Guest Columnist: Speaking math to the lay public By Bill Marsh
A well intentioned, partially informed and very political group of Washington citizens has convinced our Legislature to implement a 19th century mathematics curriculum in our schools. Since they believe that the half-century of work in mathematics education that started when Sputnik went up in 1957 was almost entirely misguided, they undervalue the ideas and research of the people who, in my lifetime, have worked hardest to better our children's learning of mathematics. Conversely, they tout the opinions of some of the louder research mathematicians who share their traditional views.
I am a mathematician with different views. I favor many progressive and reform ideas in mathematics education. But I am well aware that, as in other difficult areas of research and scholarship, mistakes are made, and ideas and opinions have to be abandoned or changed -- including some I once held.
Statements by practicing mathematicians should of course be taken seriously in mathematics education. Any reasonable person who has learned from mathematicians that there are an infinite number of primes would reject out of hand a fourth-grade curriculum built on a finite number of primes. The Washington State Board of Education would be justified in rejecting any curriculum that introduces real numbers in second grade, given that the mathematician it hired to review our state's standards has told them: "The point is that fractions are an essential intermediary step between whole number and real numbers." And since a renowned mathematician on the National Mathematics Advisory Panel recently convened by President Bush tells us that "...one must know what fractions are and how to add fractions before a decimal can be defined," surely no one should consider a curriculum that introduces decimals before fractions.
These two prominent mathematicians are honest, hard working scholars speaking the truth as they see it as a public service. Unfortunately, they often make statements about or in mathematics education and public policy in a manner that suggests these statements are mathematically certain. The two statements just quoted sound as if they are statements in mathematics. But they are not certain. In fact, they are not true.
There is a "naming trick" based on iterated halving with which second graders can understand and use real numbers, which they can call "measuring numbers," as "good names for dots on number lines." A six-year-old, who may or may not know what a tenth is, explains the trick in six minutes at http://www.youtube.com/watch?v=d90wWqYBMOQ
The idea behind this trick can be extended to decimals in third and fourth grades, before students have to face the horrors of fractions.
Mathematicians, it seems to me, have a special responsibility to be careful in how they speak to the lay public. Everybody knows that even the best knowledge in other fields is subject to revision, but that mathematics is different. I was told in high school chemistry 50 years ago that inert elements did not form compounds. Then along came xenon difluoride. I'm sure that our two mathematicians would agree that statements in mathematics education, including their own, have to be viewed and held more tentatively than those in chemistry.
Bill Marsh lives in Port Angeles. He taught in several secondary schools and colleges. He testified last year before K-12 education committees in the Legislature.