William (Bill) Thomas
-----Original Message-----
From: John M. Flanigan <johnf@HAWAII.EDU>
To: Edward Laughbaum <elaughba@MATH.OHIO-STATE.EDU>
[snipped]
>Ed:
>
>I think you may be missing the point. We're not complaining about the
use
>of calculators to teach. We all do it, I assume. But when
children--we're
>talking about students who can't do basic arithmetic
calculations--are
>given calculators, they WILL (I use the capitals advisedly) use them
to
>get answers, when the goal is not to get answers, but rather to learn
HOW
>to get answers. The students have the calculators at home. They use
them
>for homework. The teacher cannot control that. In most cases, it
lessens
>their felt need to develop the mental ability to calculate--a
capability
>that is necessary to compete successfully in higher math and science
>classes.
>
I whole heartedly agree that the potential for calculator misuse
exists, not only at the elementary level, but at all levels of
mathematic instruction. I have seen several anecdotes to support that
cited on the list. Perhaps an anecdote showing how calculators can be
used for good might be instructive.
Many of you are probably aware of Marilyn Burns, 2nd grade teacher in
CA. She gave her students a "real life" project dealing with
subtraction of two-digit whole numbers which necessitated borrowing.
The children where not taught the borrowing algorithm but given
calculators with which to do the calculation part of the problem
solving. After solving several such problems, the children were asked
to create an algorithm for borrowing. Several came up with the common
algorithm. Others came up with more creative ways (e.g. If subtracting
75 - 37, add 3 to the 37 to make it 40 and 3 to 75 to make it 78.)
children shared their ways but were never told to use one algorithm or
another. Subsequently students were given the usualy practice problems
and told not to use a calculator except to check their answers. There
were assessed on doing both problem sovling with and without the
calculator as well as doing skill based problems without the
calculator.
What, you may ask, was the upshsot of this? On a national test (whose
name escapes me. It may have been NAEP, SAT, or Iowa), her class
performed at the average computation level (which tends to be very
high on all these test because much time is spent on that activity.)
However, on the problem sovling portion, her class was significantly
above average. Now, the use of the calculator alone did not cause this
to happen. It was the skillful blending of calculator use in a problem
solving context that gave students more time-on-task with problem
sovling that made them better.
This brings me to a point that has been made, and should continue to
be made, on this list. The calculator does not itself possess virtue
either to teach or to hinder teaching. It is a tool that knowledgeable
teachers can use to promote students learning not only at the lowest
levels of Bloom's taxonomy but at the synthesis and evaluation levels
as well.
[snipped]
William (Bill) Thomas
Univ. of Toledo Community and Technical College
Toledo, OH 43606-3390
(Voice) 419.530.3338, (Fax) 419.530.3194
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