They realize that if you are going to advocate far-reaching changes in the teaching and assessment of school mathematics which have no bearing on the horrendous conditions which impair learning in many classrooms, which have meager research support and with which you have had little or no classroom experience under normal teaching conditions, there are three things you must do.
1. Ignore the fact that conditions that are severely deleterious to learning exist in many school systems throughout our land, even though many citizens regard this as a national disaster. Ignore the fact that many "students" attend school sporadically, and are often in no condition to learn when they do attend. Ignore high drop out rates. It would be politically incorrect to attribute the failure of our schools in the field of mathematics, and elsewhere, to the distressing social conditions that prevail in the communities served by these schools.
For the Standards writers, it would also be a strategic blunder because these distressing community conditions are obviously not going to be ameliorated by modifying the mathematics curriculum and imposing a complicated assessment system on mathematics teachers. Indeed, the whole "Need for change" argument is undermined. Maybe, just maybe, the lower achievement levels we have observed in recent years are largely due to deteriorating social conditions in the home and community, which are not amenable to the "solutions" proposed by the NCTM Standards. Viewed in this light these solutions seem tragically irrelevant.
But they must have some "need" argument. This has been provided by insisting that a large number of our mathematics teachers have, inexplicably and in direct violation of their training, become drillmasters concerned only with developing mechanical skills. I say "in direct violation of their training" because I do not believe that there exists a text on the teaching of school mathematics, written in this century, which advocates developing mechanical skills at the expense of concept building.
So it has come about that a large number of our experienced math teachers are regarded by the Standards writers, not as colleagues whose experience might be valuable in solving the problems that confront us, but rather as an obdurate group to be enlightened and indoctrinated so that they will no longer constitute a barrier to progress. The existence of this hypothetical group of drillmaster teachers is absolutely necessary to make the Standards recommendations seem plausible. The Standards writers are constantly slaughtering strawmen by providing remedies for dire conditions without establishing that such conditions exist.
2. Claim that you have had a vision, individually or collectively experienced, in which these superior procedures were revealed to you. This will obviate the need for supporting research and validating classroom experience. Moreover, this "vision" approach appeals to many people, including some who write about "The Reform Movement in School Mathematics" for the Sunday supplements.
You can endow your vision with some measure of credibility by shamelessly including some teaching principles that have long been accepted by the profession.
Examples:
The producers of the Standards reports undoubtedly know the twentieth century history of school mathematics in the United States but, for some reason, seem determined not to draw upon it. Perhaps they feel that revealing that some of their more acceptable recommendations have deep historical roots would dim the luster of their "vision" in the minds of their readers who, of course, cannot be expected to know this history.
It is when we consider Standards recommendations that are really new that we enter controversial territory. Examples:
3. You must discredit standardized tests that aim for objectivity, so that they will no longer be accepted as valid measures of student competence in school mathematics. You have been endowed with keen perceptions of certain important aspects of mathematical competence which not only are not measured by standardized tests, but cannot be measured by such tests, no matter how they are revised. If this proposition is accepted, two results that are absolutely essential to your campaign will be attained:
Your complicated assessment system will be more acceptable.
Accountability will no longer be a concern because comparisons with past performance, heretofore largely based on standardized test data, will no longer be possible. There will be no way to determine the success or failure of the reforms you advocate.
The foregoing analysis is now summarized with the quotation and verse used to introduce an OPEN LETTER I sent to NCTM President Price on 3/25/95, to which he did not reply. It is my belief that, when any member of NCTM expresses concern about Council policies in a letter to the President, he is entitled to a reply.
The OPEN LETTER, supports the analysis presented above. It will be presented, section by section, below.
The question before us is as vital for free speech as it is for the future of school mathematics in America. Shall the highly controversial recommendations made in those parts of the three NCTM Standards reports that are really new, be openly debated, or shall all opposition to them be suppressed?
["If the past has nothing to say to the present then the present has nothing to say to the future."
Probius 501-443 BC]
Pity the NCTM today
A worthy group that's gone astray
A group completely under the sway
Of theoreticians, far away
From schoolroom events of everyday
It matters little what they say
This is the message their deeds convey:
Standardized tests are an awful bane,
They reveal little or negative gain,
And we regard them with disdain.
A little logic might cause some pain,
From proof that's tough we will abstain.
We'll appeal to the hand instead of the brain.
Subject teacher time to a terrible drain,
With an assessment system that's hard to explain.
We'll repeat sixth grade, like an old refrain,
Recycling the facts all over again."
"If you disagree with us at all
You are a Neanderthal."
If we can't stop them then let us pray
For secondary math in the USA.
Frank B. Allen
Past President NCTM
1962-64
I have no idea who Probius was, but he sounds like a very wise man. Judging by the dates he was a contemporary of Socrates. Surely, we should not discount his wisdom merely because he is, so far as I know, apocryphal.