Subject: RE: [MATHEDCC] calculator misuse, etc.
From: Ginny Keen (gkeen@bgnet.bgsu.edu)
Date: Wed Feb 09 2000 - 17:47:57 EST
I don't think teachers should carry the weight of the burden of guilt. In
fact, many teachers have no idea how to teach WHEN it's appropriate to use
your head or when it is reasonable to use a calculator. This isn't because
they are intentionally ignoring it. Rather, they (the teachers) have
little experience developing their own mathematical thinking using their
heads OR their calculators. So, wouldn't it be better to develop
opportunities for teachers and their students to gain this understanding?
Those of us who have any contact with (prospective) K-12 teachers (and that
is EVERY post-secondary instructor) should think of ways to incorporate
this into their classroom experiences.
But then we run into the situation that the K-12 teachers are not the only
ones who lack experience thinking about appropriate use of calculating
devices (including the brain). It takes time and energy to develop these
kinds of opportunities - and many mathematics instructors fail to see that
this is their responsibility, too. I would challenge each of us to spend a
little time thinking through this and perhaps suggesting some "good
moments" or situations that you see as instructive.
For example, there is the exercise (usually for a lower grade level) of
dividing the class into two sides, half with calculators. Assign them all
a set of simple addition and subtraction problems to complete. The
calculator kids MUST enter all problems into the calculator before putting
down their answer. When time is called, see which side was able to
complete more problems more accurately.
When my son was just exitting kindergarten, we went on a trip. The
neighbor had given him a calculator to "play" with on the trip. I wondered
to myself just what she thought he'd do with it. He only got to take a
limited number of things along in the car and this included, by his choice,
the calculator. At a point well into our drive, he asked me, "Mom, what is
1-0-0-0-0?" I told him 10,000. He then said, quite proudly, "Do you know
that 10,000 + 10,000 is 20,000, just like 1 + 1 = 2?" I was amazed and
thought about how the retired elementary teacher neighbor was wiser than
I'd given her credit for. He continued to find patterns and see sensible
answers, that he predicted mentally, as he played. Now, he didn't just do
this with no experience. I often asked him questions to compute using
mental math or estimation. This experience of doing those with numbers
freed him to use the calculator in a more investigative way.
On a different point, I have a difficult time with the statement, "One
change I would make is to delete the words "reasonably bright" from your
last paragraph," made in response to a comment about a student who had
difficulty doing an easy (to those of use who have good mathematical
thinking developed) percent problem. If you don't think that your students
are all reasonably bright, perhaps you need to think about on what basis
you are making that assumption. Is not having learned something you have
no trouble with indicative of poor intellect?
There is too often the sense in the general public that people who "catch
on" to mathematics quickly form some sort of elite, but odd group. Some
mathematicians seem to perpetuate this as a way of feeling above the common
folk. I hope that we'll try to discourage that perception so that all
people see themselves as capable of doing the mathematics required by any
literate human being.
Ginny
>My thought is that what they (k-12 ed) have accomplished is to help create
>students who can't think and who believe god is machine and machine is god,
>who can't estimate, can't measure, and cannot think abstractly about
>mathematics.
>
>The idea to keep pushing calculators down to lower and lower grades is one
>of the largest educational frauds ever perpertrated upon the american
>public.
>
>DavidBeach
>Labette Community College
Dr. Virginia L. Keen
Assistant Professor, Division of Teaching and Learning
Mailing Address: 529 Education, EDTL
BGSU
Bowling Green, OH 43403
Campus Address: 133/135 Life Sciences Bdlg.
Office Phone: 419.372.7363
Office Fax: 419.372.7291
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