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To the Editor:

What is the story with Barry McGhan ("'Keep the Faith,' Math Teachers,'' Commentary, Feb. 17, 1993)? Did Chester Finn say something nasty about his mother or what? Mathematics instruction is serious stuff, but this is silly.

Mr. McGhan seems mightily annoyed that anyone would dare to question the new standards of the National Council of Teachers of Mathematics. How can it be wrong to ask for some review of the evidence that a proposed course of action does or does not make sense?

What is shallow about knowing that 5 x 11 = 55? Of course people get satisfaction from being able to solve problems. The question is whether one particular approach will help children solve problems more effectively than other approaches. Simple assertions answer nothing.

And what about the ad hominum silliness of "antediluvian''? The question is whether older methods are more effective than newer ones. To call older methods older does not tell us much.

Is Mr. McGhan saying that computers and calculators mean that children should no longer learn how to do long division? If E.D. Hirsch is too simplistic, tell us why. Assertion is not proof. Talking about buried heads and sand is polemic, not proof. And what place does Mr. McGhan's rant against conservatives have in this discussion? Why would conservatives be afraid of wider ranges of people learning to think and to solve problems? I am a conservative. I think that if more people thought better there would be more conservatives. Liberals must think the same. Mortimer Adler is educationally quite conservative, and he advocates that the most traditional and rigorous of academic educations, including rigorous mathematics, be given to all students.

Are these new standards really the "old 'new math''' as Mr. McGhan asserts? Is this cause for celebration? How are we to know? Certainly there was widespread unhappiness among parents and teachers of mathematics regarding the old new math.

Talk about "essence'' is disquieting. Cannot math be involved with things ranging from computational skills to problem-solving? Must it be one or the other?

Mr. McGhan asserts that the "best way to produce problem-solving ability in students is through student-centered practice'' which, he says, is called "constructivism.'' Is this the best way? How does he know? Saying something is the best takes us back to research that Mr. McGhan agrees is less than convincing. From what I have seen of constructivism, it seems sensible enough. Not all constructivists deny the need to know how to do long division. Do any? The main complaint about constructivist approaches seems to be that they take a great deal more time than many teachers feel they have available.

In sum, I do not think Mr. McGhan's "faith'' is one that ought to be kept. I do not know what Mr. Finn knows about math or about the N.C.T.M.'s proposed standards. Whether what he says is accurate or not is what needs to be addressed. The question here is are we being led by these new standards toward or away from improved student math performance. I know less about the answer to this question as a result of Mr. McGhan's harangue. If his is the best defense the N.C.T.M. can produce, then I hope we will proceed with great caution.

If, however, Mr. McGhan is not representative, then let us hear in these pages from more responsible people who wish to rebut Mr. Finn and to support the new standards. Do the standards make sense? What evidence is there that they make sense? What evidence is there that they can be implemented with the facilities and staff now available? What do real math teachers in real school rooms think? These are the questions that need to be answered, but Mr. McGhan's name calling is not the way to go about it.

Paul W. Johnston
Advisory Service on Private Schools
Mamaroneck, N.Y.

To the Editor:

In an "Editor's Note'' after my letter in the March 10, 1993, issue, you chastise me for failing to note that "the proportion of students at or above that level [650 on the Scholastic Aptitude Test]--3 percent in the verbal and 7 percent in math--remained the same over the decade.'' You are factually wrong again and the implication of your comment reveals a fundamental lack of understanding of norm-referenced tests.

First, the proportion of those scoring above 650 on the S.A.T. mathematics did not remain the same over the decade, nor is it 7 percent as you assert. In 1992, 104,401 students out of 1,034,131 test-takers had math scores above 650. My calculator computes this as 10.1 percent.

Second, your comment implies that these proportions are too small. But it is in the nature of tests like the S.A.T. that few people score very high. When you force a normal distribution on the scores, as was done with the S.A.T., you exclude most people from the upper reaches.

We know from the characteristics of the normal curve that 6.68 percent of the all-white, mostly male, elite S.A.T. standard-setters of 1941 scored above 650 (650 = 1.5 standard deviations above the mean). Even if your 7 percent figure were correct, it would be the same for our contemporary, polyglot, democratized test-taking pool as for this elite. But the proportion in this rarefied atmosphere currently is actually 10.1 percent, which represents a great gain.

The proportion of students scoring high on the verbal section did fall from 1941, but has remained quite constant for almost 20 years (since 1974). The most-analyzed decline started about the time television became prevalent and colleges opened up to minorities (although the average verbal score had already fallen 25 points to 475 by pre-TV 1951). I expect that as we become even more of a multi-media, multicultural society, as hypermedia invades the classroom, the average will fall some more. The S.A.T. is book-based. Our society is becoming less and less so, even as a higher and higher percentage of citizens do not speak English as their native language. This is not the end of the world except for those who write for a living.

Unless I missed something (always a possibility), what you call "considerable attention'' to my work and that of others in the same arena consists only of two articles in one issue, plus mentions in your school-reform chronology.

Gerald W. Bracey
Alexandria, Va.

To the Editor:

As I was glancing through the list of chief state school officers provided in your March 3, 1993 issue, an interesting disparity struck me in regard to the proportion of elected versus appointed men and women. Of the 51 chief state school officers listed, 11 (22 percent) were women. Of those 11 women, nine (82 percent) were elected by popular vote and two (18 percent) were appointed (one by a governor and one by a state board of education). Of the 40 men on the list, five (12.5 percent) were elected and 35 (87.5 percent) were appointed to their positions.

One does wonder why almost two-thirds of the elected chief state school officers are women, while 95 percent of the appointed officers are men. Surely there are women qualified to be the top state educator in more than two of the 37 states that appoint their chief school officer. The general public apparently is confident that women can serve effectively in this position; perhaps governors and state boards of education need to take a hard look at their appointment practices.

Margaret L. Potter
Moorhead, Minn.

Vol. 12, Issue 26

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