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Re: Multiple variable reasoning (Was: Appropriate for Gen Phys? was: comprehending electric/magneticinteractions)



As far as I know there is little evidence that conventional teaching of
either proofs or logic improves student reasoning ability. Indeed there
is evidence that courses in logic only improve student ability to use
the terms, but their ability to actually use logic does not improve.
The statement used to justify the need for proofs was an opinion. Can
anyone cite actual research that shows that teaching proofs actually
increases student thinking ability?

I know that my students have been exposed to proofs, but they
particularize this memorized skill to math and carry it no further.

One problem that physics has is the load of preconceptions that students
have. When asked to make judgments using a formal model they come up
with arguments involving their preconceptions, and not the model in
question. One of the ways that actually works in getting students to
drop their preconceptions and consider other evidence is through the use
of the physically surprising result which refutes their reasoning. This
is consistent with Piagetian experiments, and has an interesting
connection to recent psychological evidence.

The memory is not immutable. When you recall something, you end up
storing it back into your memory and in the process it is changed. When
students are forced to come up with their own ideas and then are
confronted by a powerful physical example, the preconception is then
stored back in changed form. Essentially you can "brainwash" students,
but in a pedagogically sound fashion.

If you doubt the efficacy of teaching students to think, look at the
papers and books by Shayer and Adey. The start with simple physical
things like conservation of mass (weight), control of variables,
proportional reasoning, combinatorial reasoning, ... and end up with
various formal models. Students show dramatic gains in science, math,
and English. Even more interesting is the work of Reuven Feuerstein who
uses puzzles to teach students various thinking strategies. Although
these bear little resemblance to conventional academic topics, students
show a dramatic increase in IQ and in ability to do school work.

Now once students have acquired these elements of reasoning, perhaps
formal math proofs may have some value. But until this is done formal
math proofs have no relevance for their education, and are useless and
probably destructive exercises.

John M. Clement
Houston, TX


On Fri, 4 Jul 2003, John Clement wrote:

Please notice that along with my comment I gave a specific example.
The
particular lesson is one where they are given a specific statement
and
then are asked to apply it to a variety of situations. One of the
difficulties they have is that they use other information instead of
the
given information.


__________________________________________________snip__________________
__
___
While I agree with the "difficulty" I disagree with John's
assessment of the source of the "difficulty".
The inability of students to apply lessons learned in one
situation to other situations is, IMO, closely related to their lack
of
understanding of the nature of proof in mathematics. Further, the
recommended curricula for K-12 seems to make little attempt to teach
this. If you haven't looked at high school math texts in a few
decades,
you're in for a treat.
On April 26 (or thereabouts) I posted a comment from a math
educator who puts the blame on pressure from us "users" of math
teaching. Here is the quote:

-----------begin quote
In practice, at the lower-division college level, I would
say (from my experience) that there is little emphasis
on proof in such courses as calculus and differential
equations that are primarily service courses. Math.
depts. generally regret this, but there is a push from
engineering and science depts. to have math. depts. teach
the students to learn to apply formulas and solve problems.
However, the situation is quite different for upper-division
math courses, which are taken mainly by math majors.
Abstract algebra, advanced calculus, and real analysis
(amongst others) require students to prove lots of theorems,
and students' competence is judged primarily by their
ability to prove theorems on their own. Little emphasis is placed
upon students' regurgitating theorems from textbooks or lectures.

______________________________end quote

As far as I am concerned, this quote is a smoking-gun example
of
grotesque miscommunication.


Regards,
Jack










"Don't push the river, it flows by itself"
Frederick Perls