Needed: A little common sense in high school math education
There is nothing wrong with American secondary mathematics education that cannot be cured immediately by the gentle application of just a little common sense. We are emerging from a period of confusion in which everyone followed the lead of experts who were trying to help us catch up with the Russians in science by improving the teaching of mathematics.
But the leadership of the ''experts'' was inept. They believed that if students were taught an overview of how numbers behaved and interrelated, then they would somehow have the understanding that would give them command of the other skills that they needed. The overview was stressed at the expense of fundamental skill building blocks. The children did not understand the overview and were denied the chance to learn the basics.
Algebra, on the other hand, is a learned skill and can be taught just as effectively as any other learned skill can be taught. Teaching a skill requires patience and the realization that understanding of concepts is not a prerequisite of the initial stages of skill development, for understanding often follows rather than precedes the ability to do. Algebra is an abstract study of the properties of numbers and of the way that numbers behave and interrelate. Algebra is not difficult. Algebra is just different, and time is required in order for things that are different to metamorphose into things that are familiar . . . .
I demonstrated this during the 1980-81 school year in a program that included 1,365 Oklahoma ninth grade Algebra I students in 20 schools. The testing was monitored and the results were certified by the Oklahoma Federation of Teachers.
In a four-hour year-end test of skills, the students who had used a prototype of my Algebra I book more than doubled the score of the control group. The same teachers taught both groups, and the only difference was in the books used.
My results were confirmed by the Oklahoma City schools in a six-high-school, year-long evaluation in which I did not participate. In a year-end test of skills, the students who used my book outscored the controls by 50.8 percent overall. Further confirmation was obtained by the University of Arkansas and the Phoenix public schools.
These results let us know that we can teach Algebra I well enough to almost double the scores on tests of skills. Then why are 82 percent of American 17 -year-olds unable to grasp and conceptualize the abstraction of area? . . .
The problem lies in the mathematics books that American secondary students have been forced to study for the last 20 years. The authors of these textbooks seem to believe that it is possible to explain overriding concepts and give the students an overall understanding before they master the fundamental skills. They insist that the students be forced to understand before they are allowed to do . This technique does not provide the time necessary to understand the fundamentals of each concept . . . or to develop and retain the nuances.
Using this approach is analogous to trying to teach the piano by giving lessons in music theory, demonstrating the major and minor chords and fingering techniques and then asking the student to put it all together and play a sonata. It just can't be done that way. The student must learn to play simple pieces before more difficult pieces are attempted.
The philosophic bone of contention is whether or not algebra consists of great thoughts that can be understood by only a select few or whether algebra is just an abstract study of relationships between numbers that can be understood by everyone. I believe that algebra, especially beginning algebra, consists of a series of skills that can be learned if explained properly, broken into increments that can be internalized one at a time, and then practiced every night for a long time to ensure retention.