Awful, Awful Math Problems

     I had a student approach me after class this week. He said there was a problem he was asked in a math class a long time ago that he'd never been able to solve, and it had stuck with him. It's a classic textbook problem:

     "You're at the zoo and look into the arctic exhibit. You see that there are 18 legs and 6 heads. How many polar bears and penguins are in the exhibit?"

     This is one of the dumbest possible problems. It's just so stupid. If you are looking in the exhibit, why wouldn't you just count the animals instead of their legs and heads? If you can see their heads, you can see what kind of animals they are! And why are the polar bears and penguins together in the first place? They live as far apart as possible on the earth. Not to mention that those polar bears might try to eat those penguins (we don't know, BECAUSE THEY DON'T LIVE WITH EACH OTHER). What a crappy zoo! Why am I at that zoo?! I hope I didn't pay to go to that zoo.

     If you were to give this problem to a young child, like an elementary school student, they would ask all of those questions I listed above. If you gave it to a high school student, they would sigh and try to get through the problem. At some point along the way those high school students were conditioned to accept these dumb parameters, where logic is thrown out so we can practice using logic. Is it any wonder a lot of students hate math? They are asked to pointless, not-remotely-applicable things like this all the time!!

    The problem is supposed to be solved like this:
     x = # of polar bears, y = # of penguins

     4x + 2y = 18    (equation for legs, 4 per bear and 2 per penguin)
     x + y = 6          (equation for heads, 1 per bear 1 per penguin, ideally)

     And then you solve using substitution or elimination/combination (there end up being 3 of each, who does that in a zoo?!).  Substitution and elimination are worth learning and practicing. This problem (and almost all the problems that come with this topic) are not worth doing. There aren't a lot of simple, entry level problems that use these ideas in mathematics. These ideas are useful in chemistry and city planning and other areas, but they are fairly complicated to start.

     This guy talks about how awful math problems and textbooks can be (his name is Dan Meyer and he teaches in Santa Cruz), and everything he says is legitimate. I am looking for problems in real life when I might potentially use systems of equations, but haven't found any. I'll work at it, and if you know of any, please send them my way. (grant.gilchrist@gmail.com)