Editor's Note: He suggests that more students need to meet high standards in those subject areas.

Of course we would all like for students to meet "high standards" and "high expectations"  in math and science.

Therein lies the problem. 

Standards that have been set for math and science are not really that high.  In fact they have been deliberately dumbed down in an effort to be inclusive of all children's abilities, obfuscated so that they are truly unclear, and then set out in a public way to give them credibility.

The "standards" that the President alludes to are not benchmarks of any quality at all.  In fact, these standards cause students to slip through their learning years without substantive science and math educations.

John Saxon was an educator who recognized the "standards movement" for what it was.

The Coming Disaster in Science Education in America
By John Saxon
Norman, Oklahoma
March 1993

I believe that the present disaster in science education in America will be drastically exacerbated in the next decade because of recent actions of the National Council of Teachers of Mathematics.  These actions are capricious at best and approach total irresponsibility at worst.  This organization has decided, with no advanced testing whatsoever, to replace preparation for calculus, physics, chemistry, and engineering with watered-down mathematics curriculum that will emphasize the teaching of probability and statistics and will encourage the replacement of the development of paper-and-pencil skills with drills on calculators and computers.  This drastic shift in emphasis will leave American students bereft of the detailed knowledge of the parts that permit the whole to be comprehended.

America is on the road to becoming a follower in technology and science rather than a leader.  Our captains of industry tell us that they are at a disadvantage in worldwide competition because our labor pool is mathematically incompetent.  This incompetence has been documented by recent tests which show that eighty-two percent of our seventeen-year-olds do not know what the word area means and also by international test results wherein American students scored near the bottom of the students in the nations tested.  The engineering and physics departments of American universities are overrun with foreign-born students and teachers because most American university students do not know the mathematics necessary to be successful in engineering and physics.

To correct this situation, we need a no-frills national mathematics program that concentrates on precocious fundamentals.  We have to get our best students (thirty percent) through advanced placement calculus in high school and get the next ability group (forty percent) prepared for calculus as college freshmen.  The rest of the students should master the fundamentals of mathematics that are required to be productive members of our labor pool, enabling us to compete with Europe and the  Oriental nations.  It can be done.  Jaime Escalante, whose exploits were documented in the film Stand and Deliver, had 150 students in advanced placement calculus at Garfield High School in 1988-1989.  This school is in the heavily Hispanic East Los Angeles area.  If all of our schools had the same percentage of students in calculus, there would be no crisis in American scientific education.

Rather than implement a program to prepare students for engineering and the hard sciences, as well as for advanced mathematics, the mathematics education "experts" of the NCTM have come up with a document called Standards for School Mathematics.  This document makes absolutely no mention of preparing students for chemistry.  It makes no mention of preparing students for physics or engineering.  The document even denigrates the idea of preparing students for calculus.  The document discusses the mathematics needed for "business, economics, linguistics, biology, medicine and sociology": and says "however, the fundamental mathematical ideas needed in these areas are not necessarily those studied in a traditional algebra-geometry-precocious sequence, a sequence designed with engineering and physical science applications in mind."

Our country is at risk and the NCTM is now insisting on a radical, totally untested shift in the mathematics curriculum that veers away from preparing students for calculus and the hard sciences.  The Standards details how this watering-down process is to be carried out.  Students will devote less attention to memorizing subtraction facts and will have less paper-and-pencil practice with fractions and less paper-and-pencil practice with long division.  Books will de-emphasize the teaching of radical expressions, conic sections, paper-and-pencil solutions of trigonometric equations, and the solutions of the old-fashioned fundamental word problems that have been used historically to teach the concepts and skills necessary to solve all problems.

The scenario is almost an exact duplicate of the scenario of the "new math" disaster which was caused by the enthusiastic and hasty implementation of another totally untested set of recommendations made by another committee of "experts."  The first scenario was in the 1960's and the committee was called the School Mathematics Study Group and was chaired by Professor Begle of Yale University.  This group was studying ways of improving secondary mathematics education in America when the Russians first launched Sputnik.  A national panic ensued because obviously "America is falling behind the Russians in math and science."  The recommendations of this committee were used as the basis of a paperback series called SMSG or the "new math."  The radical, untested shift in emphasis contained therein was forced into every American classroom because anyone who objected to this nonsense was branded as being unpatriotic.

Most of us are afraid of people who know mathematics because each of us feels that our knowledge of mathematics is inadequate.  Thus we fear that someone who does know mathematics can somehow peer into our souls and detect this gross inadequacy of which we are so ashamed.

