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Handheld ICT Devices, Including Calculators and Palmtops

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:

  1. What math knowledge and skills to "store" in students' heads.

  2. Appropriate roles of "paper and pencil."

  3. Appropriate use of mechanical aids to computation, such as an abacus.

  4. Appropriate roles of hardcopy reference materials.

  5. Appropriate roles of easily portable and relatively inexpensive handheld electronic ICT devices.

  6. Appropriate roles of electronic reference materials.

  7. Appropriate roles of less portable and/or more expensive devices such as laptop computers and microcomputers.

  8. 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:

  1. 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.

  2. 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.

  3. 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.

  4. 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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