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I’ve been teaching math at the college level for several years now, and many years ago taught some math on lower levels, but only recently have I become aware of the trends in math teaching of the last decade or so. In 2002 I became aware that the National Council Of Teachers Of Mathematics had published the “Standards” in 2000, so I decided to find out just what the standards said. I found them on the internet, and over the course of a few months studied enough to decide that there were some things to disagree with. In fact I decided I would write an article on my disagreements with the standards, and perhaps I could get it published. The writing went slowly for a number of reasons, but finally in February 2004 I sent my article to the editors of The Mathematics Teacher, hoping that they would publish it. Then I began to learn more about the “California math wars”, and the more I learned the more it became apparent that the NCTM would not be interested in my article. Click here for Some Disagreements With the Standards
The opposing sides of the “math wars” can be framed in different ways. Some would argue that reformers want to teach in new ways which use higher order thinking skills and stress understanding, while the “traditionalists” want to continue teaching by stressing rote memorization. Others would argue that the reformers are entertaining unrealistic ideals that have been tried, and abandoned, many times in the past, and that the “traditionalists” are really pragmatists who stick to tried and true methods simply because they are effective. I am of this latter view. Others might view the opposing sides as “child centered” versus “teacher centered”, or as “learner centered” versus “subject matter centered”. Yet another way to frame the sides has advocates of “constructivist methods” opposed to the advocates of “direct instruction”. In general I think it can be said that the two sides are advocates of the ideas favored by the NCTM versus the critics of those ideas. The critics like to use the term "fuzzy math" for the NCTM favored ideas.
A few of the basic facts of the California situation are as follows: In 1992 California adopted state math standards “aligned with” the NCTM standards. These state standards endorsed a number of math texts, or series of texts (“programs”), and local school districts began to adopt these. Substantial parent opposition ensued. HOLD (Honest and Logical Debate) and Mathematically Correct are two California organizations started in 1995 in opposition to this “new math”. Similar organizations were begun elsewhere. In 1997 the critics in California prevailed and new state standards were adopted that reverted to more sensible (some would say “traditional”, others would say “back to the basics”) ideas. In 1999 U. S. Secretary of Education Richard Riley issued an list of a number of math programs, all aligned with the Standards, endorsed as either “exemplary” or “promising”. This elicited a response from a number of mathematicians, who disagreed. Within a month over 200 people, mostly mathematicians, signed an “Open Letter” to Secretary Riley, published in the Washington Post, stating their concern with these programs and asking that the endorsements be withdrawn.
This open letter (or a link to it)can be found on the internet at the Mathematically Correct website, which is http://www.mathematicallycorrect.com. There are also many other links to sites of interest. I have not been able to explore them all yet, but one very important one is a rather long article by David Klein about the recent history of math teaching in America. I have been studying this for a month or so now and have found it to be most valuable.
I have a personal interest in these matters, not only as a math teacher, but also as a parent. There has been some reason to believe, or at least to suspect, that my children received a math education in some ways inferior to what I received as a child. Of course this is very hard to judge. What I remember learning in eighth grade math may be very much colored by my subsequent education and experience in math. At any rate, when my youngest daughter was in the seventh grade I was so impressed by her seventh grade math book that I spent a lot of time with it, and over a period of months wrote up my thoughts on it, which were not favorable. This was at a time when I had not taught or studied math for a number of years, and a couple of years before I decided to get back into math on the graduate level. I wrote it primarily as a way of organizing my own thoughts.Click here for Chicago Math.
And I want to mention a book that I have found invaluable, Left Back, by Diane Ravitch. It’s a history of American education through the 20th century. I have been amazed how far back the current educational trends go. Some ideas that excite educators today also excited educators in the 20’s and 30’s, until they got swept under the rug as other fads took their place. All of these ideas can be called progressive education. At times progressive education had a very individualistic flavor, at other times a collectivist flavor, sometimes both at once. At times progressisve education was anti-intellectual. At other times it had intellectual pretensions (such as now). It has always invoked "democracy", but with different meanings at different times. I would argue that the only common thread among all the ideas that have made up progressive education would be the idealistic promise of enlightenment, at long last, as if the history of education began yesterday morning. I wonder if the advocates of the various “reforms” constantly being promoted have much knowledge of the history of their ideas.