This is the reason that no one, with the exception of the mathematician Morris Kline, had the gumption to question the arrant nonsense emphasized in the "new math" books, nonsense that knowledgeable authorities have  refrained from speaking out against even to the present day.  Many of our prominent "experts" in math education today were gofers for the originators of the "new math"" and have built their careers espousing the "new math" philosophy.  To admit that the "new math" was a horrendous error would cast aspersions on their careers as experts in math education.  The National Council of Teachers of Mathematics has backed the "new math" philosophy for thirty years and to suggest that SMSG was a terrible blunder would be a stain on the escutcheon of this organization.

In the late 1970's it became apparent to some of the insiders that all was not well in math education.  Calculators and computers for the classroom use had been recommended since 1972.  Neither of these instruments had been shown to be effective at that time, but a drowning man will grasp at any straw.   The NCTM felt that leadership was necessary, so they threw together a document called "The Agenda for the Eighties," in which it was recommended again that calculators and computers be used in classrooms and that the emphasis in math classes be shifted to "problem solving of real-world problems."

The efficacy of the use of calculators in elementary schools still had not been proved and many people questioned the wisdom of introducing calculators before students had become proficient with paper-and-pencil exercises.  In 1984, a meta-analysis of all the tests on the use of calculators in elementary schools was compiled.  One of the tests in this analysis showed that calculators were significantly damaging to the calculating ability of average fourth-graders. This one significant negative finding would cause a prudent man to proceed with caution.  But the NCTM ignored this finding and recommended that calculators be made available in every elementary grade and that "students be allowed to decide when it was better to estimate, to use paper and pencil, or to use a calculator."  They even used the meta-analysis to justify this recommendation and said that the findings for the use of calculators outweighed the finding against the use of the calculators.  So they again heavily recommended calculators for use in elementary schools.  Can you imagine what would happen to the Federal Drug Administration if it approved a drug that was damaging only to average ten-year-olds?

Had the NCTM said that this finding was enough to require further tests and had it conducted large scale tests for several years in inner city schools, rural schools, and suburban schools with no negative findings and with very positive findings, a foundation for a tentative approval of calculators in elementary schools might have been established.

I dwell on the calculator issue, not because it is so important, but to emphasize the mentality of the committees of experts who have been and are directing mathematics education in America.  Jack Nicklaus is an expert golfer because he has won more major golf tournaments than any other man.  Boris Becker and Steffi Graff are members of the pantheon of kings and queens of tennis because of their successes.  Only in American mathematics education do people with a track record of abject failure arrogate the title of "expert."  We have implemented their recommendations for years and years without requiring proof of efficacy first.  I say that the time has come to question the experts, especially since they have asked the country to join them in another untested and questionable shift in pedagogy that I believe will cause great harm to America and should be called the "new new math."

The major thrust of this program will be an attempt to teach students the art of solving  "real-world problems" without first teaching the concepts and skills.  The idea is to let skill development and concept understanding evolve from the use of the concepts and skills in the solutions of real-world problems.  The initial concept understanding is supposed to result from the explanation of the teacher (which seldom occurs) and then the emphasis is to be on applications of the concept.  Of course, the "experts" believe that there is no need to prove that this approach is feasible before it is forced on the students of America.  They have talked almost every responsible organization in American education into endorsing the Standards. They list the endorsement of forty organizations, including the National Association of Secondary School Principals, the National Society of Professional Engineers, and the American Association of Physics Teachers.  Even the astronaut Sally Ride has endorsed the Standards. Who could be against standards for American mathematics education?  I assume that these people endorsed the program without fully realizing what they were endorsing.  Certainly everyone is in favor of doing something about the sad state of math and science education in America and, as do our "experts," they grasp at any straw.

I began visiting Jaime Escalante soon after his success in teaching calculus in Garfield High School in  East Los Angeles was reported by Reader's Digest.  Mr. Escalate sees high school calculus as a lever that Hispanic children can use to enable them to get college scholarships in engineering and thus to become full participants in our technological society.  Mr. Escalante is certainly in favor of standards for his students.  How does it happen that he was quoted in the press as saying that "whoever wrote [the standards] must be a physical education teacher"?  It is because the NCTM Standards comprises another flight of fancy by putative experts.  These "experts" recoil in anger when asked why they should not prove the expected results of their recommendations before they are implemented.  Jaime Escalante has proved his methods before the entire world.  Why should the NCTM not do the same?  I was happy to see Mr. Escalante's comment.  I had read the Standards carefully and was convinced that they had been compiled behind the looking glass with Alice at the Mad Hatter's Tea Party.  The document is replete with nonsense such as the following:  

'Our premise is that what a student learns depends to a great degree on how he or
  she learned it.  For example, one could expect to see students recording  measurements of real objects, collecting information and describing their  properties using statistics and exploring the properties of a function by examining  its graph.  This vision sees students studying much of the same mathematics  currently taught but with quite a different emphasis.  It also sees some  mathematics being taught that in the past has received little emphasis in schools.'

