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Topic: Four Reactions to the Galertner - Re: Calculators
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Jerry P. Becker

Posts: 16,576
Registered: 12/3/04
Four Reactions to the Galertner - Re: Calculators
Posted: Oct 5, 1998 6:54 PM
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First response:

Just a thought or two on this whole calculator business. Mainly, I would
like to point to the calculator discussion as a good example of the harmful
effects of the so-called math wars. One person noted the irresponsible
hyperbole and pure misrepresentation in the anti-calculator article. I
agree that this was despicable and has no place in what should be an
intelligently conducted discussion. But the worst part about it is that
when someone uses this kind of attack, they almost completely destroy the
hope that their valid points might see the light of day. It takes much
more discipline than the average reader uses to look to see if there is
anything useful in something that is otherwise filled with reactionary,
inflammatory, and unjustified baloney.

I think there is a critical and valid issue being raised, or maybe just
alluded to, and that is that "inappropriate" use of calculators could
possibly be detrimental to learning. Of course, much of the whole debate
is really about defining what "appropriate use" is, but well-intentioned
reformers often fail to think about questions like "what if this curriculum
gets into the hands of a teacher who doesn't understand math, or doesn't
want to think, or is just coasting to retirement?". Whether we like the
idea or not, it is quite possible that children will be better served by a
curriculum that many of us would see as sickenly rote-based and boring, if
the teacher presenting it doesn't understand math very well. We often
dismiss this idea without careful consideration by saying that we'll do
"teacher training" to make sure that the teachers know how to use it. But
that's not a trivial problem, given that the teacher in question may have
been "hating" math for 40 years. Are you going to turn that around in a
3-week summer program?

I'm not saying that I know the answer to any of these questions, only that
the polarizing effect of nasty, immature debate (on either side of the
conflict) tends to keep us from carefully investigating the middle ground.
Which is not guaranteed to be where the best course is--but we are
guaranteed not to see what it has to offer if we don't look.

Michael South


Second response:

I am commenting on the comments to article on calculators Jerry posted

One responder to the article said:

>I'm in complete agreement.

>My basic position, stated approximately 3 zillion times (a number not
>accessible even on the most powerful calculator) is that students should
>be given calculator licenses the same way that we give driver's licenses.
>Only students demonstrably competent in arithmetic should be allowed to
>have them.

I am not in complete agreement. I am not in complete disagreement.

It has to do with my basic philosophy of what it means to learn
mathematics. For example, I want students to understand scientific
notation. Thus I want them to understand the effect of multiplying a
power of ten on any number.

Consider 7.09 x 10^3
I could just tell them to memorize "move the decimal as many places to
the right based on the value of the exponent."

But, I would rather present it in a way that they will come to this
conclusion on their own. Thus, I see calculators as a pedagogical tool
for understanding the mathematics.

Consider the following set of problems provided by the text:

7.09 x 10^0
7.09 x 10^1
7.09 x 10^2
7.09 x 10^3
7.09 x 10^4
7.09 x 10^5

Next I have them compute each answer and list them beside each problem.

Consider the time it might take to do each calculation pencil and paper
(using no shortcuts). It is too time consuming. We usually just tell
them "the rule" and move on.

BUT, after I teach them how to use their X^y keys and their "constant"
keys and "memory" keys, they actual enjoy the challenge of mastering the
calculator and keys they heretofore could not use.


We next review their answers

7.09 x 10^0 = 7.09
7.09 x 10^1 = 70.9
7.09 x 10^2 = 709
7.09 x 10^3 = 7,090
7.09 x 10^4 = 70,900
7.09 x 10^5 = 709,000

and note how the decimal "moves" to the right with each answer. (I call
it the "vertical" pattern.) We next consider the relationship of where
the decimal was in the factor and where it moves to in each product. (I
call it the "horizontal" pattern). This horizontal pattern is discovered
by the teacher rather than decreed by the teacher. It is something the
students conclude themselves and the teacher facilitates. It is

It was all facilitated by a tool (the calculator) that made data
generation quick and easy, thus providing more time for analysis of
patterns. I would have never consider approaching this topic (and many
others) in this manner with technology to facilitate the data analysis.

Food for thought,

Bill K. kunnecke@APEX.NET


Response 3:

I agree with Tony (Ralston). This business of elementary children not using
calculators because they have to learn the basic facts is getting a lot of
flak that is unnecessary. Good teachers know that children need to learn
their basic facts for the four basic operations of mathematics. I have been
across the state of Kentucky in Sept. and last year and have never talked
with a teacher who let their elementary students use calculators to solve
basic arithmetic. Most teachers still do timed tests. However, elementary
teachers do let their students use calculators for higher order thinking
with problem solving. It is in this way that students are grasping higher
levels of thinking. Children are also being taught to estimate so they will
know if the answer the calculator gives them is a reasonable answer. If
California is having a problem with elementary students using calculators
for basic arithmetic then they need to beef up their monitoring of what is
going on in elementary classrooms, not say that the children should not be
using them at all. Maybe their teachers need to learn when it is
appropriate for elementary children to use calculators and when it is not
appropriate. My final comment is that children can not learn the basic facts
all on their own or just when they are in school. It takes parents or
someone working with them outside the classroom so they don't forget them.
How many times have we all heard a teacher say at the beginning of the year
that "this class does not know their facts. didn't they learn them last
year?" Yes teachers, most of them learned them the year before, regardless
of the grade level; however, over the summer these were not reinforced.
Therefore they have been forgotten. My suggestion is to have the students
use these basic facts at the beginning of the year in some meaningful way,
not just drill, drill, drill again and again. Doing 50 problems of the same
nature is not going to necessarily help them with their basic facts and
knowing how to use them.


From reading the Readers' Digest by David Galernter, I see no evidence of
a background in TEACHING or MATHEMATICS TEACHING by Mike McKeown & David

I feel concerned when academics generalise about how calculators are
used, after acquiring the briefest of snapshots from some classroom.

In my experience as a teacher and advisory mathematics teacher, is there
is a wealth of innovative approaches and strategies developed by
classroom teachers that engage students in rich activities. Many of
these activities create conditions where students have to confront their
understanding of mathematical concepts, and are encouraged to take risks
in a supportive environment. I sense that Mike McKeown & David Gelernter
have a very Newtionian construct of what mathematics and mathematics
learning is.

Many Australian researchers and teachers (Paul Swan & Alistair McIntosh,
both from Edith Cowan University in Western Australia) have captured many
wonderful ideas from the classroom, that involve the use of calculators
as an instructional tool.

Paul has worked with a new calculator that has the ability to have some
keys temporarily disabled, which allows for further innovation by the
classroom teachers.

I implore readers of this list server to be more discerning of what they
read. Readers' Digest does have an important role in our society
(probably the single biggest factor in encouraging me to read), but it is
not exactly the pinnacle of journalism...more like right wing propaganda,
once readers view it at a meta-level.

Australia is currently in the grip of similar influence with the rise of
the One Nation Party, spewing out propaganda in such volume and intensity
that the masses who are 'radiating averageness' accept her ideas without
question. In a similar vein, Readers' Digest must be viewed similarily,
including its flawed arguement about calculators.

Sure, many calculators are misused. But the innovation and wisdom of
classroom teachers should be valued and encouraged.


Matt Skoss.
Maths/Computing/Year 9 Coordinator

Alice Springs High School


"Fester, or Perish!"


Jerry P. Becker
Dept. of Curriculum & Instruction
Southern Illinois University
Carbondale, IL 62901-4610 USA
Fax: (618)453-4244
Phone: (618)453-4241 (office)

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