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Re: [Phys-L] bathwater +- baby (invert and multiply)



John Denker wrote:
<<<
The idea of "invert and multiply" is not a dirty trick. If you want to
call it a trick, that's OK, but it is about the most un-dirty trick I
can imagine. It is only half a step removed from the axiomatic
definitions of "division" and "inverse".

This does not change the main point of the argument, insofar as the
teachers are learning the trick in a dirty way, without seeing its
connection to the axioms of arithmetic ... but we need to see that as a
problem with how the trick is taught and learned, not as a problem with
the trick itself.

Please let's rescue this baby from the bathwater.


Agreed. The method is not in and of itself a mindless trick. My point
is that there are many different ways of dividing fractions. Memorizing
one, without knowing why it works and simply using it to bypass any
understanding of what the division means, is to use it as a trick. I
simply used this particular "trick" as an example because many, many
students use it in just that way (all of my students know about "invert
and multiply" but many do not realize that 1/(1/2) is equal to 2).

In the same way, the kinematic equations are not in and of themselves
mindless tricks. It is just that many, many students use them in just
that way.

One solution is to provide the "tricks" but, at the same time, teach
them to understand the basic idea of where the tricks come from and why.

I do not think this works for many students, as they will continue to
ignore anything other than the "tricks". A lot of students are really
good at "faking it".

So, I guess I am asking whether a better solution would be to simply
remove the "tricks" from the student's arsenal. Yes, teach them how to
solve problems without the tricks. But don't provide students with
anything that could be potentially used as "tricks."

Robert A. Cohen, Department of Physics, East Stroudsburg University
570.422.3428 rcohen@esu.edu http://www.esu.edu/~bbq