The Statement Of James Milgram, Professor Of Mathematics, Stanford University, Stamford, California.

Mr. Milgram. Okay. Mr. Chairman and everyone, I am honored to be here today to talk about the state
of mathematics in this country with the distinguished members of this joint committee.

Let me start out by saying that the K through 12 teachers in this country are dedicated professionals.
I have the utmost respect for them. But all too often their knowledge of mathematics is extremely
superficial, and when this happens they are easily swayed by trendy and unproven programs which
typically offer a superficial or shallow treatment of the subject, leading to weak backgrounds in
their students.

I am a research mathematician at Stanford University, but two things obligated me to spend much of
my time for the past three years studying issues related to K through 12 mathematics. The first was
a sequence of courses I gave in New Mexico where I had too many bright, very highly motivated students
in my math classes, whose third-rate K through 12 educations in mathematics could not be overcome no
matter how hard these students were willing to work.

The second came from the Commission designing President Clinton's proposed national 8th grade
mathematics exam. The Commission, including many of the foremost math education specialists in the
country, distributed a list of 14 proposed problems. I and my colleagues at Stanford were amazed to
find that three of the problems have serious errors. One was so ill-posed that it could not be solved,
one had an incorrect solution included with it.

We later testified to that Commission about these difficulties, and it became clear that the level of
mathematical understanding on the part of the educators . . . math educators on that panel was
unimpressive. I was disturbed when I realized that it is these people who are determining the
mathematics that our children learn in school.

I was especially disturbed in view of the dramatic drop in content knowledge that we have been seeing
in the students coming to the universities in recent years.

This has been mentioned. Since 1989, the percentage of entering students in the California state
university system, the largest state system in the country, that were required to take remedial courses
in mathematics has increased almost two and a half times from 23 percent in 1989 to 55 percent today.
And CSU's mission is restricted to the top 30 percent of high school graduates.

This failure has important consequences for the nation. Although large numbers of U.S. students entering
the universities say they are interested in majoring in technical areas, very few get such degrees today.
In fact, the number is approximately 28,000 annually.

On the other hand, there are about 100,000 new jobs in these areas each year. Last year, Congress had to
mandate an additional 142,000 new work visas for technically-trained people, and these visas were used
up by June 11, 1999, so great was the demand for these qualified non-citizens. A large part of the blame
rests with the mathematics programs of the type recommended by the Department of Education recently as
exemplary and promising.

These programs are all designed to closely align with the 1989 NCTM math standards . . . standards which
explicitly assume that calculators are always available, and as a consequence of this students never
develop a mastery of basic arithmetic operations.

The standards also require . . . and this is, in a way, more important . . . that skills in algebra be
downplayed. And as was mentioned, again, skills in algebra . . . not the formal skills with changing
letters, understanding that numbers can be represented by letters, but the skills with symbolic
manipulation . . . are the single most important determining factor for success in college.

And so let me explain this a little more. The co-chairman of the expert panel, Steven Leimwand, who was
also one of the designers of the 1989 NCTM standards, recently stated that the curricula endorsed by the
Department of Education, and I quote, ``create a common core of math that all students can master.'' Not
material that all students need to know or should master, simply material that he believes all students
can learn.

The support for these programs in the Department of Education is ultimately the responsibility of EHR at
the National Science Foundation. EHR funded the development of at least six exemplary and promising
programs. And it is also probably worth noting that at the present time there is no valid research that
shows that any of these programs of this type are effective.

In conclusion, I believe that the sad state of mathematics knowledge among high school graduates in this
country is primarily the responsibility of two agencies . . . the Department of Education and Human
Resources at the NSF, and the Department of Education. The programs they develop and aggressively push
simply set too low a standard.

Thank you.