IN THE LOOMING NATIONAL ELECTION WHERE EDUCATION IS ONE OF THE MAJOR ISSUES, THE ROLE OF THE NATIONAL COUNCIL OF TEACHERS OF MATHEMATICS MAY BE CRUCIALLY IMPORTANT. IF THE NCTM CONFIRMS THE NEW POSITIONS, TAKEN AT THEIR MEETING IN CHICAGO LAST APRIL, THEY WILL REGAIN LOST CREDIBILITY AND CONTRIBUTE SUBSTANTIALLY TO THE SURVIVAL OF PUBLIC EDUCATION IN AMERICA.
At their meeting in Chicago on last April, the National Council of Teachers of Mathematics (NCTM) unveiled, with much fanfare, a revision of their three "Standards" reports, the first of which was published in 1989. This revision, labeled "Principles and Standards for School Mathematics", was an attempt by NCTM to allay the parental concerns and cope with the intense opposition triggered by the original reports. This attempt resulted in some startling reversals of some of the crucially important policies which had been widely applied in mathematics classrooms throughout the nation in compliance with the earlier "standards" reports. Two examples are especially noteworthy. The original reports (1) minimized the importance of correct answers and emphasized the "critical thinking" the student must do in order to get any answer, correct or not, and (2) minimized the importance of memorizing number facts and acquiring facility in performing the fundamental operations of arithmetic.
The NCTM's reversals of policy on these and other matters were widely publicized in the national press. For example, in the New York Times for April 13, 2000, under the heading Math Teachers Back Return of Education in Basic Skills, we find an article by Anemona Hartocollis, in which the following statements appear.
In an important about-face, the nation's most influential group of mathematics teachers announced yesterday that it was recommending, in essence, that the arithmetic be put back into mathematics, urging teachers to emphasize the fundamentals of computation rather than focus on concepts and reasoning.A decade ago, the National Council of Teachers of Mathematics galvanized math educators from kindergarten through high school by preaching that it was more important for students to understand how they arrived at an answer, rather than the answer itself. In the process, they de-emphasized such basic computational skills as memorization of multiplication tables. As their proposals were put in place by hundreds of school boards, parents and even some teachers and university mathematicians began to rebel.
Yesterday, after being on the defensive for years, the council issued a revision at its national convention here that critics and even some supporters of the old curriculum said was a retreat. While not abandoning its original agenda, the council added strong language to its groundbreaking 1989 standards, emphasizing accuracy, efficiency and basic skills like memorizing the multiplication tables.
The message, said Joan Ferrini-Mundy, chairwoman of the committee to revise the standards, is: "Get the right answer." Releasing the revised standards at a news conference here, during a convention attended by 18,000 math teachers, Ms. Ferrini-Mundy said that students must be fluent in arithmetic computation, use efficient and accurate methods, and understand those methods. They should know their basic addition, subtraction, multiplication and division combinations as well as understand them.
These statements clearly indicate that the NCTM is beginning to free itself from domination by the Education Establishment (EE) where, according to professors of education, all memory is "rote", all facts are "mere" and teachers are no longer expositors who explain and transmit the cultural heritage of the race to the next generation.
Our graduate schools of education, which dominate the EE, have become arcane realms where professors promulgate theories which have no foundation in either research or experience and which they themselves have never applied in the classroom. James Taub and John Leo give us a glimpse of the "thinking" that prevails there.
Taub, a New York Times writer, states: "I was invited to participate in a round-table discussion of school reform at Harvard ... The prevailing attitude around the table was that schools were far too preoccupied with assuring academic skills, that we've gone berserk in this country with standardized testing, that we need to cultivate emotional intelligence." (Teachers too preoccupied with academic skills? Is your doctor too preoccupied with healing?)
John Leo notes in the US News and World Report for 1/11/99, "A study by the Public Agenda Group found that only 7 percent of education professors think teachers should be conveyors of knowledge, 92 percent believe teachers should just enable students to learn on their own".
The NCTM must not be dominated by the EE whose destructive policies include endorsement of:
These policies, left unchecked, will destroy public education in America. They have already damaged the learning of English, Science and History (Social Studies) even more than they have damaged the learning of mathematics. Indeed, the controversy now raging in school mathematics is just one battle of the EE's many-fronted War on Learning.
I spent 35 years (1929-42 and 1946-68), teaching mathematics in the public high schools of Illinois. I very much want to see public education survive this war. It has, for many years, provided the only hope for kids who were as poor and disadvantaged as I was when I attended public schools. The only way it can survive is for the power of the EE to be broken. The only way this can happen is for some strong organization to openly rebel against EE policies. This would dispel the aura of invincibility that the EE now enjoys. It would also trigger immediate and powerful support from concerned parents, employers and college admission officials throughout the land.
