What's the deal with fractions? Say it like Seinfeld and it's kind of funny. Say it exasperated while shaking your head, as I usually do after class, and it's not really funny at all. Really? What's the deal with fractions? It's one of the things I'll never understand as a teacher. Let me explain, I've broken down things students do into two categories: things I understand and things I'll never understand. As you can probably expect, that first category grows ever smaller while the second increases without bound. Don't misunderstand me though, I'm not completely unreasonable, there's plenty in that first column. For example, I can totally understand why a student would have trouble with logarithms the first time they see them; after all they require a complete backwards thinking that we haven't quite felt since learning that division was the opposite of multiplication (which by the time you hit logs was a long long time before). There are plenty more, keeping integration rules straight, dealing with Z mod 2 the first time and learning that 1+1=0 there and so on. Though as time goes on I start to wonder if I'll ever be able to stop adding things to this second category. Things I'll never understand include: How can a student solve an equation with xs but give them the same equation with zs then they're lost? Why does a student, who made it all the way to calculus, need their calculator to find 5-0? And of course, fractions, fractions blow minds, and I'll never understand why.
