By Ellen Hoerle
June 7, 2005
Letter to the Editor
The Washington Post
(Not published)
Dear Editor,
Jay Matthew's attempt to bring clarity to the math wars ("10 Myths (Maybe) About Learning Math", May 31, 2005) was unsuccessful. He gave National Council Teachers of Mathematics (NCTM) the last word, even though their document "Principles and Standards for School Mathematics" (P&S) was written without input from Users or Scholars of mathematics. As a result, the document redefines mathematical proficiency as anything goes, rather than a set of specific skills Users and Scholars of mathematics have found to be necessary to ensure success and define competence in their selected careers. P&S appeals to many teachers because it (and NCTM's responses in Matthew's article) lends credence to the idea that success can be defined differently with each student, with each teacher, and in each classroom and that there is no one way to teach math successfully, to learn math successfully, or to compute and solve problems successfully. In reality, the NCTM and their P&S document facilitate a great tragedy -- they unwittingly sanction woefully under-prepared teachers to hold their students to a level below their own competency and rob many students the opportunity to reach their full potential and true mathematical proficiency.
NCTM's statement, "the issue of effectiveness is more likely to be attributable to instruction than to any specific curriculum" is all too true, but this statement's purpose is to deflect criticism away from curriculums inspired by NCTM's P&S, not to focus attention on much needed improvement in teacher training and preparation that would actually improve effectiveness. In fact, their last statement appears to contradict the statement above by summarizing the group's main focus--to "support local communities using P&S as a focal point in the dialogue to create a curriculum that meets their needs." So which is it? If NCTM insists, "we have the responsibility to teach them all" what is more likely to contribute to reaching that goal? Improving effectiveness of teachers, or using a curriculum guided by their P&S?
NCTM's responses in Matthew's article are peppered with phrases that make it appear the group promotes computational accuracy and efficiency, learning basic math facts, and to "think, reason and apply mathematics". Their response to Myth #1, however, "Students must build their skills on a strong foundation of understanding" succinctly states their overriding philosophy. In their view, computational accuracy and efficiency is not developed through practice or repetition, but rather through understanding of why math works. In their own words in response to Myth #3, "What is most important is that an algorithm works and that the student understands the math underlying why it works." In other words, multiplication tables should not be learned through memorization exercises dubbed "drill and kill", but by understanding that multiplication is really repeated addition. The theory is that if a student understands that multiplication is repeated addition, and is required to demonstrate his or her understanding of this concept repeatedly when solving trivial problems, students (especially the bright ones) will discover math is unbelievably mundane and become bored out of their minds. No, that's not it. The teacher will need to spend less classroom time developing computational proficiency because the student's understanding of why math works will miraculously lead to mastery of computational and problem solving skills. Yeah, that's it.
It is the disproportionate amount of emphasis placed on requiring demonstration of understanding of the most basic concepts versus challenging students to solve complex problems accurately (which just happens to conveniently provide proof and an objective way to determine if students truly understand and builds a sense of accomplishment at the same time) that squelches so many of our students' desire and ability to develop true mathematical proficiency. This in turn places our nation's ability to compete in the new global economy at risk. Currently, China produces four times as many engineers as the United States, the European Union, three times as many, South Korea, with one-sixth the population, nearly the same number, and Japan, with less than half the population, twice as many engineers as the U.S. Yet NCTM's response to evidence that students from these same countries repeatedly outperform U.S. students is to claim NCTM's P&S "also recognize[s] the needs of 21st century learners." When is it going to occur to NCTM that "the needs of 21st century learners" are to reach a level of mathematical proficiency that allows those learners to participate on the same playing field with learners in other countries? When is going to occur to Jay Matthews that NCTM and their P&S are completely irrelevant when it comes ensuring our students will be prepared to compete in the new global economy? They neither earned nor deserve the right to have the last word, much less participate in the debate.
Ellen Hoerle
Eden Prairie, MN 55347
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