I have read the essay. He captures in a beautiful way everything that is wrong with the way mathematics is taught. I think everyone who has an interest in the teaching of mathematics should read it: http://www.maa.org/devlin/LockhartsLament.pdfRobert1986 said:I have been enamoured with the Moore Method ever since I read Halmos' "Automathography". It seems like it would be very cool. Also, it sort of ties in very nicely with The Mathematician's Lament. (have you read this essay? its very good)
jk said:I have read the essay. He captures in a beautiful way everything that is wrong with the way mathematics is taught. I think everyone who has an interest in the teaching of mathematics should read it: http://www.maa.org/devlin/LockhartsLament.pdf
Robert1986 said:Not to mention, it is hilarious. Were you going "Yes this is exactly how my high school life was!" 'cause I was!
jk said:The best math class in my experience is a class where there was no book - in fact, we were forbidden to consult any book on the subject. The instructor did not lecture, and students took minimal notes. First day in class, instructor comes in, writes a few definitions and proves a couple of simple theorems. Then he writes a theorem on the board with no proof. Asks someone to prove it. The student then goes to the board and works out a proof. The rest of the class can not help him or her but can criticize the proof and find the gaps. Instructor only gets involved to clear up misconceptions, point out holes in the arguments by questioning the students in a socratic manner. If the student can't solve it he is invited to try during the next class and the class moves on to another problem. The first student now has "homework"
As the class progresses, the theorems and problems becomes harder and more substantial until we were proving pretty advanced stuff. Students really enjoy this as they are "creating" mathematics. You don't really need to take notes until the whole class has agreed on the solution that was presented on the board. Sometimes it takes two classes to solve something. You can spend hours working on that one thing in order to present it at the next class.
This way of teaching (called the Moore Method) is closer to the actual practice of mathematics. Once you have had a course based on this method, it is hard to go back to the traditional method where the instructor lectures for an hour and you just sit there and passively try understand it or are furiously scribbling notes so you can read them and understand later
jk said:The best math class in my experience is a class where there was no book - in fact, we were forbidden to consult any book on the subject. The instructor did not lecture, and students took minimal notes. First day in class, instructor comes in, writes a few definitions and proves a couple of simple theorems. Then he writes a theorem on the board with no proof. Asks someone to prove it. The student then goes to the board and works out a proof. The rest of the class can not help him or her but can criticize the proof and find the gaps. Instructor only gets involved to clear up misconceptions, point out holes in the arguments by questioning the students in a socratic manner. If the student can't solve it he is invited to try during the next class and the class moves on to another problem. The first student now has "homework"
As the class progresses, the theorems and problems becomes harder and more substantial until we were proving pretty advanced stuff. Students really enjoy this as they are "creating" mathematics. You don't really need to take notes until the whole class has agreed on the solution that was presented on the board. Sometimes it takes two classes to solve something. You can spend hours working on that one thing in order to present it at the next class.
This way of teaching (called the Moore Method) is closer to the actual practice of mathematics. Once you have had a course based on this method, it is hard to go back to the traditional method where the instructor lectures for an hour and you just sit there and passively try understand it or are furiously scribbling notes so you can read them and understand later
Robert1986 said:Not to mention, it is hilarious. Were you going "Yes this is exactly how my high school life was!" 'cause I was!
That is correct. Putting a bunch of students in a room with no ground rules and guidance will probably result in disaster. The instructor's role is very critical in that he or she has to break up the material into manageable chunks, correct misguided notions, gently hint at possible lines of attack (as a lost resort) etc...but this should be done in a very subtle way. The instructors should let the students struggle even if it looks like time is being wasted while the class seemingly goes nowhere. He should act as a referee and settle disagreements when someone is being unreasonable (It does happen that there is usually someone in the class who is stubborn and strong-willed and will not acknowledge errors).Robert1986 said:I haven't taken a Moore Method class, but (and someone correct me if I'm wrong) part of the idea (as I understand it) is that the instructor is there to sort of walk you through the stuff. So, its not a bunch of undergrads (or grads) in a room all re-discovering calculus. It is an instructor asking very well-placed questions and then usually forcing the students to work it out.
Sankaku said:I have had a class that tried to use some Moore-type presentations for part of it. I admire the general idea, but it takes a capable professor to guide the discussion and keep things on track. I can see that it wouldn't be the right thing for some people's teaching styles - and traditional lectures done properly can be beautiful in their own right.
http://en.wikipedia.org/wiki/Moore_method
After the endless "technique-driven" classes in early undergrad, more of this kind of thing would be great (if done well). If you learn to think and really understand the core ideas, then you can easily learn anything that you didn't have time to cover, later.
It is better to learn less material really well, and gain real insight, while you have a mentor available. At some point you will end up having to do all your learning on your own, anyway.
jk said:I think combining the traditional approach with the Moore approach in the way you suggest would not work very well for two reasons: 1) It would be hard to split the material into parts that are proved by the instructor and other parts by the students. If the instructor is solving things for you in the "main" class, the motivation to do it yourself in the lab section is gone. 2) In a Moore Method class, you end up working much harder than in a regular class, at least in my experience. I don't know if a lot of students would have the time for both approaches in the same class.
dkotschessaa said:I don't know. I don't see it any differently then a physics class where you are given a lecture and then a separate lab period. The motivation may just be to get it over with, but you end up learning quite a bit. I've always learned more in labs than in lectures - usually against my will! And the work *is* much harder, because you have to think on your feet.
It's likely many students would not like this, especially if they have no real interest in math.
-Dave K
dkotschessaa said:I am very happy though that a professor has invited me to study with him during a summer session where he will be mostly bored teaching a precalculus summer course, but available all day, so he wants to do something. I am stoked.
Is it the "abstract-ness" of the course that makes it difficult? Or is it not having a solid grasp of calculus?
ZombieFeynman said:I took Abstract Algebra and Analysis using the moore method. The pace is slower, but i find it to be a far better method for upper divisional proof based classes.
ZombieFeynman said:I took Abstract Algebra and Analysis using the moore method. The pace is slower, but i find it to be a far better method for upper divisional proof based classes.
dustbin said:Can I ask where this was at?