Those who have mentioned the disconnect between math education and
real-world reasoning are on target. Some have also mentioned the
inability to do word problems (we call them "story problems" around
here).
One of my favorite sad stories concerns a math major who dropped my
calculus-based physics course. The Math Department here does try hard
to get their students to take physics, but they are only successful with
perhaps 1 of 10 students. One math major who did enroll in physics
already had a typical year of calculus plus courses in differential
equations, multivariable calculus, discrete math. She was a junior and
had a 4.0 GPA. We were about 4 weeks into the term when she came to my
office with a "drop slip" for me to sign.
I asked her why she was dropping my course. She said, "I'm afraid I
won't get an A in this class. I know I am not dumb because I am a math
major and I have a 4-point GPA. But your class is so hard I just don't
have the time to put in the effort I need to get an A, and I don't want
to ruin my 4-point."
I said, "Well, I can't guarantee you will get an A or any other grade,
but you ought to be able to get an A in this class; or at least a B.
What do you think is the problem? For example, why aren't you getting
better grades on the problem sets?
She said, "I hate story problems. I've never been any good at story
problems. Every problem you've assigned is a story problem. Of course
you didn't have much choice with the book you chose. Did you ever
notice that story problems are the only kind of problems in this crazy
book?"
I then got her a little angry because I made the mistake of a little
chuckle as I said, "But story problems are about the only things that
matter because that's what the world is all about."
She then started giving me a list of all the things she could do. For
example, "Give me an integral and I'll solve it for you. Give me a
differential equation and some boundary conditions and I'll find the
solution."
And I understand from talking to the math profs that she could indeed do
those things reasonably well. Now... want to know the real kicker? Her
major was math education, and she is currently teaching high-school
math.
Please understand that the math profs at my institution are as
exasperated over this type of student as I am. That's why they try to
get their students to take my physics course. But their 10% success
rate at getting their majors to take physics is abysmal. Furthermore,
their majors are about 70% math education, so they just keep cranking
out more teachers who will graduate and perpetuate a system that teaches
high-school students to believe that learning math means learning all
the procedures to deal with various equations, but with a total
disconnect of how to come up with those equations and what the equations
represent.
If that is not problem enough, add to that what others have mentioned...
the average junior-high and high-school student didn't even learn the
math techniques very well, and much of what they did "learn" they forgot
by the time they got to college. When I show them the connection
between the math they "already learned" and the "real world" it often
seems brand new to them. A few remark, "I remember seeing something
like this before, but I never knew what it was good for." But most
don't even remember or admit they have seen it before.
That brings me to another common professor-student discussion. At least
once a year a struggling student is in my office complaining, "This is
so hard. I've never seen any of this before. I don't understand any of
this stuff."
To which I reply, "Well that means you are getting your money's worth.
You wouldn't want to pay all that tuition just to have me teach you
stuff you already know, would you?" Unfortunately that is exactly what
many of them do want.
Michael D. Edmiston, Ph.D.
Professor of Physics and Chemistry
Bluffton University
Bluffton, OH 45817
(419)-358-3270
edmiston@bluffton.edu
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