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Topic: Word Problems-a view from a student
Replies: 19   Last Post: Dec 16, 1995 5:38 PM

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Lou Talman

Posts: 876
Registered: 12/3/04
Re: Word Problems-a view from a student
Posted: Dec 4, 1995 11:33 AM
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Marc Vidulich recently posted a paragraph or two (written by
a former student of his who is now a freshman at USC) about
word problems.

We should observe that this student is unusually articulate,
even for a college freshman. At the risk of being flamed for
bringing up standardized tests, I would like to point out
that just about everyone I've ever met who was successful at
mathematics had rather high verbal scores (frequently even
higher than their math scores) on the SAT or similar exams.
My own experience in having students write journals in
college mathematics courses at the freshman/sophomore level
suggests that there is a high correlation between verbal
strength and the ability to succeed at mathematics. We
probably should not be surprised to find that students who
solve word problems well also handle semantics well; after
all, the troublesome part of most word problems for most
students is the essentially *semantic* transformation from
natural language to formal language.

Someone recently posted some remarks (which I seem to have
deleted in an uncharacteristic bout of housecleaning)
lamenting deficiencies in students' formal training in
grammar. I think that's another piece--the syntactic
piece--of the puzzle, though my memory of the post was that I
thought it was a little off the mark. I think that the
connection that author seemed to perceive between grammar and
linguistic skills wasn't the important one. Having taught
both algebra and programming, I'd say that the important
connection is in a student's ability to handle syntax; the
student who makes consistent troublesome syntactic errors in
programming is the same student who mishandles algebraic
transformation consistently. (Other people have remarked on
this phenomenon, too--especially folks in the Calc-Reform
movement who've been trying to integrate computer algebra
systems with calculus.) But I think that this has little
bearing on the word-problem problem, because the word
problems we usually pose in our algebra courses involve very
little syntactic difficulty *once one has made the necessary
semantic transformation*.

These are, I am sure, only pieces of the puzzle, but
important pieces. I haven't a clue how they fit together,
nor what other pieces there may be. Where the observation
that linguistic abilities are important in mathematics takes
us, I don't know.

The big paradox here is that the students who need help the
most are seemingly the very ones who aren't articulate enough
to describe their troubles...

--Lou Talman





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