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Handheld ICT Devices, Including
Calculators and Palmtops
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Throughout recorded history, humans have worked to develop
aids to computation. The abacus is an early example of a
very successful aid, and is still used today in various
parts of the world. Moreover, an abacus-like device called a
bead frame is a useful manipulative in math teaching and
learning.
We now have available very powerful handheld
calculators and computers. We have cell telephones and other
portable Web access devices. We have palmtop computers. We
have handheld GPS devices. WE have wristwatches that receive
radio signals from an atomic clock in Colorado and
automatically reset themselves to the correct time. And, of
course, laptop and desktop microcomputers are steadily
growing in capability.
From a math education point of view, we need
to consider:
What math knowledge and skills to
"store" in students' heads. Appropriate roles of "paper and
pencil." Appropriate use of mechanical aids to
computation, such as an abacus. Appropriate roles of hardcopy reference
materials. Appropriate roles of easily portable
and relatively inexpensive handheld electronic ICT
devices. Appropriate roles of electronic
reference materials. Appropriate roles of less portable
and/or more expensive devices such as laptop computers
and microcomputers. Appropriate roles of supercomputers
(including those that are readily accessed over networks
and may be widely available).
Here are a few important ideas to
consider:
Knowledge and skills stored in one's
head are portable and always available. Of course, such
knowledge and skills tend to decay over time, especially
if they are not used. Moreover, it takes considerable
time and effort to store knowledge and skills in one
mind/body. Pencil and paper are inexpensive,
easily portable, and tend to be readily available. Pencil
and paper are a powerful aid to the human mind. Thus, it
is not surprising that pencil and paper arithmetic has
grown to be an important component of K-12 math
education. But easily portable handheld calculators (and
computers) are a significant challenge to this approach
to learning and doing math. Hardcopy reference materials are useful
both in learning math and in using math to solve problems
. (For example, books containing tables and formulas are
quite useful.) Calculators and computes can both store
the formulas and tables, and can carry out the
computations as one uses the tables and formulas. This is
a significant challenge to the "traditional" math
curriculum. Etc.
The point to be made is that we have developed
relatively inexpensive, easily portable, rugged, solar
battery powered devices that can have a major impact on the
"traditional" math education system that arose from decades
of careful consideration of #1-3.
We all understand that the amount of time
available for learning is limited and that there are a wide
range of potential demands on this time. We understand that
the totality of math knowledge is both huge and continues to
grow rapidly. To address the math education problems that
this situation creates we can do things such as:
Develop ways to help students learn
math faster and retain their math learning
better. Argue that math education needs to
receive a bigger slice of the formal and informal
learning time that is available. Make changes to the math curriculum
content--adding and deleting topics.
References
Calculators On-line Center. Accessed 11/24/02:
http://www-sci.lib.uci.edu/HSG/RefCalculators.html
This Website contains information
about more than 16,500 differerent calculators. The wide
range of calculators that have been developed provides
good evidence of a widespread interest in developing aids
to computation in many different areas of study, work,
and play.
http://www.math.ohio-state.edu/~waitsb/papers.html
http://www.k12.wa.us/publications/docs/MathBook.pdf
http://www.t3ww.org/t3/therole.htm
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