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Next: Seeing  changes  and  differences. Overlooking stationary states Up: No Title Previous: Barrier of first concepts,

Barrier of scale crossing

Stanley Hall, a psychologist, said that a child is interested in things that lie within her own reach. This horizon of accessible events expands with the development of the individual. However, without special effort on the part of the learner, without conscious learning it remains limited not only to phenomena and scales of the macroworld but - even within this macroworld - to a very narrow strip of spacetime and energy spectrum. Most physical units (kg, m, hour, kWh) are chosen in such a way that small number values describe known phenomena and sizes quite well. And this is correct. However, students encounter problems, or a barrier to conquer, when units are not well "adjusted" to phenomena and one has to use numbers that are extremely large or small. And thus, the amount of flour needed for baking a cake is one or two kg but the mass of a train carriage or that of a sea vessel may be thousands of tons. Pressure has to be specified in hectoPascals, electric current in mA, and capacitance in pF. In such cases "large" units often function separately from the basic ones, like a ton and a kg, a meter and a light year, or even simply a second and day-and-night, hectare, squaremeter. The ability to relate these separate units requires experience and training.

Large unimaginable numbers are difficult for the children; whether it is a million or a billion is unimportant to them. On the other hand, there is a kind of fascination with large numbers (this phenomenon has ontological backround).

Didactic methods meant to help students cross the barrier of scale are quite well developed. The old booklet of Boeke [8] is a classic here. Starting from a picture of a girl sitting on a chair in a school yard, in subsequent pictures the author shows the world at larger scales (increased each time by a factor of ten), thus reaching far-away galaxies, and at smaller scales thus going as deep as the structure of nuclei. Many teachers have developed quite efficient methods of their own. Good effects can be obtained with models (e.g. the solar system). "Shocking" examples may also lead to desired results.


next up previous
Next: Seeing  changes  and  differences. Overlooking stationary states Up: No Title Previous: Barrier of first concepts,
Krzysztof Malarz
2000-01-14