the model into a more accurate representation.
That's why good teachers are so rare. Because it's easy to "teach" a complex system by describing each component in detail, but it's harder to come up with a series of models from low-fidelity to high-fidelity that bootstrap up from zero knowledge to expertise.
The first time a teacher teaches something, the teacher learns. The second time a teacher teaches something, the students learn. After that nobody learns!