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.
> ----------
> From: Vern Kays[SMTP:vkays@RICHLAND.CC.IL.US]
> Reply To: Vern Kays
> Sent: Monday, October 25, 1999 12:50 PM
> To: David Beach; 'mathedcc@archives.math.utk.edu'
> Subject: Re: [MATHEDCC] Re:What's wrong with education anyway?
>
> I agree with every thing except the Pencil and paper limitation. There is
> much more to be learned if taught appropriately with appropriate
> technology. There needs to be both components. Just because we are near
> the next 1000 years does not mean going back to the mathematics of the
> 1700's
>
> Vern Kays
>
> At 10:37 AM 10/25/1999 -0500, David Beach wrote:
> >Bottom line is this folks. When a system is wrong, there needs to be a
> >"reset" button.
> >
> >The disease is the fact that we have let attention spans decline in our
> >society. We are all addicts of "brain candy". Those fast-paced programs
> >that we can tune out while at the same time watching them. The 15-second
> >sound bites that we let pass for news. The brainless, non-educational
> video
> >games we let our children play (using them as a baby sitter) when we
> could
> >be inducing them to be out doing something, reading something, learning
> >something.
> >
> >We have produced a generation of students who are merely reacting the way
> >they have been taught to act by the society in which they live. The
> >chronological age of students is the same, but their world of experiences
> >are certainly different. The problems that we face in any academic field
> >still require that a person or group of persons get together, concentrate
> on
> >the problem at hand, and then work together for a solution. What we've
> done
> >is produce a bunch of people to not concentrate and to not be able to
> break
> >the problems they face down into parts that they can analyze and handle.
> >
> >The best learning in math still comes down to a student, a piece of
> paper, a
> >pencil and a brain in full concentration upon the concepts that they are
> >trying to apply to solve the problem.
> >
> >It's not that students can't learn. It's that we have been extremely
> >successful in teaching them the wrong things.
> >
> >David Beach
> >
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