(Many things, and at great length...; I will respond only to one)
> III. MATH EDUCATION IN CALIFORNIA
> In Hake (2003d), I wrote:
>
> "Regarding the STAR [CDE 2003] results I suspect that the gains are
> primarily in low cognitive level skills that are emphasized in the
> California math standards and can be elevated by the drill and practice
> so revered by the Mathematically Correct contingent. But then, as Sowder
> says, this is primarily a question of values."
I am glad that Hake does not dispute the large recorded gains in California
mathematics achievement since the (supposedly "drill and practice") math
standards were adopted in late 1997. Hence, his criticism turns to the
"meaning" of those gains. Hake "suspects" that they are primarily in the
"low cognitive level skills that are emphasized in the California math
standards."
I shall not attempt to convince him that he is wrong about California math
standards, although readers are encouraged to judge for themselves those
"low cognitive skills" by perusing the California Mathematics Framework at http://www.cde.ca.gov/cdepress/math.pdf . I urge you to pay particular
attention to the scope and depth of Framework's sample work, as illustrated
in appendices C, D and E.
It is interesting to note though that Hake, a physicist, chooses to present
the issue as a question of values. In other words, "don't confuse me with
empirical data - I will choose what to think based on my beliefs." Zalman
Usiskin of the University of Chicago, and one of the fathers of the current
math reform movement, was at least open about it:
"Let us drop this overstated rhetoric about all the old
tests being bad. Those tests were used because they were quite
effective in fitting a particular mathematical model of performance -
a single number that has some value to predict future performance.
Until it can be shown that the alternate assessment techniques do a
better job of prediction, let us not knock what is there. The
mathematics education community has forgotten that it is poor
performance on the old tests that rallied the public behind our desire
to change. We cannot pick up the banner but then say the test are no
measure of performance. We cannot have it both ways."
Z. Usiskin. What Changes Should Be Made for the Second Edition of
NCTM Standards. UCSMP Newsletter, n12 p. 10 (Winter 1993)