Thursday, May 05, 2005

From the Final Exam

Going back over the exams to exerpt the amusing answers, they weren't as funny as I remember them being. Sure there were the answers to the financial questions that were off by orders of magnitude, but that is more sad than funny. And their complete inability to work with fractions, well, we've already covered that ground. (One glass is half full of grape juice and another glass twice its size is one-quarter full of grape juice. Both glasses are filled with water and the contents mixed in a third container. What part of the mixture is grape juice? My students appeared to get their answers from a random fraction generator.)

One amusing answer was in response to:
Name one mathematican mentioned in the textbook. What is this person known for?
Answer: Steve Fisk came up with the art gallery theorem while on a bus with chickens on top in Afghanistan.

Anticipating my students' misconceptions, I constructed some very nice questions. In one I asked:
When a piece of toast with peanut butter falls on the floor, it could land either peanut butter side up or bread side up. How would you determine the probability that it would fall peanut butter side up?
In unintented irony (as they could get the question right or they could get the question wrong), about half the class recognized that just because there are two options doesn't mean that the probability must be 1/2. If they watched more television they would have known that they had to carry out an experiment.

Also keenly aware that the calculator trumps all and if their calculators told them to jump off a bridge that they WOULD do it, I got them on the rational vs. irrational question. Asked to determine whether the number 2/49 is rational or irrational, most students opted for "irrational," as the decimal does not repeat on their calculator display. Also when asked to find the remainder when 50!+1 is divided by 7, most of them reported it to be 4.3^63. Unfortunately, their calculators did not help them at determining whether or not 247 is a prime number. (Noted one student: "Yes, it is not the sum or cannot be broken down into a list of natural numbers.")

[Calculator aside: When exponentiating, they will write the ^ symbol on their papers next to the exponent.]