Burden of Proof

For me the proof in mathematics is nothing but a simple transparent argument for why something should be true. Students tend to struggle with proofs - both because a large emphasis is placed on clarity and order and also because there is seldom a single right answer. There are acceptable proofs, which proceed somewhat haphazardly but address the necessary points, and there are elegant proofs which illuminate the nature of the problem being addressed.

This semester I designed my own class, MCS 471 -Numerical Analysis. Alot of decisions were invloved, including how to grade, what to present, and how to present it. I made some mistakes, but overall I think it has been a good class. Recently I made a mistake during lecture, something I will certainly do from time to time, and as a result 90% of my students missed this question on a quiz. I related the story of the mistake to some colleagues this Friday and recieved a host of contradictory responses. Ranging from "Professors don't make mistakes, they just write typo's" to "My students never seem to notice" - I don't think I got any real advice. In light of my recent mistake I found myself thinking alot about whether I was doing a good job teaching. After some reflection, I decided that what I want to improve on as a teacher is basically what I want my students to improve on in their proofs.

I want my presentation to be clear and logical, just like their proofs. I would like it to be neat on the board, with an obvious order (similarly their proofs on the page.) The analogy breaks down if I try to list everything a teacher (or a proof ) should be. Both however, should be honest, and correct. Last week I failed on the later, so on Monday I will have to eat some crow with regard to the former.