I am feeling like an infidel who
has been permitted to sit in on the Council of Clermont and listen to Pope
Urban II call for the first Crusade. It wasn't a total surprise -- last spring
Washington took its place among the battlegrounds for the Math Wars. A group of
parents with various complaints about the teaching of mathematics, many of them
legitimate, gathered together. Their will and energy are admirable.
Unfortunately the solution they propose is to throw out everything that the
state has been working on for the past ten or fifteen years, as well as
everyone who has been working on it. There may also be suggestions for what to
do once the assault succeeds, but the only ones I have heard hitherto have
been "Be like California!", or possibly "Be like Singapore!"

On Friday, at their
invitation, we had a visit from Jim Milgram, arguably the originator of the
Math Wars and certainly the five star general of Mathematically Correct. With
him was his colleague and collaborator David Klein. Both spent the day at the
University of Washington. One may say many negative things about Jim Milgram
(and I am about to), but of his sincerity and the energy he is willing to pour
into his cause there can be no criticism. I know of a Thursday evening dinner
meeting, and on Friday a radio talk show, a TV interview, a lunch meeting, a
two hour presentation in the afternoon and another in the evening. Impressive
-- especially given that he was still going strong as the evening presentation
ran into overtime.

My own connection to his visit
began with the talk show, which went very smoothly -- almost too smoothly, in
fact. I wished some of his off-hand comments, such as that he doesn't believe
in any of the research on learning that has been done in the past decades, had
been picked up for amplification. When I pursued that comment later he said he
liked the work of some of the Russians in the 30's and 40's and some parts of
Vygotsky's work, but felt the rest was worthless. I think his casual rejection
of a half-century's worth of work in mathematics education and educational
psychology might interest a lot of people. On the other hand, I did appreciate
the level of civility maintained for the hour's program, so perhaps my
complaints should be taken with a grain of salt. . You can hear the show,
if you like, by going to http://kuow.org/ , clicking on "podcasts"
(no, it does not require an i-pod!), then "Weekday--First Hour", then
"Finding Common Ground in the Math Wars".

The afternoon session, on the
other hand, even though I was braced for it, still shocked me a bit. It was
addressed to a campus audience, with a fair amount of "We academics know
that...". I hope that we academics were generally able to notice that in a
field which is unquestionably very much in debate he never stated anything as
opinion, or considered the possibility of interpretations different from his
own. I was particularly struck by the problem he presented in which students
were given the first five entries of a function table and asked to fill in the
sixth, describe why they had chosen that particular value and justify the
choice symbolically, verbally or with a diagram. Milgram spent a considerable
amount of time holding this problem up for ridicule, pointing out that there
are an infinite number of correct answers, and giving a few absurd ones. He's
right that the problem as stated had an error. Instead of saying "Give the
value for s when r = 6 and justify it", it should have said, "Give
*a* value for s when r = 6 and justify it." Others of the considerable
collection of essentially isomorphic problems that he used to demonstrate the
horrible state of mathematics in the schools I agreed with him more on, having
been annoyed by such problems on standardized tests when I was in grade school.
On the other hand, he ridiculed the whole idea of mathematics as a
science that uses patterns, and poured scorn on a statement in one of the sets
of standards to the effect that students should be allowed to experiment with and
justify ideas ("Never knew math was an experimental science, did you?
(chuckle, chuckle)"). It caused me to wonder how he managed to do his
research without generalizing (i.e., following up on a pattern) or checking to
see which version of a statement might work (i.e., experimenting with
it.)

The evening session managed to be
worse. This session was the centerpiece of the visit -- a presentation directed
to the members of "Where's the Math?" (the local branch of
Mathematically Correct) and the folks they had invited with an eye to
recruiting them. With a sympathetic audience that they really could wow with
their academic credentials, he and Klein ratcheted up their sarcasm and very
successfully swept away any possibility of disagreement by producing a caricature
of any opposing view and lampooning it for laughs. I was especially impressed
by Klein's method of disposing of anyone subscribing to constructivist theories
as being a romantic who believed, like Rousseau, that a child's knowledge
should be left in freedom to grow on its own, like the trees in the forest. He
got a good laugh out of that each time he used it. I was struck by the
parallels between his use of the word "Constructivist" and the
use of the word "Communist" in my youth.

In fact, that parallel became even
more striking at the end, with Milgram and Klein's exhortation to
"Where's the Math":

-Go to the legislature and make
them get rid of everyone in the OSPI from the Superintendent herself on down
who has in any way been involved in the past ten years' work on the state
standards and the WASL.

-Get rid of the standards and
replace them with a set of "world class standards." Get rid of any
vestige of any "Reform" curricula (they didn't quite say to burn
them).

-Make sure that no one in power
has been involved in any curriculum development or had anything to do with the
National Council of Teacher of Mathematics.

-Make sure that no decision is in
any way influenced by any educational research or anything else that might have
been said by anyone from a College of Education.

- Install a really good set
of textbooks (currently Milgram is favoring ones now being produced in Russia,
which are even better than the revered Singapore curriculum

- Be sure to keep all power
in the hands of mathematicians and good teachers. It was implicit in the
instructions that mathematicians who do not agree are classified as mathematics
educators (a rung or two below the night custodian), and teachers who have any
sympathy with constructivist notions are not good teachers.

The focus, strikingly, was
on destruction, with an almost complete lack of discussion of its follow-up.
There were frequent references to the weak mathematical background of American
teachers, especially as compared to countries like Hungary and Singapore,
but no hint of a suggestion how the newly empowered mathematicians and
classroom teachers could deal with that (very real) problem. And most notably,
in the entire day's discourse, in all its forms, there was no reference to what
might best enable children to learn. He appears to believe that, with a really
good textbook based on world-class standards, children will learn mathematics
by sitting, rapt, and absorbing everything the teacher and the book tell
them.

This is the kind of handling that
we have come to expect in our politics (a friend of mine dubbed Milgram
"Rush Limbaugh with a PhD"). Milgram makes heavy use of his status as
a research mathematician and respected academic. I am willing to assume that
Milgram's position as full professor at Stanford University means he is a
highly qualified research mathematician. But how can he claim academic
respectability when his definition of a good collaboration is one in which the
other party sees the light and imitates him? He praised the new NCTM Focal
Points, remarking that he had had considerable influence on them and smirking
slightly over their similarity to his version of California's Standards. And
indeed they are similar if one expunges, as he did, all reference to
understanding or building on understandings. How can he claim academic
respectability when his response to the fact that he is laying down the law on
an issue about which he knows nothing -- how people learn -- is to dismiss all
research in the field because it happens to conflict with his ideology? How can
he use his academic position to carry out the sort of smear and sneer campaign
that we have quite enough of elsewhere in our national life?