Now, this was not a carefully controlled experiment, but it does suggest an
interesting hypothesis: that the "point of diminishing returns" for class
time spent on these type of problems is reached very quickly. Those that
will get it, will get it after one or two examples; those that don't, will
most likely not become proficient even if you spend a month on it. If true,
this has significant implications for the way we conduct our classes.
I have a second hypothesis that the difference between the groups correlates
closely with *general* reading comprehension skills (as opposed to the
specific tactics that we teach for word problems), but have not tested this
yet. I think these hypotheses would make a good dissertation topic for some
erstwhile grad student in education...
Chuck Lindsey, Ph.D. clindsey@fgcu.edu
Director of General Education
Associate Professor and Program Leader, Mathematics
Florida Gulf Coast University
10501 FGCU Blvd South
Fort Myers, FL 33965-6565
Phone: (941) 590-7168 FAX: (941) 590-7200
http://itech.fgcu.edu/faculty/clindsey
> -----Original Message-----
> From: Bret Taylor [SMTP:bret@IAG.NET]
> Sent: Monday, October 25, 1999 9:42 PM
> To: mathedcc@archives.math.utk.edu
> Subject: [MATHEDCC] Why Johnny can't read.
>
> Anybody remember that book? Popular about 25 years ago.
>
> 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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