>It just occured to me that when I teach the junior-level mathematics >analysis course here at the University of Kansas things go a lot better if >I have students do little projects in which they are forced to grapple with >situations underlying difficult concepts *before* the concepts are defined >-- after all, that's where the concepts come from.
>I suspect that this is true to some extent at every level.
>This is not saying that we should always go from s. to g.; just that >sometimes it really works.
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?