Newsletter #94     Math Pacifism [AWM]

Not long ago a colleague whom I like and trust gave me a severe jolt: because I am rather vocally in support of the views on education commonly labeled the Standards-based reform movement, he attributed to me several quite radical opinions which I do not share at all. My first reaction was to feel attacked and wounded. Later I began to wonder: just how often am I doing the same thing to those who do not support Standards-based reform? While I was brooding about this point, there came to my attention an article written by Judy Roitman in the mid-nineties which in effect supplied the answer to my question: probably quite often. Furthermore it is not only my colleague and I who are making these incorrect assumptions, it is an appalling percentage of the mathematical community. The result is the so-called "Math Wars", which Roitman very articulately maintains to be far more of a perceived disagreement than an actual one. The article itself is too long to reproduce here, and furthermore some aspects of it are now dated (Roitman plans to provide an update for us sometime soon.) What I am hoping to provide here is a capsule version of the portions of her article which resonated with the ideas I was just beginning to formulate.

The most basic of her contentions is that there is no Math War. Real differences of opinion do exist, and there is certainly room for a lot of discussion. However, the tendency of both sides to focus on the most extreme statements from the other side, or to take part of an idea and use it to form a caricature by pushing it to an absurd extreme, has obscured a huge common ground. Roitman lists and responds to some of the most prevalent caricatures:

Some of the false charges made against the NCTM Standards:

  1. No conventional algorithms are to be taught.
  2. Constructivism rules: children must invent all of school mathematics.
  3. Individual work is discouraged: children must not only invent all of school mathematics, they must invent it solely by working in small groups.
  4. Proof is essentially eliminated.
  5. Facility with arithmetic and algebraic manipulations is discouraged.
  6. Mistakes go uncorrected --- everything is okay in ``fuzzy math."
  7. Contextualism rules: all of school mathematics must be motivated by real-world problems.
  8. Teachers never lecture, they facilitate.
Some of the false charges made against critics of the Standards:
  1. Only conventional algorithms are allowed.
  2. Children must do as they are told.
  3. Only individual work is allowed --- worksheet after worksheet after worksheet, with no chance for class discussion.
  4. ``Proof" means dry and dull two-column proofs in geometry of obvious statements from other obvious statements; no other reasoning is encouraged.
  5. Except for Euclidean geometry only facility with arithmetic and algebraic manipulations is the focus of the curriculum.
  6. Mistakes are to be corrected immediately by the teacher, without discussion.
  7. The only word problems allowed are those for which the teacher can present a precise algorithm for solution.
  8. Teachers only talk at students; teachers never listen to students and are insensitive to student needs.
These statements have just enough grounding in truth (it doesn't take very much) to be believable: for example, children in traditional classrooms often spend a lot of time working on worksheets, and children learning from NSF-sponsored curricula often spend a significant amount of time working in small groups. But they are also caricatures: good teachers of all sorts involve their classes in discussion, and children learning from NSF-sponsored curricula also spend a significant amount of time working on their own.

When discussion focuses on these caricatures, we become sidetracked. They are all false, and that is all that needs to be said about them. [from Roitman, Judy. "Beyond the math wars", Comtemporary issues in mathematics education, Gavosto, Krantz and McCallum (ed), Oxford University Press, 1999, pp 123-134]

Elsewhere in the article, Roitman demonstrates the overlap in the views of the two sides by quoting a series of statements, some made by folks strongly aligned with one side of the argument, some by folks strongly aligned with the other. Each addresses some issue on which the sides are commonly held to have irreconcilable differences, and each expresses a view which caricaturists would attribute exclusively to the opposite side.

Her argument, as I say , is highly convincing. Suppose we accept her conclusion: there are no Math Wars. What then, aside from general unpleasantness and acrimony, is the harm from their perceived existence? Well, for a start, there does exist a genuine problem, as almost anyone will agree: far too many of our students are not learning the mathematics they need to learn. It is not a new problem. The results of TIMSS (the Third International Mathematics and Science Study) provoked a great deal of uproar, but in fact we did quite badly on SIMSS (the Second International Mathematics and Science Study) and FIMSS (you guess). Since the latter two antedate the Standards this problem does not represent evidence against the current efforts. The problem of poor math achievement runs deeper than that. How to solve it is not clear. What is clear is that ignoring our areas of agreement and focusing on our differences is not conducive to any kind of solution.

This situation in the mathematical community has been under discussion for a number of years now, as is clear from its central position in Roitman's article (written in 1996). What has changed since she wrote is the stakes. In the nineties most of us were watching, non-plussed but non-involved, the playing out of the Math Wars at the state level in California. Before our eyes, educational decisions turned political and leapt from the hands of educators and mathematicians into those of politicians. But to most of us California seemed far away, and a world unto itself. Surely nowhere else would we see such bizarre handling of matters educational.

Have you looked at DC lately? Education, in particular mathematics education, has suddenly become a highly charged issue at the forefront of the Washington scene. Decisions are being pushed by people whose motivation it is extremely difficult to see as anything but political, and whose underlying objective appears to be to take control of mathematics education away from both educators and mathematicians. Massive mandates which are demonstrably detrimental to current student learning and even more so to the education of future students are in the works and are highly likely to be carried through. These are not plans that one side of the famous Math Wars would support against the other - they are plans that none of us will find acceptable. And even to the extent that some of us may agree with some of their agendas, politics and education make dubious bedfellows. To quote Judy Roitman once more (not from her article) : those who live by the political process may find that later they die by it. Or, more gently put, the political process is often quite non-collegial, with winners and losers who find themselves trading places as political winds ebb and flow.

Do we really want Lynn Cheney making our decisions for us? If not, it is time for us to stop taking pot shots at each other. It is time for us to step back, look around, and join forces in support and protection of what every one of us values: the future of mathematics not just in academia, but in the world at large. --

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