Wednesday, June 29, 2005

Do teachers need to know math?

Joanne Jacobs writes that teachers in Virginia will be relieved of the onerous math component in Praxis I (unless they teach math in high school, I guess). She links to sample test prep questions for Praxis I. These are the type of questions that constitute an insurmountable hurdle for some teachers. If they are elementary teachers, wouldn't they still need to know some math?

While most questions look very easy, this one could be a bit of a challenge:

If Sam can do a job in 4 days that Lisa can do in 6 days and Tom can do in 2 days, how long would the job take if Sam, Lisa, and Tom worked together to complete it?
I'll post the procedure in an update. (Not that most readers need it).


Garbo said...

This item is a good test of problem solving that does not require advanced mathematical skill, and I believe all teachers should be able to break it down and solve it. The willingness and ability to do this kind of thinking is important for good scholarship in general.

However, the answer choices presented on the practice test are ridiculous and misleading. They are numbers of days to the nearest hundredth, while the numbers in the problem are given to the nearest whole day--much more realistic when talking about an actual "job," such as the one two painters are now doing on my house.

It would make some sense mathematically to leave the answer in fraction form (exact), even though it would be unrealistic in the context presented. But as soon as we convert the fraction to a decimal and round it off somewhere, we are reporting the answer to a specific degree of precision. Can we really have any idea whether the time this job will take these three workers will be closer to 1.09 or 1.23 days???

Better answer choices would be:
a) about two hours
b) about a day
c) about two days
d) about three days

This may sound like nitpicking, but in fields such as engineering it can be dangerous to believe that a quantity is known to a greater precision than it is, and this happens all the time now that computers will divide out any quotient (or give any root) to n decimal places. The reason engineers make this mistake is that that during their schooling, they have been taught to give the silly sorts of answers that appear on this test. I recognize that the Praxis is testing teachers and not engineers, but I'd hope that some of these teachers' students will be headed for technical fields.

I don't dispute the value of having some "real world" math problems in textbooks and on standardized tests, but if they are not vetted by people who understand how math is properly applied, they can do more harm than good.

IB a Math Teacher said...

These are about the worst math problems to give to kids. I hate these! It is easy to teach:

1/4 + 1/6 + 1/2 = 11/12

So "1" job would take 1/(11/12) = 12/11 days, but that is assuming that their jobs are somewhat independent of each other. If the job was mowing the lawn, as it is stated in many old textbooks, then it would probably take longer, or involve medical bills.

If they have to go this route, at least ask the question about hoses filling up a pool.

Anonymous said...

But, filling up a pool would be biased against students who lived in places where pools were uncommon!