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About Mathematics Education Paul B. Hinds Much mathematics instruction is poor. Only 5% of 17 year olds are competent in basic high school mathematics (algebra and geometry). The mathematics scores on the SAT tests have fallen (yes they have risen recently but the reason is in question: was it due to renorming?). What should be an easy subject to learn has been made into a educational disaster. Mathematics is an invention of humans and, as such, mirrors the human brain. It is human nature to order objects and count them, and all mathematics (even the most sophisticated calculus) is based on counting. For background: keeping track of a herder ’s sheep was one of the first utilizations of counting. A tally stick with a notch for each sheep allowed a herder to move his finger over the notches as each sheep was counted. These earliest of mathematicians found that it is hard to determine the number of objects in a collection of more than four objects. For this reason and because people have hands with five fingers, the number five mark on the tally sticks was often made differently. Often it was shaped as a V notch, which eventually gave the Romans the symbol V for five. At ten, another unique mark was made. Often this mark was an X. From this, of course, the Roman ten became an X. The natural divisions at five and ten and the fact that humans have ten fingers led to a number system based on ten. With few exceptions, all over the world most of the counting systems were based on ten, with a few based on five or twenty. One notable exception was found in the ancient civilizations between the Tigris and Euphrates rivers, Assyria, Babylon, etc., where they devised a system with a base of sixty. We still live today with remnants of this system: —60 minutes in an hour, 60 seconds in a minute, and 360 (a multiple of 60) degrees in a circle. It is interesting that the mathematicians who devised the metric system, putting a measurement system to the base of 10, did not change this over-3000-year tradition. Initially, written numbers were useful only for recording; when computation systems were needed, the abacus was used. Objects were placed in fixed orders which usually represented ones, tens, hundreds, etc. and manipulated so as to add and subtract. It was not until the Hindus invented our present number system that written numbers became useful for computation. This new system, brought to Europe by the Arabs, is often called the Hindu-Arabic system. It is believed that in Europe the abacus and the Hindu-Arabic system were used side by side for a hundred years before the abacus was replaced. A new abacus has now appeared in the form of a calculator. Many in the mathematics community consider this abacus to be the natural replacement for our present paper and pencil calculating system; and they are not content to wait one hundred years for the new system to prove itself as an educational means. But with the adoption of the calculator, they have decided that memorizing the addition and multiplication tables is not necessary. They have concluded, correctly, that calculators will do most of the computation in the future.

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