> From: "Katherine G. Harris" <firstname.lastname@example.org> > Date: Mon, 7 Aug 95 12:05:18 EDT > Subject: re:ideal student
> Michael, thank you for your response to my question (complaint?) that > students do not seem to understand that having to work for something is > normal. (On July 30 you wrote : I would propose that one difficulty in > the issues you raise has to do with the mathematics is performed by > teachers and professors (and I use the word 'performed' advisedly). > Very few students at the K-12 level get to see mathematics done at the > board. What they see is the cleaned-up results of a canned computation > (and let's assume the case in which the instructor has actually worked > the problem out him/herself).
> I am quite sure that for the students who are not simply looking for an > excuse this is very accurate and, frankly, I had never even thought of > it. I can learn math and I think I can teach it, but I could not > create new mathematics if my degree depended on it! When I look back, > I have never seen anyone create and struggle with math since I did not > go beyond a BA level in mathematics (and my BA is in economics anyway). > > Does anyone out there have any suggestions on how to illustrate that work > is a normal and expected process and that not being able to "get it" the > first time does not indicate that the task is impossible?
You don't need to invent a new discipline in mathematics to create new math. It's easy to present "not canned" math simply by not solving the problem before you present it.
The book _Aha! Insight_ by Martin Gardener, or the two Marylin Burns books _I Hate Math_ and _Math for Smarty Pants_ both present wonderful collections of problems. Don't read the answers to some of these before sharing them with your class.
With practice it's easy to make up problems you do not know the answer to. Last school year I drew a giant's footprint on the black top, and asked students (2nd/3rd graders, in groups) to figure out how tall the giant was and how much the giant might have weighed, by comparing the footprint to their own footprints.