Ideas do not grow in a vacuum. On the contrary, ideas are a definite platform between the existing state of affairs and the desired state, however, always in the frame of what is possible, practicable, and socially attainable.

The division of thought: "what is desired, possible, practicable, and socially attainable," must not be based on rhetoric to swing the mood of citizens to this or that side or on the defending of the status quo. Yes, we are humans, most of us are apprehensive of the changes and tend to support the familiar state of affairs. However, we must recognize that by taking the status quo position we will impede a progress of mankind. Let the test of time prove or disprove new ideas.

We have well educated and dedicated teachers, however, the knowledge of the subject material will not necessarily assure teaching effectiveness. Arithmetic, taught at the elementary school level by a teacher with a PhD in math, would be a disaster if the teacher is not adept at using the teaching methods that show, explain, and guide the students to learn the subject material at their level of understanding.

Publishers of the series of books For Dummies, mostly related to the application of computer software, sold more than 40 million copies. Why are these books so popular? Because the authors of these books use certain methods of instruction, namely they are written at the level of understanding of the vast majority of software buyers, while manual books are written by the software technicians at their own level of understanding. Therefore, for most of us, manual books are not simple or easy to use, but are often incomprehensible and in some cases, practically useless.

In the London Free Press article (April 3, 2000, page A3) "Students find math tougher than ever, " reporter Hank Daniszewski writes: "Almost 40 percent of students at Catholic high schools failed or just scraped by in math class last semester.  About 14 percent failed."

After analyzing various math textbooks I must note that we can't blame the teachers and certainly not the students for poor test results. The textbooks were written by authors at their level of understanding, conferring a wide gulf between their level and the students' level of comprehension.

Textbooks show the solution of math problems by using fixed mechanical processes (rote learning) and rarely by the application of math principle(s) and concept(s). This seriously hinders the teachers' effectiveness in imparting students with math understanding and comprehension. The authors of math textbooks, by using their imagination and ingenuity, managed to create methods of math teaching/learning that lacks simplicity and harmonious reasoning. Principles and concepts, which are the keys to math comprehension, are occasionally missing, the method of solution of simple problems seems complicated, and the solution of problems with a certain degree of difficulty is often barely comprehensible to students.

The subject of math is cumulative. This simply means that each consecutive step in math study, if it is to be successful, will solely depend on the students' proficiency in the substance of the subject matter taught at the preceding step(s).

All textbooks should be teacher/student friendly, giving teachers an innovative step-by-step source of math instruction that promotes learning of the underlying concepts and principles of the math structure and enabling students to easily master the subject matter.

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