I taught geometry for teachers course last semester. Towards the end I showed them an animation which depicted a geometry classroom in which students were given a problem to work on, to come up with conjectures and to prove them. The way I went about this was to give my students exactly the same problem before they saw the movie. They came up with conjectures, but didn't have to prove them immediately. Then they saw a movie. I guess I should point out that the students in the movie gave a partial solution, but there were loads of misunderstandings both on the side of students and the teacher. The goals were many, but one of them was for my students to be able to follow what students are saying at a pace at which things happen in reality and to try to determine what is correct, what is incorrect, what they should follow up and what they should leave alone. Things went fairly well, and now I am thinking whether to stick with the same plan or to alter it slightly. One questions is: Is it fair to show them the movie and expect them to be able to follow the action live :) When I saw the movie for the first time, although I have not worked out the problem before hand, I could see where the students were going, and why, and what was causing misunderstandings. Is it fair to put my students into the same position? Should I expect them to be able to do the same? Will the benefit for them be as big as if they had enough time to think about the problem themselves? Why the title above? If teachers have a tendency to assign problems they have not worked out beforehand (I've been guilty of that) then this could potentially show them dangers in doing so. Is that a valuable lesson? On the other hand, if they see the movie first then they loose the perspective of the student trying to solve the problem for themselves. A solution is thrown at them and will they try to come up with something different from what they've already seen? What say you?
P.S. Jonathan, you still didn't tell me why you hate teaching geometry :)
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I prefer algebra to geometry. Frankly, I like arithmetic more than trig. I like working with coordinates. I don't like logs.
I do turn virtue into vice. I share my feelings with my students (well, some of my feelings) and invite them to establish preferences within mathematics.
In the same vein, when a kid finds an approach, a method of solution, a different algorithm, or even a variation on an algorithm, I name it for the kid: "Janna's method" "Bill's approach" "Chris' way".
Ownership is a big deal. Being able to like some topics and not others, that is related.
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