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K-12 Math Education

Essays By Bill Quirk

What is Math Reform?

The National Council of Teachers of Mathematics (NCTM) equates "math reform" with the ideas currently found in Principles and Standards for School Mathematics (PSSM), a 402 page revision of  the NCTM Standards.  The NCTM calls it "standards-based" math.  Opponents call it "fuzzy" math or "new-new math."  Regardless of the name, "reform math" is characterized by a rejection of traditional K-12 math content and an endorsement of  "constructivist" teaching methods.

The NCTM has redefined the meaning of "K-12 math content."  They believe that that $5 calculators now cover most of arithmetic, graphing calculators now cover most of algebra, and computers now cover most of the remainder of K-12 math.   The NCTM also claims to be worried about students who have difficulty learning math.  Although they won't admit it, they also know that most teachers don't know much math.  Putting it all together, the NCTM emphasizes math appreciation and social goals, not traditional math content.  They promote easy, everyday math, with the constant use of hands-on manipulatives and calculators.

The NCTM is also excited about "constructivist" teaching methods.  Purists will argue about the meaning of this term, but this philosophy is associated with the following beliefs:

  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.

The Key Fallacy Behind Fuzzy Math (Constructivist Math)

Fuzzy math "thinkers" reject the need to remember math content. They believe it's possible to separate (NCTM-valued) "thinking skills" from the (NCTM-despised) step-by-step process of building a remembered knowledge base (in the brain) of specific math facts and skills. This is the key fallacy behind the new-new math.

Traditionally, K-12 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 child is led, step-by-step, to remember more and more math, continually moving deeper and deeper into the structured knowledge domain that comprises traditional K-12 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 information that is narrowly relevant to their targeted knowledge domains, frequently without the possibility of transfer to other domains.

But this old-old fact is too sad for today's new-new educationists.  So they deny it!  They reject the importance of content knowledge stored in the brain. They preach the power of general, content-independent skills, and believe it's possible to become an expert in any knowledge domain without remembering domain-specific facts and skills.  They argue that knowledge is changing too fast, and that today's content will be irrelevant tomorrow. They say the new-new way is to depend on reference materials and computer tools to access "just in time" facts.

Who is Bill Quirk? (wgquirk@wgquirk.com)

Bill Quirk is a graduate of Dartmouth College and holds a Ph.D. in Mathematics from The New Mexico State University. Over a span of 8 years, he taught 26 different courses in math and computer science at Penn State, Northern Illinois University, and Jacksonville University.

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, and The Travelers.

Beginning in 1996, Bill embarked on a public service endeavor to help parents besieged with new "math" programs.  He is a major contributor to Mathematically Correct (http://mathematicallycorrect.com/) and a national advisor to NYC HOLD  ( http://www.math.nyu.edu/mfdd/braams/nychold/).

Bill Quirk lives in Guilford, Connecticut.

About This Site

We are opposed to the NCTM version of "math reform."   We know that math is a vertically-structured knowledge domain, with arithmetic as the foundation.  We know it can be all over by the end of the fifth grade, if a child hasn't mastered the facts and skills of pencil-and-paper arithmetic.  We are concerned about the math education of all students.  We know that the poor suffer most from NCTM math, because there's no supplemental input from tutors or well educated parents.

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About Copyright

You may print and distribute essays by Bill Quirk.  You may sell copies to recover printing costs, but not for profit.

Copyright 1997 - 2003 William G. Quirk, Ph.D.