> >When you say things go a lot better if you have students do little projects >in which they are forced to grapple with situations underlying difficult >concepts *before* the concepts are defined, does this mean you have tried >teaching these same concepts without having students do little projects >first? If so....and you find that spending the time on the projects works >better....then without a doubt you should continue using these little >projects. If doing these projects prior to introducing the concept forces >you to teach only 3/4 the curriculum due to the time the projects require, >would that influence your decision on continuing these projects? > >Take Care Harvey Becker
You've set up a false dichotomy, Harvey.
I have taught the course both ways. Before we did the little projects at least half of the students did lousy on complicated ideas (stuff like lim sup and lim inf for those who learned & remember college analysis) and proofs (getting straight what the hypothesis was, what they were trying to prove, etc.) The first time I did the little projects the class was a real bunch of, you should excuse the expression, losers -- about 25% had flunked it previously at least once, at least half had math grades with an average below a B, only one showed any mathematical promise (in this class you expect about 1/3 of the students to be pretty good). Well we *did* cover everything I'd ever covered in the class -- as usual in my classes with at least 2 classes to spare for review for the final. Except for a few students who didn't do any work everyone got an honest B in the class; their performance was much better on average than the performance of previous classes that were better prepared.
For those who are curious about time, we spent about 20 minutes a week on little projects; classes here generally meet for 3 hours a week. So 1/9 of our time was spent on the little projects. Naturally this would vary with subject, grade, particular bunch of students, etc. But a little sure went a very long way.
You *can* have your cake and eat it too.
==================================== Judy Roitman, Mathematics Department Univ. of Kansas, Lawrence, KS 66049 firstname.lastname@example.org =====================================