Monday, February 01, 2010

Is That All?

The number one problem that my gen-ed students have is that they have absolutely no mathematical common sense. These are the students with the lowest placement scores, the ones who do not qualify to take any of our algebra-based courses. These students have no expectation that math should make sense. For them math is much like conjugating English verbs. Irregular verbs.

One of the problems on the review sheet was about three-digit codes for a photocopier. It asked how many three-digit codes were possible (leading zeros are OK). Many students in the class were unable to solve this problem. They tried to find another problem that we'd done so that they could model their responses after. They were unable to reason out that there were 1000 codes ranging from 000 to 999.

Another problem was to show that if p is an odd prime, then p + 1 is not a prime number. For this one, they tried to adapt the proof that there are infinitely many prime numbers instead of trying to reason it through and recognize that even numbers (other than 2) are not prime.

Every time they ask a question, they are shocked at how simple the problem is. They are consistently amazed to find out that math is not that hard.