Subject: [MATHEDCC] Comment on David Beach
>
Thanks for raising this question again. We discussed it on this list some
Let me try now.
Yes, many students are slavishly dependent on the calculator; and yes, this
I have known students, not many these days but more commonly some years
It seems to me that the problem here is not which tool the students learn
(Let me detour into a science-fiction scenario to make the point. In the
A real exploration of the number system and its relation to or
A simple example: Why require students to memorize 6 + 7 is 13? Why not
As for the major algorithms: There is nothing sacred about them; many
Yes, the algorithms provide some ground for teaching -- provided the
The problem, fellow teachers, is not the tools students have at their
Road's in front o' me,
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This archive was generated by hypermail 2b28
: Mon Jan 31 2000 - 16:22:12 EST
From: Dr. Frank Pecchioni (fpecchio@pop.jcc.uky.edu)
Date: Mon Jan 31 2000 - 15:27:18 EST
>I totally disagree with the idea of introducing calculators at lower and
>lower grades. The result of this for the students I see is an ability to
>conceptually understand how to solve an equation, but an inability to do
>simple equations quickly because they are slaved to the machine and cannot
>seem to think without them.
>
time ago, and I wanted to address it, but just was not ready.
is a bad thing.
ago, who were slavishly dependent on the hand-calculation algorithms. They
had no more understanding of or appreciation for what they were doing than
the calculator-bound students of today. When challenged to defend an
answer as reasonable, for instance, they would crank out the algorithm
again. (Quis custodet custodes?)
to use. The problem is, they have been taught to use the tool -- and
nothing else.
near future, we may implant co-processors at the base of every child's
skull. Perhaps we will do this at a very early age, even before they learn
to talk. They will all be able to do quite complex computations 'in their
heads'; all they will have to do is think the question and the answer will
come to them. Will there be no work left for math teachers? I don't think
so.)
mainfestation in the physical world would leave the students familiar with
numbers and their properties, including those that show up in calculation.
encourage them to see 6 as two three's, one of which can go with seven to
make 10 and the other can stay in the one's place -- or see 7 as 3 and 4,
with the 4 joining 6 to make 10. Of course, there is some memory involved
here, but it is brought in with a web of relations that make the whole
collection of mathematical facts more memorable.
others have been used in the past and there is even some variation among
the ones taught today. If they are taught as "do this, then do that"
without any reasoning involved, they will provide no more insight than
"push this button, then push that one."
students understand how they work, they carry their own clues about when to
use them. But calculators also provide some ground for teaching -- "Watch
the display as you enter the second operation; sometimes it changes
immediately, and sometimes it doesn't. What do you think is happening?"
disposal. The problem is, we have not taught them to _use_ those tools to
their full extent.
Nothin' to do but walk.
Langston Hughes
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