Lots of good, interesting advice. Bowen Kerins said:
Another way to deal with speed demons is to give several problems in a row that are related and have the same answer. Speed demons may not even notice this happening, and the result is they're more likely to "look around" a little more before and after working a problem.I liked that. And it made me think about an interesting thing that happened to me today.
I'm teaching beginning algebra at a community college. My first two mastery tests are on pre-algebraic topics. There is one fraction story problem. On version 3 of the test, it goes like this...
I have a lot of books at my house, especially after all the math books I bought during my sabbatical. Right now 3/7ths of my books are math-related; 3/10ths of those are kids’ books. What fraction of my books are kids’ math books?I had marked my student's subtraction problem wrong, and was explaining to her why it would be multiplication. As I finished up, she pointed to her answer, which was the same as mine.
I said I hate marking people wrong when they have the right answer, but that this was a fluke. Subtraction doesn't solve this sort of problem. On the spot, I made up another problem, 1/2 of 1/3. Guess what.
Both answers are the same again.
Optional homework: When does this happen? ;^)
(I give my students lots of optional homework. Most of it is: "Read this cool book and write a review.")