A Paradigm shift is a major change from one way of thinking to another. A revolution. A metamorphosis driven by agents of change. Thomas Kuhn said “awareness is prerequisite to all acceptable changes of theory.” It would seem that the necessary awareness already exists when report after report shows the sorry state of mathematics education in this country. The recent release of Harvard’s latest report shows that the US ranks 31st of 56 countries, and only 6% of our high school students take higher level math courses. Another statistic which actually explains the other two is the fact that the failure rate of 1st year Algebra in the country is 50%, and this statistic has stayed consistent of at least four decades. How much more awareness is needed?
A major paradigm shift in something as complicated as our education system is certainly not to be taken lightly. We must first be certain that every possible attempt at positive change has been tried and shown to be a failure. Over the years, there have been at least six major philosophical changes. See my article “The Current State of Mathematics Education In This Country–Caution! You May Not Want To Know This” for a detailed explanation of those philosophical changes. That article also describes the various changes in both textbook series and educational techniques that have been tried over the past several decades. A quick look at No Child Left Behind results will show that there has been no benefit to mathematics education. An extended look at the long-term of effects of NCLB will show that, as with “New Math,” the state of mathematics education has actually made a step backward.
This simply can not be allowed to continue. We are no longer able to compete in a global market. The long-term effects of the Algebra failure rate on both society and the individual student are so harmful that it seems criminal for us to allow either to continue. And, yet, while we all agree that the consequences are bad, no one seems to be trying very hard to find solutions. The educational system for mathematics is quite literally being allowed to flounder. School districts are simply rotating though the same techniques that have failed in the past.
So where do we look for solutions to the problems of mathematics education? I believe that the wisest approach would be to look at what has been successful in the field of education and duplicate that.
It seems that nothing in the field of mathematics education has been successful, but, just the opposite is true for reading and writing education. Our very young children enter school eager for the challenge of learning to read and write, and they seem to possess an ingrained sense that they have the ability to learn. They never doubt their ability to learn. Teachers are able to hit the ground running with these students. These children with their enthusiasm, persistence, and confidence in their own abilities stay successful for many years.
With this in mind, the first obvious question is why do our children excel in reading and writing? Answer? Societal expectation. There has always been a “given assumption” or “generalized understanding” that parents–even the extended family unit–have a role to play in preparing pre-school aged children to enter elementary school ready to read and write. Every mother, father, sibling, aunt, uncle, cousin, grandmother, grandfather, and even neighbors take an active interest and role as babies learn to make sounds, say words, crawl, walk, and talk. Babies are incredibly persistent at each of these very difficult tasks because every person in their small universe is quite literally cheering them on. We encourage their every attempt and we reinforce their successes at the same time that we encourage them to “try again” when they fall down. The word “failure” is non-existent at this stage of their little lives.
As the child grows the family unit plays an equal role in language development. Everyone reads to the child and encourages new vocabulary words and correct grammar begins to be evident; and all the while the child is surrounded with reinforcement and encouragement. In some homes, children actually start to read before they enter school. In most homes the necessary preparatory skills for reading are in place for the day school starts. The same has been happening with writings skills. Children are prepared with the alphabet, letter sounds, and letter shapes. They are ready to go to school to learn to read and write. They are filled with excitement. We have filled our children with so much encouragement and reinforcement that they never doubt their own ability to learn to read and write. They know they can learn because we taught them so.
Are the same things happening for mathematics? NO! At most, parents work with their children on counting without realizing that counting is actually a language skill not a math skill. Learning to say “one, two, three, four, five” is the same skill as learning to say “a, b, c, d, e.” Should we be angry with parents for not doing with math what they so wonderfully accomplish with reading and writing. Again, NO! There is no societal expectation for parents to work with anything math related.
The next obvious question then becomes why not? Why does society think that not having parents lay the foundation for math success is desirable? The blame for this can be placed squarely on Jean Piaget (1896-1980). Piaget was a biologist who studied molluscs, but eventually moved into the study of childhood development. He divided a child’s cognitive development into stages based on age. His proclamations that preschool children were capable of learning language and that children were not capable of abstract thought until age 11 have driven the course of education since the early 1970’s. Parents work with preschool children on language because Piaget said they should. And nothing is done with abstract mathematics until almost the teen years because of Piaget. Over the years, we have come to learn that many of his original assumptions were incorrect and that much of his research was flawed. And yet we hang onto those “proclamations” as if they were handed down from God himself. Piaget was wrong! And because of this, the field of mathematics education has been suffering and our children have been failing.