Mathematics Instruction Needs Discussion

Recent local events show the need for much greater discussion of mathematics instruction at all levels of pre-college (K-12) education.  K-12 education is generally obtained either from a public school system or from a private school.  This discussion and links is interested in public schools. 

There is a continuing decline in the number of technical degrees awarded to US residents.  In fact, the only growth area in technical degrees is for business computing.  Degrees in mathematics, physics and engineering all show declines since 1990.  At the same time, the technical job market has expanded dramatically leading to a disparity between jobs and qualified people.

Parents in public schools have some opportunity to influence school policy.  The effort required can be surprising.  Here are some of the techniques available:

First, we must learn something about K-12 mathematics.  I prefer to find sources other than the people trying to sell us their textbooks.  The Math Links page is such a collection and it does include links from the suppliers or developers of texts proposed for local use (even if I disapprove of them).  I do not endorse these documents although I agree with many points in several. 

Learning about K-12 mathematics is challenging.  There are at least two major camps of thought in K-12 mathematics.  One view holds that the primary responsibility of K-12 math is to prepare students for life after high school as if those students do not go to college.  This view also holds that the only legitimate goal of K-12 mathematics is to assure that the least prepared student is adequately prepared.   That is, the only goal of K-12 math is to "bring up the bottom."   This appears to be the view of the National Council of Teachers of Mathematics (NCTM).  Some will undoubtedly challenge me on this, but the NCTM's 2000 standards show this quite clearly in the general discussion of high school curricula.  Also, the courses designed to follow NCTM guidelines (1989 or 2000 standards) also show great attention to the bottom and a decapitation of the top.

The other view, to which I subscribe, believes that as worthwhile and socially desirable as "bringing up the bottom" may be, more is needed because a blind implementation of NCTM curricula results in "bringing down the top."     About 75% of US high school graduates immediately attend a 2 year or 4 year college.  These students should be prepared to continue their mathematical educations without repeating material.  That is, they should not find themselves required to take remedial mathematics courses if they did well in high school math courses.  To be less vague, if a student got a "B" or better in their last high school math course which was called "pre-calculus" then that student should be able to take "calculus" in college.  Occasional exceptions would be disappointing but a consistently large percentage having to repeat high school math in college is a concern.

The discovery made in California in 1995 or so was that nearly 90% of the students who needed to take calculus in college first needed to take pre-calculus.  My rough estimates for Washington State suggest that a similar disaster has already reached us - but we simply do not know it.  By disaster, I mean that it looks like 80% to 95% of the students at the University of Washington, Seattle needing serious math need to take remedial math first.  This estimate is quite rough and there may be more reliable data available to the university if not to the general public.  The UW is the most selective of the public universities and colleges in Washington, so we can expect worse results at other schools.

Bringing this closer to home, the 1992 California Mathematics Standards and Frameworks are among the documents a Washington commission relied on to develop the Essential Academic Learning Requirements (EALRs) and then to move on to the Washington Assessment of Student Learnings (WASL).  About the time that Washington finished the EALRs, California junked its original standards and frameworks completely.  The 1997 California standards are very different from the 1992 standards. 

Here is a suggested reading list for newcomers to the debate:

This is not an exhaustive list, of course.  This is intended as a quick start-up to forming an informed opinion.

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Last modified: July 21, 2001