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Topic: How technology can enhance math learning

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Subject:   RE: How technology can enhance math learning
Author: Mathman
Date: Apr 29 2005
On Apr 29 2005, Silver wrote:
>If we had NOT used calculators, exploring
> this simple science concept would have been VERY difficult for my
> fourth-grade mathemeticians.

Sorry, but I can't agree.

It need not be more difficult.  Would it not be easier if they rounded their
measurement of distance, which needs be done only once, counted the seconds, and
then performed a normal division using arithmetic to a specified number of
decimal places?  [They can divide?] They could have some fun devising their own
units by dividing the distance into any number of equal smaller units, and count
even "blinks" instead of seconds.  They could do their ordinary arithmetic and
average group results [usually results in individual errors not being effective
in varying the true value.]  Then they could do a graph, but they would need
some way to measure slope to take that into account. ...

Are you certain that S = D/T is appropriate when the marble *accelerates* down
the slope?  They would need to know that it is an average speed that they are
calculating, and what relationship would they get from their calculations other
than the fact that the average speed increased; a fact that can be stated by
simple observation without measurement?  Also, are they only concerned with the
fact that the average speed will increase as the slope increases?  That is; just
what is the lesson, aside from an excuse to use a calculator?  I still recall
the public school teacher so long ago not believing me when I divided a circle
into exactly six parts using compasses; she had "Pi" in mind.  I say that in
order to indicate that concepts taught at an early age stick with them, and it
becomes difficult to convince them otherwise later on if necessary, calculator
or no calculator.


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