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:
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.
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.