There's something about slide rules! I remember the first one I acquired: it was given me by my, then, boyfriend. He had a brand new one as a birthday present. It was a bigger, classier model than his hand-me down--and I coveted it! But even the lesser model was a step-up in mathematical gizmo status to tatty, dog-eared log books.
My next slide rule was a birthday present to me by my future (and still) husband. It was circular--so much easier to use than the straight version. I still have it. The plastic slider is brown with aging sticky tape, and I have forgotten many of the subtleties of its operation.
Using slide rules effectively meant that one should accumulate all the numbers in a calculation into the final, rather daunting looking expression that could then be resolved by some slick sliding to give the final solution to the problem. The recording of the final calculation provided a way of checking solution steps, and the logic of the steps taken in arriving at the final stage. Two insights were thus gained: one, that a number can be expressed in many ways, not simply as a unique numeral, and that often this could be more mathematically useful than the unique solution; and, two, that rounding errors accumulated rapidly if one simply tried to carry out each intermediate calculation, and rounded these to a convenient number of decimal places.
In later years, it was almost impossible to insist that my high school students, armed with calculators, leave off calculating until the last step. Their thinking tended to remain as a step-by-step understanding, instead of having to think about the relationships between all the numbers in the calculation--and the logic was all but lost inside the little black box.
Thus, Paul Scott's "back to the future" look at making and using slide rules as an introduction to discovering e may spark many memories. In much the same vein, by having students construct their own protractor, Ian Sheppard describes how this activity contributed greatly to their understanding of both the tool and the use to which the tool can be put.
This is not to deny the very obvious advantages that electronic technology (as opposed to the mechanical technology of slide rules and protractors) brings to teaching. It is particularly powerful in its ability to produce many similar examples quickly, and without the attendant cognitive load that can distract novice learners from the focus of a mathematical investigation. When this technology is skilfully integrated with other classroom activities, students' experiences of mathematical concepts become broader and richer--and that leads them generalise.
Serendipity has brought together, in this issue, articles that discuss classroom examples of student investigations that incorporate both electronic and mechanical technologies. As a final thought to this issue, sparked by my slide rule reminiscence, I wonder if readers would like to contribute to a short piece to be published in the final edition of this year called "My first calculator." Archival photographs welcome.
University of New England
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|Publication:||Australian Mathematics Teacher|
|Date:||Jun 22, 2009|
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