Mathematics: A Skill Not a Frill Part II

In the article Mathematics: A skill not a frill, I used the term "counting" to represent the totality of basic mathematical skills taught in the grade schools. Some readers were misled by this choice. The purpose of this writing is to clarify my use of the term " counting" and to present some suggestive illustrations.

I chose the term "counting" because the elementary processes in mathematics, as taught in grade schools, can be viewed as different ways of counting. Each process uses a different counting scale with its own unit. For instance, consider let's consider percentages.

A percentage is the unit used to count one-hundredth of a whole. The whole is assigned 100% or the 100 parts. Thus 50% percent means I can count 50 of the 100 units of the whole, or half of the whole. Of course half the whole is a measurement. But I have interpreted this measure by counting the number of units within it.

When I say I am 74% certain about a claim, I am using a more sophisticated counting process. I refer to my confidence level of the predictive ability of the method I used to make the claim. When I made the claim, I could have used my own experience or a method based on some theory. In either case, the totality of times I used the method I take my whole, the 100 parts. Now how do I get the 74%?

In my mind I paired a "success" to each correct guess the method yielded during past use. To each incorrect guess, I pair a "failure". The seventy-four percent is the percentage of correct guesses the method yielded during my use.

In this explanation, I referred only to my experience to measure my confidence in the method. Suppose I have the results of others who have used this method in the same way. I can combine their successes and failures to mine then compute the percentage of success using the combined totals. So the 74% could be the result of a combined effort or my personal efforts.

Interest is method of counting payout from a process. Of course the scale is based on the rate of payout of the process. An investor who gained a 21% payback on his money while the standard payback is 7% has a blessing of 3 times as much as the standard payback.

Probability is a measure of counting the likelihood of an event occurring in a stream of unpredictable observations.

Also it can be viewed as a counting process. As an example, suppose I seek the probability that a certain outcome of a process occurs. I observe the process a large number of times. Then I count the number of times the outcome appears. I take the percentage of times the outcome appeared to be the probability of the outcome.

One can interpret many numerical measures as a count using these methods. For this reason I chose to call the elementary methods in mathematics, "counting".

Mathematics is indeed more than counting or determining measurements as taught in grade schools. Its universal appeal is its ability to record, highlight properties and in some cases predict. Thus it is a useful tool in many fields. Some fields that exploit these mathematical attributes are the sciences, insurance, banking, medicine, technology, social and political disciplines, and even library science.

So what is mathematics? Volumes have been written to this question. None gives a definitive answer. Unknown Quantity by John Derbyshire, is an excellent history of the development of algebra. With its easy-to-read style, it requires little mathematical sophistication. Home school leaders who aren't formally trained in mathematics will invariably find this interesting read. For it gains them an invaluable peek into a world known by few.

What is mathematics? by Courant and Robbins is another book that attempts to answer the question of its title. A high school mathematics maturity exposes its reader to the beauty of the treated topics in a clear and easy format to follow.

After having read this volume, the home schooled gains a panoramic view of mathematics, a glimpse of its potential and a survey of its successes. Home schooling leaders might assign readings or written reports from various chapters to their students.

The importance of mathematics should always be at the forefront of the home school leader's mind. For it has been the engine of technological success in western culture over the past 100 years as petroleum has been the fuel of industrial success in western culture over the past forty years. In this age of information processing, it is not likely its role will change.