I strongly urge the NCTM to take this course. To move in this direction and confirm its commitment to the redemptive course set by Ms. Ferrini-Mundy, the NCTM should publicly endorse the following ten statements each of which is completely consistent with the Council's revised position.
- In order for our students to acquire mastery of the fundamental operations of arithmetic, as recommended by Ferrini-Mundy, which provide the indispensable foundation on which the understanding of algebra is built, we follow the lead of countries that outscored us on the objective tests administered by the Third International Math and Science Study (TIMMS) and ban the use of calculators in grades K-5.
- Deficiencies in the mathematical preparation of teachers is, by far, our most serious problem and little improvement is possible until this disgraceful condition is remedied. ("Thirty eight percent of our high school math teachers don't have even a minor in mathematics" Gail Burrell).
- The teaching of mathematics is a highly individualistic art and teachers must be free to use any methods that they believe will enable their students to do well on objective standardized tests. Their options should not be limited by supervisors. For example, the prescription of cooperative learning in the classroom on the grounds that it parallels the procedures employed by research teams in industry, is based on a complete misunderstanding of the latter process. Actually, the two situations are so different that no valid parallels can be drawn. The use of cooperative learning groups should be only one of many options available to teachers.
- Properly constructed objective, standardized tests provide valid measures of student achievement in school mathematics. We must not try to avoid accountability by downgrading the objective standardized tests on which it is based. The extensive and disgraceful cheating currently elicited by these so called high stakes tests must be eliminated, not by eliminating the tests but by restoring integrity to the testing process.
- A good assessment system must be highly objective and well understood by the students. It preserves the integrity of individual course grades and contains a strong diagnostic component which enables the teacher to adjust instruction to the needs of the class and assign individually prescribed remedial work when necessary.
- "Critical thinking" in mathematics is a disciplined process which requires a factual base and a language which furnishes a logic-oriented vocabulary. (See Language and the Learning of Mathematics.) It is misleading to suggest that critical thinking fosters "Higher thinking skills" when the language necessary for acquiring and using those skills is NOT provided. The alleged dichotomy between "getting the right answer" and "critical thinking" is false. There is nothing about "getting the right answer" which implies any deficiency in the thinking process.
- Parents who complain to school officials about policies applied in mathematics classrooms are entitled to factual, jargon-free replies and must never be subjected to personal attack.
- The conditions under which mathematics teachers work must be substantially improved. They must have parental and administrative support and the respect and pay due a skilled professional who continues to study his subject after having completed a rigorous training program. They must have time during the school day to plan presentations, grade student work and consult with colleagues. This may require a drastic reallocation of resources.
- We will apply only those research results that have real validity, can be replicated by responsible investigators and have control groups where appropriate. We will never use biased or flawed research results to justify failed policies.
- The slogan "Drill and Kill" is replaced by the maxim that has served students well for centuries, "Practice and Learn".
If the NCTM follows this course it will again deserve to be called The National Council of TEACHERS of Mathematics.
In making the concessions noted above, the Council has taken a long step in the right direction. Now we must ask the NCTM to confirm its commitment to this redemptive course. This is urgently necessary (1) because administrators, supervisors and teachers need assurance that the NCTM is sincere in making this commitment and (2) because of the bizarre behavior of Lee V. Stiff, NCTM's newly elected president.
At the same Chicago meeting (April 12-15), where this retreat was announced, Prof. Stiff gave a strong defense of constructivism which provides the philosophical basis for the now partially repudiated false doctrines in the old NCTM Standards.. Two weeks later, he went to Los Angeles to urge the Board of Education to ignore the recommendation of its own expert panel which had recommended a strong mathematics program, and adopt one of the ten weak programs against which over 200 mathematicians had protested in a letter to the Secretary of Education. He did this on the racist grounds that Blacks and Hispanics cannot learn structured mathematics. Later in the summer, he went on a similar mission to Massachusetts where he lost. When asked about the lost generation of mathematical illiterates produced by nationwide application of now rescinded NCTM doctrines, he snapped "There was no such generation". Oh yes, there was, Prof. Stiff, although we would never have known this had we relied on NCTM's "authentic assessment". Nevertheless, we respect a man for standing up for his convictions. We must inquire about the nature and extent of the classroom experience which provides the basis for this conviction. We direct the same inquiry to each member of the writing team and to each member of NCTM's Board of Directors.
For many years this organization meant more to me than any other. I hope that I live to see the day when the NCTM is again recognized as the positive force in the teaching and learning of mathematics, which in 2000 helped us to save our schools.