All men by nature desire to know. Aristotle To know what? To know what "is" really is. We must not assume we know a thing until we have deduced the "why" of it.

As we live in a world of constant changes and advancement, it is imperative that children be given the opportunity to learn the necessary math skills that will enable them to compete in today’s diverse market place.

The math structure consists of a series of closely interconnected, pertinent, building blocks of knowledge, each of which must be learned first before the next one can be mastered. Math should not be taught by rote. That method is void of the underlying math principles and concepts that tie the math structure together.

What does "teaching" mean?
It means to show, explain, and guide how to do something.

What does "teaching math" mean?
Teaching math means to show, explain, and guide students to learn at the level of their understanding: "how" to think about a number of things in an implicit way, and "why."

What does "learning" mean?
Learning means comprehending the taught subject and assimilating what is comprehended. The students’ comprehension of the arithmetic lesson will chiefly depend on the method of presentation by the teacher.

We should not only centralize the teaching of arithmetic on understanding rules and illustrating "how" the number system operates in the various number operations. We should equally concentrate on the properties of numbers and their underlying structure and on the comprehension of "why" we do operations in a certain way. It is as important to know, for example, that 1 + 2 + 1 = 4 as to comprehend "why" this process occurs in the first place.

Math thinking is based on deductive reasoning. This means that we start with a premise or a proposition, assuming to be true. By logical steps we deduce from the given premise a result, which again can be used as a premise for the next step of deductive reasoning. All truth and errors lie in propositions.

The students that comprehended the "why" of the properties of numbers and the structure of the number system can learn and think more effectively. Learning is a thinking process. Students should understand the relationship of ideas, laws, principles, and concepts that underlie the basic structure of the number system. Skills in addition, subtraction, multiplication, and division are essential in solving problems. However, deciding which operation and what sequence of operation is necessary to solve a given problem belongs to the art of number thinking, that is, interpreting and correlating the given facts into a coherent, logical relationship.

In Business Week December 13, 1999, it stated how a group north of Chicago area school districts, calling itself the First in the World (FiW) Consortium, used a similar method of math instruction that Komotech Publishing promotes in their textbooks. When students in grades fourth, eight, and twelfth from these districts took the Third International Mathematics & Science Study (TIMSS) math test, they ranked amongst the top five countries in the world. In contrast, the U.S. as a whole placed no higher than thirteenth.

It is crucial that children develop the ability to think and reason independently - to gain confidence, motivation, better grades . . . a future.

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