>Kent Luteman wrote: ><<The lecture is still the most effecient way to impart "certain kinds" of >knowlege to a large group of students. >> > >Kent has brought up, for me, an important issue with the words: "'certain >kinds' of knowledge" I can only think of one type of mathematical knowledge >that is best conveyed via telling and that is the terminology that is in >common usage for communicating with others about certain conceptual >understandings. Can anyone please tell me other kinds of mathematical >knowledge that are best transmitted by telling as opposed to constructing? > I have a hard time understanding how students will learn to think up their own proofs without a good bit of teacher directed discussion (lectures). I still think we owe it to our students to teach them something about proof and its role in mathematics. I also think "lecturing" as a good way for me to share with students the special knowledge I have that they don't, particularly the ability to solve problems that are original. I do believe that students will only become problem solvers if they are given the opprotunity to solve many interesting problems, but they also need guidance and that is the sort of thing I can do better than any of my students, because I am a better problem solver and becuase I have thought about the metacognative part of it, while they just sort of do it.
I would say proof and problem solving are two places where my explanations make a difference in student's leanring. It goes without saying, I hope, that they will need to do some original work in these areas before they will improve.
Just a few thoughts to add fuel to a roaring fire.
>--I just thought of another----historical perspectives that might add to the >student's appreciation of the development of a mathematical idea? > > >Lucille > > > >Lucille L. Peterson >Math Leadership Program >Bank Street Graduate School of Education Tel: 212-875-4665 >610 West 112th Street Fax: 212-875-4753 >New York, NY 10025 E-mail: firstname.lastname@example.org > > John Benson Evanston Township High School 715 South Boulevard Evanston Illinois 60204 Evanston IL 60202-2907 (708) 492-5848 (708) 492-5848