This premise and vision gibberish is followed by statements that students should learn to value mathematics, become mathematically confident, become mathematical problem solvers, learn to communicate mathematically, and learn to reason mathematically.  If one reads the entire Standards document carefully, it is really difficult to decide whether it was written behind the look glass by the Red Queen or if it was written by a physical education instructor, as Jaime Escalante contends.

We need to get as many students as we can through calculus in high school.  We need students who are competent in the use of fractions, decimals, mixed numbers, percent, and ratios.  We need students who know trigonometry and analytic geometry.  We need a work force that allows Americans to compete successfully in a technological world. We do not need guidelines that  recommend leaving student ill-prepared for chemistry and physics and that ridicule preparation for calculus.

This violent shift in emphasis recommended by the NCTM stems from the failure of the experts to find a way to teach the concepts and skills first.  The first draft of the Standards stated that because we have been unable to teach the concepts and skills first and then teach the applications, we must have been trying to do it the wrong way.  Thus we should try to do it the other way.  We should try to teach the concepts and skills through the study of real-world problems.  Can you believe this off-the-wall reasoning?

I was aghast at this wild surmise and was chagrined that one of the authors of the Standards deleted this statement before the final version was printed. This statement was a dead giveaway to the pie-in-the-sky fuzzy thinking that lay behind the whole document.  America has depended on our "experts" in mathematics education for 30 years and they have let us down.  Now they propose that we accept a set of nebulous recommendations that are totally unproven.  The book companies will work feverishly to publish books that try to meet the guidelines and the result will be an acceleration of the disaster in mathematics and science education.  It will take at least ten years for the full extent of the coming disaster to become apparent.  College math enrollment will decline and the number of American students in physics and engineering will decline even further.  And no one will be to blame.  They will all say, "It wasn't my fault."  I guess that is the advantage of being just a member of a "committee of experts."

The mathematical knowledge required for success in chemistry, physics, and engineering has not changed.  High school students avoid chemistry, not because they fear studying electron orbital, but because they lack the concepts and skills necessary to work problems that involve chemical combinations by weight and other problems that require mastery of the basic manipulatory skills of algebra and the basic concepts of trigonometry.  An article discussing the poor mathematical abilities of physics students at the University of Houston appeared in the December 1989 issue of the Physics Teacher. It reported that only one-fifth of these students knew how to handle trigonometric functions of large angles and only one-third could solve parametric equations or work simple problems that required two steps. It stated flatly that students are not coming to college prepared for the algebra and trigonometry  required for success in physics.

The Standards document stresses that there must be a shift in mathematics education away from practicing problems categorized by type, such as coin problems, age problems, digit problems, work problems, and trains-leaving-Detroit-at-midnight problems. There is absolutely no way that this shift in emphasis can be justified.  These problems have been developed by teachers over the years to teach the thought processes and skills that are necessary to solve other problems that are new and strange.  The document says that "type" problems should be replaced with "non-standard problems" and with "open-ended problems" and "extended problem-solving project."  The idea of non-standard problems is ludicrous.  Don't the authors of the Standards realize that all of the problems in the first course in algebra are non-standard to students who have never studied algebra before?  "Non-standard" must mean problems that the algebra teachers have never seen before or tried before or used as teaching tools before.  Throwing out a tried-and-true method and replacing it with something new that is untested is the height of irresponsibility.

The answer to the problem just outlined lies in the market place, the unique entity that allows the free enterprise system to work effectively.  If secondary schools in America demand books that prepare students for physics, chemistry, engineering, and other mathematically-based disciplines, the major book companies will publish books that do the job.  Science teachers should insist that the book companies to extensive testing of their math and science books and present proof of efficacy before books are considered for purchase.  The books should prepare the students for the hard sciences and should also encourage the development of critical thinking and the use of higher-order though processes. The science teachers must use all their powers of persuasion to see that their schools adopt only math books that have been tested and proved to be superior.  Books that follow highly recommended pedagogy but have not been proved to be effective should be rejected out of hand.  Book companies are in business to make a profit.  Period.  But every other American company is in business for  the same reason, and it is unfair to require book companies to be more altruistic than other companies.  Book companies will product and test books that can be used effectively in the classroom if that is what is required to stay in business and make a profit.  Science teachers can cause the revolution we need in American mathematics educations by seeing that their schools purchase only mathematics books that do the job.  What a simple solution to a very complex problem!!!