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How is Making Math Meaningful different from the Saxon math program?

This question could be rephrased:

Does it really make any difference how math is taught?

 

People often ask me, "Does it really make any difference how math is taught?" Yes, it makes a world of difference. Actually a world view of difference … the Biblical world view or the secular world view. Which world view do you want to impart to your children?

The Look-Say System

In the Look-Say system for teaching reading, four colored illustrations and alphabet symbols exist side-by-side in the hope that words will be memorized. Words like dog or cat are printed upon a page with the corresponding pictures. Repeating a word over and over to oneself … looking at the picture … hoping to remember the word is a poor teaching system. Although the Look - Say System has been recognized as a failed methodology in the teaching of reading, it remains the major teaching methodology for teaching math.

Repeat to yourself 3 x 5 = 15 until you can remember it is often the advice given by arithmetic textbooks. In this application four colored illustrations are associated with numeric symbols in the hope that math facts will be memorized.

Even though a child can repeat such a phrase, does it mean that he understands what he is saying? Just as the Look-Say teaching methodology does not teach a child to read, neither does it teach a child to think mathematically - that is, to understand and use mathematics. Just as to read means more than a child mindlessly parroting back words, thinking mathematically means more than repeating back a table of facts. The Look-Say approach to teaching math uses a certain technique of instruction known as drill and practice.

Drill and Practice

Drill and practice is a technique of instruction based upon the Look-Say teaching method. This technique is absolutely necessary for the memorization of math facts when the Look-Say method is used. A child is taught a specific skill. This is followed by page after page of similar problems in the hope that the child will memorize the facts.

An adaptation to the drill and practice technique was introduced into math instruction by John Saxon. It is called Incremental (or developmental) Review. What is incremental review? It is a technique of instruction that breaks the whole skill into many bits and pieces or fragments. Each fragment is then taught in isolation from the other parts. The individual fragment is usually repeated over long periods of time. The initial instruction involves many problems of the same kind. The child practices this same skill over and over again for many days. However, the number of similar problems is reduced as time goes on. Incremental review simply spreads out the drill and practice over many months. Incremental review is the same technique used by animals trainers to "teach" an animal to do tricks. What is the theory base for drill and practice and the incremental review?

Behaviorism

The Look-Say teaching methodology and the associated drill and practice techniques are based upon a certain belief about people and how they learn. The theory base - or the world view, if you will - for Saxon's Incremental Review and the Look-Say teaching methodology is behaviorism. This system of education is based upon the thoughts and ideas of psychologists B.F. Skinner and Ivan Pavlov. In "Manipulation and the New Elite" from How Should We Then Live? Dr. Francis Schaeffer explains that man, according to the behaviorist view, "has no soul, he has no mind; he neither initiates, originates nor creates.… Man is accepted as a machine and he is treated as a machine … Behaviorism is not something that we can simply dismiss. Its power is too great."

This is part of what it means to look at life from a world view perspective. Man is not an animal to be conditioned or a machine to be programmed. He is created in the image of the personal God. Using or encouraging others to use educational programs based on behaviorism, does not treat children as created in the image of God.

Biblical View

Making Math Meaningful is based upon the idea that people are a special creation of God with abilities and needs to worship, to create, and to reason. With Making Math Meaningful children are taught to reason, to understand, and to apply what they learn … not simply parrot back information!

Making Math Meaningful teaches children to understand the idea or concept before they are taught the associated skill. When math is reduced to simply a set of skills to be memorized understanding is lost. Math becomes fragmented into many pieces much like a painting by Picasso. You may be thinking, "But it is still necessary to provide drill and practice." When a child understands something, when an idea has real meaning, the amount of drill is certainly reduced. Making Math Meaningful incorporates an adequate alternative to the meaningless repetition of drill and practice. Making Math Meaningful incorporates the use and application of an idea and skill. For example, after the child has learned the multiplication tables from 1 to 5, he then uses a combination of these facts to learn the others. 8 x 7 is taught as a combination of 8 x 5 plus 8 x 2, both within the 5 and under tables. The application of these previously learned facts to a new or different situation is far better than simply drilling the facts. Children using this approach are less likely to throw up their hands and give up.

Christian parents and educators we must base our instruction upon the proper view of man. "Don't be tossed here and there by every wave of doctrine, by the trickery of men"… rather, build your family upon the cornerstone of the Biblical world view! Your children will thank you for Making Math Meaningful!

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