## Hammer and Nail Problem

Believe it or not, I have been at MathFest for three days and have only managed to attend four sessions (besides the one I presented in). But I talk to a lot of people and talk to a lot of the exhibitors and because MathFest is a lot more research-oriented and focuses more on upper level math, there are actually not a ton of sessions that I am interested in – although, as is always the case, the sessions I did want to go to were all scheduled for the time I was speaking. I haven’t seen Kien Lim since graduate school – I saw him walking down the street one night in Madison and recognized him. Kien and I used to be involved in some great discussions about how students learn. He invited me to his talk on the “Hammer-and-Nail Problem in Mathematics.” His talk (10 minutes) was briefly about his interest in math education and his experiences with students in Math for Elementary Ed. What he’s seen in teaching future teachers, is the same problem that I think we’ve all seen in different courses. Here are some examples that I’ve seen in math classes: After you teach algebra students how to multiply polynomials, some can suddenly no longer add polynomials and will multiply an expression like (x + 3) + (x – 4). In Calc II, I...

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