Mathematics: A Skill Not a Frill

The fundamental responsibility of a teacher is to instill within each student the God-directed mandate to dominate his world -- in particular, his personal world. Teaching the young to dominate his world is a training that leads to learning how to read, how to write and how to count. " How to count " translates into mastering the basic skills of mathematics. Falling short in these skills positions a student on a path to mediocrity or possibly failure in later life.

Reading, writing and counting are skills. In themselves reading, writing and counting accomplish nothing. When the ensemble of the student's native ability and his internalized mandate to dominate his world operate on his reading, writing and counting skills, new worlds open to him. For these skills facilitate ones desire to seek, to find, and to offer optimal ideas that transform existences into meaningful personal and societal advances. For this reason alone, the responsible teacher resists his delight to teach his love of literature, science, geography, law, etc. and succumbs to eradicate all deficiencies his student has. He is ever aware of his answer to the question, "Which among the following would I rather my student to forget? Reading, writing, counting or geography?"

The conscientious teacher dedicate every energy to eliminate
deficiencies. As students develop at different rates, teachers must have developed plans targeting the moment each student's arrival at proficiency. Thus knowledge of a student's strengths and weaknesses and his corrective actions to eliminate them are paramount for the teacher. With this knowledge teachers plan daily activities to ensure arrival at proficiency is timely. Upon arrival at proficiency, the teacher, through applications, must then turns to the development of the student's acumen to dominate his world commences.

A student need not be taught to a mathematician, but he should be held to master the principles of mathematics. His teacher must expend enormous amounts of time asking questions and teaching him the how's and the why's of asking questions. This is the only way he learns what is important to others and how one obtains the information he needs to satisfy questions. Equal zeal must be devoted to developing the student's insights into massaging a problem for preparation into a mathematical investigation. This is the accepted means of analyzing the problem by a cogent investigation. Exercises on ratio, proportions, interest payments, present value of money, predictions, techniques of estimation, method to determine the optimal value of a quantity, as well as how to estimate likelihood of future success through observations, recognizing patterns, observing things that do not change as a situation advances are but some of the critical tools on which the teacher must focus during daily activities. For these activities are necessary building blocks for the exploration and domination of the world as well as oneself.

Where does all of this go? At the beginning of these thoughts, counting was introduced as a set of skills to aid a student to dominate his world. Now, the conscientious teacher must view and teach it as, a science of suggestions. Here the science and its symbolism are not constrained in any manner. This claim is made clear by example.

The symbolism, "a+b", is recognizable to counting. When you see it, what thoughts accompany it? For most, numbers and additions of numbers is a certain response. If one does not limit the symbols, it is possible one may interpret " + " to be "is the brother of " and the symbols "a " and "b" as elements from a set whose elements are males who are brothers. So one now interpret the symbolism, "a+b", to mean "John is the brother of James" where John and James are elements from a set containing brothers. So thinking of things from the counting world as suggestions for others things gives the statements from counting a new life in a world beyond numbers. Being so, the mathematics from which it sprang, suggest other possibilities beyond the commonplace. Now the statement, "a+b=b+a", might translate into the expression "John is the brother of James is the same as James is the brother of John." Clearly I interpret the symbolism "=" to mean "is the same as". Failing to viewing the symbols and ideas from counting to be constrained to numbers and their world, a new level of generalization opens to us. Think about the many other advantages this may provide towards dominating one's world. These are some of the things a teacher must be ever vigilant to point out to his student.