Mathematics: A Skill Not a Frill (Revised)

The fundamental responsibility of a teacher is to instill within his student the God-directed mandate to have dominion over his world -- in particular, his personal world. This mandates that a student understands himself and the world about him. Progressing through life, one needs ready skills to continually interpret the world and to perform self-monitoring. Reading, writing and counting1, once learned, always stand ready to serve their master. Failing to master these skills, positions a student on a path that falls short of the mandate to have dominion over one's world. This, being a possibility, compels a responsible teacher to do everything in order to guarantee each student success at reading, writing, and counting.

Reading, writing and counting are skills. In themselves they accomplish nothing. Harnessed to a student's native abilities and his drive to fulfill his mandate, they open to him new worlds, discipline his investigative powers thereby, making easy the generation of ideas that transforms mere existences into meaningful personal and societal advances. For this reason alone, the conscientious teacher places eradication of all deficiencies above his personal delight to teach his love of literature, science, geography, law, etc.

Conscientious teachers dedicate themselves to eliminate their student's deficiencies. They subject themselves to high directives, by posing to themselves the question, "Which among the following would I rather a student to forget? Reading, writing, counting or geography?" Their answer propels them to know each student's strengths and weaknesses.

This knowledge becomes input into a strategy against student weaknesses and it suggests strategies to plan daily activities ensuring proficiency in the least amount of time. Then and only then, does the training of a student to have dominion over his world truly begins.

Students need not be prepared for a career in mathematics, but he should be held to master the basic principles in mathematics. Teachers must expend enormous amounts of time instructing the "how to" s and the "why's " of asking questions. For this is the only means through which the student will learn what is important and how one might obtain the needy information to satisfy his questions.

With equal zeal teachers must instruct the art of massaging a problem into a suitable mathematical investigation. For mathematical analysis is presently the accepted means to analyze problems through cogent investigation.

Exercises on how to formulate and use ratios, proportions, interest payments, present value of money, predictions, techniques in estimation, methods to determine the optimal value of a quantity, as well as how to estimate future likelihood of success through observations are but a few of the critical tools the teacher must focus during daily activities. For these are necessary building blocks for the exploration and domination of the world as well as oneself.

Where does all of this go? When I began these thoughts, counting was introduced as a skill to aid students to gain dominion over their worlds. Now, the conscientious teacher must elevate his focus to explain the wider world to which rules of counting continue to rule. In this world the symbols and symbolisms of mathematics are freed of their normal interpretations however the statements on rules of counting remains true. I clarify this with an example.

Most recognize the symbolism, "a+b", as a statement in counting. Their thoughts are of numbers and additions. If one opens the symbols to other possibilities, in particular, interpret " + " to be "is the brother of " and the symbols "a " and "b" as elements from a set whose elements are brothers. The symbolism, "a+b", then means "John is the brother of James" where John and James are particular elements from the set of brothers.

So freeing the symbolism from the counting interpretation opens a new world beyond numbers to the user. Being so, the mathematics from which the symbolism sprang suggests other possibilities beyond the commonplace.

Now consider the statement from algebra, "a+b=b+a". Translate the symbolism "=" to mean "means the same thing as". Now a+b=b+a translates to "John is the brother of James means the same thing as James is the brother of John." This idea of seeking ideas beyond mathematics that obey "laws of combinations" in mathematics provides another advantage to an inquiring student.

A teacher must be ever vigilant to point out such things to his students. They are the tools that will part the veil of ignorance a mere centimeter but thrust mankind a quantum leap forward.

1 " How to count ", for our discussion, is mastering the basic skills of mathematics.