🚀 go-pugleaf

Brian,

You said:

-> I think homework is overrated to begin with.  When I was a high
-> school student, most of my math homework involved solving 20
-> equations, all basically the same but with different numbers.  How
-> deadening!

I agree with that. If homework is going to be something like that, then
might as well skip it. In this discussion about homework, I am assuming
that it is slightly more meaningful then that.

-> *Start* the day with in-class work.  A couple of problems reviewing
-> yesterday's ideas, and a bunch of problems that introduce new ideas.
-> Ideally, they should be "guided discovery" problems that lead kids to
-> invent today's new topic.  Let them work in groups.  *Then* give the
-> lecture.

You know, this is EXACTLY what I did in my geometry class yesterday. I
wanted to cover how one proves that a quadrilateral is a parallelogram.
So I had a handout I had prepared where I gave them a quad. with both
pairs of opposite sides congruent and asked if they could prove it was a
parallelogram, etc... (there were two other set ups, three in all. Two
could be proved parallelograms, one could not).

Anyway, I put them in groups of four and said they had 20 min. to decide
if they could figure out whether they had to be parallelograms or not.
They didn't have to write out formal proofs. Just a couple of sentences
about why they knew it had to be a parallelogram (if indeed it *did*
have to be one). After 20 min. we went back to our traditional seating
arrangement and I spent about 5 or 10 min. summarizing the lesson with
the help of students explaining how they knew it was a parallelogram. I
hope the lesson was clear to the students. It seemed a lot more
enjoyable than my standing in front of the class listing the 5 ways to
prove a parallelogram. I guess I'll find out next week when we correct
homework. (NOT 20 equations with different numbers) and there'll
probably be a quiz.

You are right that even the students who didn't figure the whole thing
out themselves seemed to have a better idea of what was going on by
having the group work first and the lecture second.

It was funny, but the kids thought that my slipping in one that
_couldn't_ be proved to be a parallelogram was a trick. Of course, I
just wanted to point out that one cannot in every case prove that a
quad. is a parallelogram.

Caution: I did do this with an honors group. A non-honors class would
probably require an entire period to work on a project like this, and
would need a lot more detailed handout than the one I gave these kids.
But it is what we should be doing with out students. Even with
non-honors kids, simply enumerating the ways to prove a quad. is a
parallelogram is quite dull.

-> *Then* give the lecture.  The neat part is that even kids who didn't
-> manage to solve the new problems, if they gave it a solid effort,
-> will understand the lecture much better than if they heard it cold.

EXACTLY!

Sheila
coming to you from Diamond Bar, CA (in Los Angeles County)
                                                                   

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