John M. Flanigan <johnf@hawaii.edu> The equation is the final arbiter.
Assistant Professor, Mathematics --Werner Heisenberg
Kapi'olani Community College The scoreboard is the final arbiter.
4303 Diamond Head Road --Bill Walton
Honolulu HI 96816 History is the final arbiter.
(808) 734-9371 --Edward Gibbon
On Mon, 25 Oct 1999, David Beach wrote:
> Mr. Kays:
>
> I do not advocate not using technology. However, we have used technology to
> replace thought. I have students who are fully aware of the processes of
> solving an equation as simple as 2(x-3)=4(x+5), but they will still take
> several minutes to solve the problem because they cannot do the simple
> additions, subtractions, multiplications, and divisions without the
> calculator. They do not recognize the equivalence between decimals and
> fractions because they were taught that the calculator would do it for them.
> They do not comprehend the true idea of a fraction and cannot work simple
> operations with them because they have always used the calculator to do it
> for them. They cannot draw a schematic and from their drawing produce a
> model or equation to solve a problem because it has always been done for
> them in the past and they often will not have the critical reading skills
> needed to solve the problem because they have never been truly asked to read
> something critically. They have trouble working with and using trigonometry
> formulas because they use the calculator to work calculations of angles that
> they could commit to memory and then never have to think about again.
> Derivation and proof are lost to them because they have never had to sit
> down, think through a process and then try to express a logical sequence of
> reasons and steps in writing. They do not realize that a few examples are
> not sufficient to prove the rule because all they have ever done is work a
> few examples on a machine. They interact with written mathematics so
> infrequently that they do not know what the symbols truly mean as they have
> not truly used them. In short they cannot think mathematically because they
> have never had to actually work it in many cases. A calculator is a truly
> valuable piece of equipment if you know what you are doing. To use the
> calculator or the computer to do calculations that should be easily
> accessible by the human mind is to use a howitzer to kill a fly. In the end
> all you know is how to fire the howitzer, whether or not you need to do so
> is matter beyond comprehension.
(Earlier posts omitted)
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