Well, I'm gonna write a sequel: Why Johnny can't do math.
And the reason will be, Johnny can't read.
I've been reading with interest some of the wonderful posts here that were
spawned with the thread started a few days ago. Vern, Martha, and several
others (sorry, I don't remember all the names) have made very good points
about students seeming lack of ability and desire to do any critical
thinking. And Martha mentioned that the problem may even get worse as the
level of math increases.
Permit me to give another anecdotal stroy to support this. I'm teaching a
Calc I class. We are presently doing optimization problems. If the
students are given an equation they can (fairly well) find maxes, mins and
points of inflection and distinguish between them (algebraically and
graphically). But understanding what they mean with respect to a "real
world problem" is a completely different story. This class is having more
trouble than any other I have ever taught in finding the proper equation to
model the problem.
And today, one problem completely befuddled them. A standard max/min
problem: How long a pipe can be carroed down a hall that has a right angle
in it. I told them to do it for homework. (We had spent two days on
applications problems in class.) One student asked me to work it today. I
asked for help and no one had a clue. They saw the diagram in the book,
showing the pipe touching both outside walls of the hall and the inside
corner. They knew the length of pipe was a funciton of theta. But, the
problem asked to find the maximum lentgth of pipe. So, they wanted to find
the length of pipe as a function of theta and then find the value of theta
that maximized the length. When I showed them that theta equalling 90
degrees or zero degrees the maximum length for the pipe was infinite, they
thought we had solved the problem and that it was a pretty stupid problem.
When I asked them to read the problem again and explain what was wrong with
our thinking, they couldn't.
I honestly believe the their problem was more a reading comprehension
problem than a mathematical comprehension problem. Not a single person in
the class could explain to me what the problem was actaully asking. Even
when I asked them if they had ever tried to move a piece of furniture (or a
ladder or a bed frame) out of a room into a hall could they see this was
that type of problem, they had difficulty seeing it.
We worked the problem, and they never really understood that the minimum
vlaue of the length of the pipe was the maximum length of pipe that could be
carried down the hall and turn the corner.
I've been using this type of problem for 15 years and don't ever remember
this much of a struggle trying to explain it before. I'm convinced the
problem is primarily a reading comprehension problem and also a lack of
desire to try and understand the problem. The problem said find the maximum
length, so we had to find a relatvie maximum. Simple.
Bret Taylor "It matters not the subject taught,
Lake-Sumter Community College nor all the books on all the shelves.
Leesburg, FL What matters more, yes most of all,
John 3:3^3+3 is what the teachers are themselves."
John Wooden
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