Basic Math in Plain English

Many students who have difficulty with math have a problem with the basic concepts, mainly because of conditioning. They spend much of their instructional time seeking answers to problems posed by the instructor or from the text. The answer usually consists of a number derived by use of a process, usually committed to memory, designed to find the answer without an understanding of the basic concepts involved. As a consequence, a habit of trying to find the answer becomes paramount—and all activity is directed toward that end. The conditioning is carried forth as an integral part of the math experience, and they immediately seek the answer before the proposed situation is evaluated. As a consequence, the focus is on the answer to the neglect of the evaluation necessary to arrive at a valid defensible conclusion. This book is intended to diminish the immediate seeking of the answer and to magnify the idea of seeking to evaluate the situation to determine the information contained in the proposed situation (problem) before an attempt is made to find that elusive answer. To accomplish that aim, a thorough grounding in the basic fundamentals of the system is attempted by introducing the basic concepts without the stress of trying to immediately solve situations by applying memorized processes rather than gathering an understanding of the basic underlying concepts. Basic Math in Plain English is an attempt to demystify math by comparing it to the basic structure of the spoken language, emphasizing the similarities, and stressing the differences. It is an attempt to show that mathematics is an integral part of our existence and how a basic understanding of the concepts that are paramount to the system of mathematics will create a greater appreciation of the role that math plays in our daily lives. I implore the reader to carefully consider each salient idea and try to internalize its meaning for future reference. Algorithms (rules) are developed as shortcuts for arriving at defensible conclusions, but they do not necessarily enhance your understanding of the basis for the algorithms. I have not taught mathematics for many years, but I was in administration and had many opportunities to interact with students. One of the basic questions was always if they were doing well in school. The answer was almost universal that math was the subject with which students were befuddled and could not understand or see any use for. The same questions posed to adults invariably elicit the same response. Why do intelligent persons have such difficulty with basic mathematics? Is math too difficult for the average person to comprehend—or is it presented in a manner that makes it incomprehensible to the average person? I believe that the focus on using numbers without a clear definition of the nature of a number and how the numeration system is structured is one part of the problem. Another part of the problem is the focus on problem-solving techniques by getting answers rather than comprehending the structure and its use in constructing the algorithms commonly stressed in the teaching of math. If a teacher asks, “Why are two and two equal to four?” the answer is invariably, “It just is.”