Subject: Re: [MATHEDCC] Comment on David Beach
I agree, and would add to "The problem is, we have not taught them to _use_
At 04:27 PM 1/31/00 -0400, Dr. Frank Pecchioni wrote:
Office phone: 419.372.7363 Fax: 419.372.7291
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: Tue Feb 01 2000 - 11:17:45 EST
From: Ginny Keen (gkeen@bgnet.bgsu.edu)
Date: Tue Feb 01 2000 - 11:17:30 EST
those tools to their full extent," that we also have not given them
experiences with determining which tool is most reasonable to use for the
task at hand. Students need to be able to decide whether calculation,
calculator, mental math, etc. is called for.
Ginny
>
>>
>>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.
>>
>
>Thanks for raising this question again. We discussed it on this list some
>time ago, and I wanted to address it, but just was not ready.
>
>Let me try now.
>
>Yes, many students are slavishly dependent on the calculator; and yes, this
>is a bad thing.
>
>I have known students, not many these days but more commonly some years
>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?)
>
>It seems to me that the problem here is not which tool the students learn
>to use. The problem is, they have been taught to use the tool -- and
>nothing else.
>
>(Let me detour into a science-fiction scenario to make the point. In the
>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.)
>
>A real exploration of the number system and its relation to or
>mainfestation in the physical world would leave the students familiar with
>numbers and their properties, including those that show up in calculation.
>
>A simple example: Why require students to memorize 6 + 7 is 13? Why not
>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.
>
>As for the major algorithms: There is nothing sacred about them; many
>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."
>
>Yes, the algorithms provide some ground for teaching -- provided the
>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?"
>
>The problem, fellow teachers, is not the tools students have at their
>disposal. The problem is, we have not taught them to _use_ those tools to
>their full extent.
>
>Road's in front o' me,
>Nothin' to do but walk.
>Langston Hughes
>
>
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Dr. Virginia (Ginny) L. Keen
Office address: 133 Life Sciences Mailing address: 529 Education Blg.
Division of Teaching and Learning
Bowling Green State University
Bowling Green, OH 43403
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