The NCTM Reform Math Deception 

The Foundations of  Algebra are Missing

By Bill Quirk [wgquirk@wgquirk.com]

Links to Sections of this Essay:

What are the Foundations of Algebra?

What is NCTM Reform Math?

The National Council of Teachers of Mathematics (NCTM) released the NCTM Standards in 1989. This document omits the foundations of algebra described in the section above.  The NCTM believes this content is now obsolete, due to the power of "technology."  Rather than traditional pre-algebra content, the NCTM promotes the reform math constructivist philosophy of math education.  

NCTM reform math now dominates elementary math education in K-6 public schools.  Reform math educators promote the ongoing use of calculators, beginning in kindergarten. Reform math programs also promote the ongoing use of hands-on "manipulatives." They say concrete tools must always be available and regularly used.  They reject the idea that children must eventually migrate from hands-on to abstract thinking.  Reform math educators believe that K-6 math education should be limited to their concept of everyday math needs. They fail to appreciated the vertically-structure of the math knowledge domain. They’re blind to the fact that students can’t learn algebra, if they haven’t first mastered the foundations of algebra.  They’re blind to the fact that algebra is the gateway to higher learning in the STEM fields, where STEM denotes, Science, Technology, Engineering, and Mathematics.

We are opposed to the NCTM version of "math reform." We know it can be all over by the end of the sixth grade, if a child hasn't mastered the facts and skills of standard pencil-and-paper arithmetic.  By the end of the 6th grade, students must understand how to add, subtract, multiply, and divide whole numbers, decimals, and fractions. These must be general skills, not limited to small, special case numbers.

The Reform Math Constructivist Teaching Philosophy:

  1. Belief that children must be allowed to follow their own interests to personally discover the math knowledge that they find interesting and relevant to their own lives.
  2. Belief that knowledge should be naturally acquired as a byproduct of social interaction in real-world settings.
  3. Belief in the primary importance of general, content-independent "process" skills.
  4. Belief that learning must always be an enjoyable, happy experience, with knowledge emerging naturally from games and group activities.

On April 12, 2000, the NCTM released a revision of the NCTM Standards. The next day The New York Times reported: "In an important about-face, the nation's most influential group of mathematics teachers announced yesterday that it was recommending, in essence, that arithmetic be put back into mathematics, urging teachers to emphasize the fundamentals of computation rather than focus on concepts and reasoning."  But this was all a sham. That same day the following contradictory statement was posted at the NCTM website: “More than ever, mathematics must include the mastery of concepts instead of mere memorization and the following of procedures. More than ever, school mathematics must include an understanding of how to use technology to arrive meaningfully at solutions to problems instead of endless attention to increasingly outdated computational tedium.”
           

Unfortunately, NCTM reform math is the “math wars” winner.  The foundations of algebra topics are now missing from most American K-6 classrooms.  Difficult to believe? Consider the writings of Marilyn Burns, the math program director for the Phil Mickelson ExxonMobil Teachers Academy.  In her book, About Teaching Mathematics, Marilyn Burns wrote: “because of the present availability of calculators, having children spend more than six years of their schooling mastering paper-and-pencil arithmetic is as absurd as teaching them to ride and care for a horse in case the family car breaks down.”  Ms. Burns claims that “the emphasis of arithmetic instruction should be on having students invent their own  ways to compute.”  But there’s no inventing.  Children are taught nonstandard methods for solving simple, special case problems. Parents and grandparents can’t help, because it’s not the math methods  they use.
Why has reform math achieved such success?  First, it’s not easy to correctly teach the foundations of algebra, and American schools of education typically offer just one 3-hour survey course in math.  So most elementary schools teachers are not prepared to teach the foundations of algebra topics.  There’s also been an extensive propaganda campaign that has praised the reform approach and trashed standard pencil-and-paper arithmetic.

The Key Fallacy Behind Reform Math

Reform [constructivist] math educators want easy, stress-free math, so they reject memorization and practice and thereby severely limit the student's ability to remember specific math facts and skills. Without specific remembered knowledge, students must regularly revisit shallow content and rely on general content-independent skills, such as "draw a picture" or "make a list."    

Traditionally, K-6  math is the first man-made knowledge domain where American children build a remembered knowledge base of domain-specific content, with each child gradually coming to understand hundreds of specific ideas that have been developed and organized by countless contributors over thousands of years. With teachers who know math and sound methods of knowledge transmission, the student is led, step-by-step, to remember more and more specific math facts and skills, continually moving deeper and deeper into the structured knowledge domain that comprises traditional K-6 math.  This first disciplined knowledge-building experience is a key enabler, developing the memorizing and organizing skills of the mind, and thereby helping to prepare the individual to eventually build remembered knowledge bases relative to other knowledge domains in the professions, business, or personal life.

The ongoing strength of our information-age economy depends fundamentally on a ready supply of millions of knowledge workers who can learn to understand and extend thousands of specific knowledge domains, from aeronautical engineering and carpentry to piano tuning and zoology.  Although the specific facts, skills, and organizing principles differ from domain to domain, genuine domain experts must necessarily remember a vast amount of specific information that is narrowly relevant to their targeted knowledge domains, frequently without the possibility of transfer to other domains.

Who is Bill Quirk? 

Bill Quirk is a graduate of Dartmouth  College and holds a Ph.D in Mathematics from New Mexico State.  Over a span of 8 years, he taught 26 different courses in math and computer science at Penn State, Northern Illinois University, and Jacksonville Unversity. For a 15 year period, beginning in 1981, Bill developed and presented courses dealing with interactive systems design.  His company, William G. Quirk Seminars,  specialized in software usability and served hundreds of organizations,  including AT&T, Bank of America, FDIC, Federal Reserve Board, General Electric, General Foods, Harvard Business School, Hewlett-Packard, Hughes Aircraft, IBM, MIT, Mobil Oil, NASA, NIH, Texas Instruments, The Travelers, and The Executive Office of the President of the United States.  Beginning in 1996, Bill embarked on a public service endeavor to help parents besieged with reform constructivist math programs.  He is a major contributor to Mathematically Correct and a national advisor to NYC HOLD and a co-author The State of State Math Standards 2005
Bill Quirk lives in Boynton Beach FL and Guilford, CT.


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