## The Five On Its Side Effect

The original source of this story is not known to this writer.

The story goes that a teacher explained the idea of infinity by using 8/0. The explanation was given that the smaller the denominator the greater would be the value obtained on division. Thus with a zero in the denominator the value would be very large. To express this result the infinity symbol is used. The teacher pointed out that the infinity symbol is an 8 on its side.

Subsequently a test was given which included the question, "What is the value of 5/0?" The following result was obtained on some papers.

Whether the story is true or not the five-on-its-side effect does indeed exist. The effect is what one would expect from result-oriented presentations. The result obtained is the focus of attention. The cognitive process by which the result was obtained is not given the prominence needed to develop thinking skills. Result oriented presentation is conspicuous in the list of numerical answers given in the appendix of textbooks, the abbreviated and inverted problem solutions shown in text books and related materials, classroom demonstration and lab experiments (particularly the reports). Being able to predict the outcome of a demonstration or experiment from basic concepts uses knowledge. Just observing the outcome does not, nor does it build knowledge efficiently. The reason for the outcome is often quite profound. Yet the student is focused on, for example, drawing graphs of the outcome, placing error bars on the graph, doing an error analysis and so forth. It is difficult to interpret this as education. Such things are more properly a by-product (a spinoff-off) of education.