This summer, I am writing a textbook for the class. Today I wrote my first problem set, which I am sharing with you all. I would LOVE any feedback. Last year, I gave seven or eight problems on a problem set. I gave one problem set just about each week. Students would get them at the beginning of the week and they would be due at the beginning of the next. One thing they said I should do is keep it to six problems. They thought anything more was too much, especially when one or two problems are often really tough.
Last year, they wrote solutions in composition books, but this time, I would like it to be on the paper I give them so that it is more structured. If they need more paper, they can staple it to the page. The back of the page is for things they learn from other students when we go over the problems (so this should not be double-sided when copied). I should explain that we go over the solutions Exeter style, which is to say, each student picks a problem at the beginning of the class and writes the solution on the board. Then that student presents it, and anyone can chime in to explain a different solution or approach. It's awesome, and I learn more from them, perhaps, than they learn from me. There are so many times that they have found a more elegant solution than me!
Some of the problems are famous ones, but many are calendar problems from Mathematics Teacher. In each set, I try to include one geometry problem, one probability problem, one number theory problem, and then the rest are just interesting problems.
I added a reflection page at the end that I will likely change after each problem set. I think I will hand the Problem Sets out each week, separately from the text, so students can't go ahead (I have some students who would do that, I think), especially as some of it will coincide with the curriculum I will be teaching them. So, without further ado, here is the link via dropbox: Problem Set 1 and below is a picture of the first problem.
