July 10, 1974

Bring Back Arithmetic, Save 'New Math'

"New math" is about to become old math without benefit of a respectable middle age.

The great educational fad of this decade is being dismantled as hastily as it was erected.

It is interesting that the demise of "conceptual sets" should begin in California, the state of its birth.  There, the state board of education has decided that the mathematics designed to help youngsters understand numerical relationships has, instead, created a generation of adults unable to balance a personal check book.

The District of Columbia and several Ohio school districts are following suit.

So, once more, a good idea is lost simply because its zealots pushed it too fast and claimed for it too much.

In the panic following the Russian launching of Sputnik - a pioneer, grapefruit-size satellite - the American public demanded a crash course in technical education.  We saw, or thought we did, a "knowledge gap" matching that of the "missile gap" and the "atomic bomb gap."

We have since learned that none of the so-called "gaps" ever existed.  Nevertheless, we rushed pell-mell into dozens of half-baked measures to "catch up."

Not the least of these was "new math."

The theory behind new math was - is - sound.  In brief, it was to teach youngsters to "conceptualize" how several numbers affect each other.  The old method of memorizing basic numerical relationships - such as the multiplication table - was thought to be of limited use in dealing with such modern technologies as astronomy, computers, missile trajectory, and celestial navigation.  And, indeed, it was.

New math ran into difficulty because its proponents made the same mistake that generations of "math teachers" have made - believing that "math" and "arithmetic" are the same thing.

Not so - by a long shot.

The dictionary defines mathematics as "that SCIENCE treating of the exact relations existing between quantities or magnitudes and operations; and of the methods by which, in accordance with these relations, quantities sought are deducible from others known or SUPPOSED." (Emphasis added)

The key words here are "science" and "supposed."  Math, therefore, is a thinking process much used by scientists.  It was the method used by Einstein to deduce the theory of relativity and by Fermi to split the atom.

Mathematics is an extremely valuable tool for technological research.  It is useless to add a grocery list or compute the interest on a loan.  For these latter, everyday, numerical problems we need arithmetic.

The dictionary defines arithmetic as "the ART of computation by REAL numbers."  (Emphasis added)

The key words here are "art" and "real".  Arithmetic is a mechanical process of counting things, whether dollars, people, or bushels.

Everyone needs arithmetic daily.  It is the tool of today, of living.

Math is needed by only a relatively small number of scientists and engineers.  It is the tool of tomorrow, of research.

It is a waste to time, talent and money to try and teach every student to think like Einstein or Fermi.  We need only a few geniuses, but millions of busy people.

Most of us develop conceptual short cuts to the few basic arithmetical computations.  For example, I can't multiply by 12 easily.  Yet, I have learned that in many instances I can quickly multiply by 10 and then by 2 and then add the two results.

Students who perceive these mathematical short cuts to arithmetical problems often go on to become scientists or math teachers.

And this brings us back to our original problem.

Teachers who were good at arithmetic because they conceptualized in a mathematic way went on to major in math so they could become arithmetic teachers.

What we need in our educational system are some  arithmetic teachers AND some math teachers.  Then we should place them at opposite ends of the school building - the arithmetic teachers in the general education department and the math teachers in the science education department.

Some arithmetic should be taught in every grade first through high school senior - just as .  reading and writing (composition) should.  The three Rs are fundamental to everything we do.  If we do these well we can succeed in 99 percent of our endeavors.

Math should be taught to those students who previously have shown a curiosity about how things work.  It is a specialized discipline such as chemistry or physics.

Many parents - including myself - were critical of new math because it was replacing arithmetic.  It was not a useful tool for everyday numerical problems, and we knew it.

Now that our educators have come to their senses about arithmetic I would urge them to continue new math as a valuable study for scientifically minded pupils.

We need a few Einsteins and Fermis.  Surely we can increase the odds of developing potential math geniuses without abandoning the rest of us to arithmetical idiocy.

Author: Lindsey Williams