Over the course of my newslettering I think there has been only one time when the content of a newsletter was mostly written by someone other than myself. Today, however, I received a document that says so articulately and clearly the things I have been attempting to say that I am going to reproduce it whole. I need to explain the context a little first: earlier this year, President Bush put together a National Mathematics Panel whose mandate is to study the state of mathematics education in the United States and then to recommend "best practices" and how to encourage them. Since the panel is heavily populated with right wing members, it has been closely watched, with increasing distress on the part of many of us. Last week Sherry Fraser decided to set the record straight. I have not met Sherry, but she certainly has my admiration and undying gratitude.
For a concise sketch of the background of the current situation, and to build some understanding of why even those of us who set out determined to maintain our equanimity have wound up deeply angry and have at times even appeared paranoid, read Sherry's testimony:
National Math Panel Testimony
Stanford, California
November 6, 2006
Good morning. My name is Sherry Fraser and I have been involved in
mathematics education for over 30 years. I have a degree in mathematics and
taught high school in Buffalo, New York, Los Angeles, California, and in
the San Francisco Bay Area. I am one of the developers of the Equals
program and the Family Math program that originated at the Lawrence Hall of
Science, University of California at Berkeley. I am also one of the
developers of the Interactive Mathematics Program, a high school curriculum
designed to meet the needs of all high school students. All three of these
programs have spread worldwide and through these programs I've had the
opportunity to visit high schools and classrooms around the world. The
transcripts of the previous meetings of this panel trouble me and I want to
be certain several points about school mathematics education become part of
the record. That is why I am here today.
1) We have failed our kids in the past when we paid most of our attention
to the list of mathematical topics that should be included in a curriculum
without factoring in how students learn, without giving attention to what
might be the best teaching strategies to facilitate that learning, and
without giving serious attention to providing access to important
mathematics for all students.
How many of you remember your high school algebra? Close your eyes and
imagine your algebra class. Do you see students sitting in rows, listening
to a teacher at the front of the room, writing on the chalkboard and
demonstrating how to solve problems? Do you remember how boring and
mindless it was? Research has shown this type of instruction to be largely
ineffective. Too many mathematics classes have not prepared students to use
mathematics, to be real problem-solvers, both in the math classroom and
beyond as critical analyzers of their world.
Unfortunately my experience and probably most of yours is what we refer to
today as the "good old days." This was when students knew what was expected
of them, did exactly as they were told, and learned arithmetic and algebra
through direct instruction of rules and procedures. Some of us could add,
subtract, multiply, and divide quickly. But many of us just never
understood when to use these algorithms, why we might want to use them, how
they worked, or what they were good for. And it showed. In 1967, when U.S.
mathematics students were compared to their peers in the First
International Mathematics Study, the U. S. learned there was a positive
correlation between student achievement at the middle school and students'
view that mathematics learning is an open and inquiry-centered process. In
the Second International Mathematics Study, in 1981, teachers were still
using whole-class instructional techniques, relying heavily on prescribed
textbooks, and rarely giving differentiated instruction on assignments.
Twenty years later, the Third International Study just reinforced what we
should have already known. We were doing a poor job of educating our youth
in mathematics.
2) This crisis in mathematics education is at least 25 years old. I
remember in the 1980's when the crisis in school mathematics became part of
the national agenda with such publications as An Agenda For Action (NCTM,
1980), A Nation at Risk (National Commission of Excellence in Education,
1983), and Everybody Counts: A Report to the Nation on the Future of
Mathematics Education (NRC, 1989). Those of you on the board who have been
involved with mathematics education should remember these documents as
well. Our country was in trouble. We were not preparing students for their
future. Sure, some could remember their basic facts, but that wasn't
enough. Something different needed to be done if our country was going to
compete in a global economy.
It was at the end of that decade that the National Council of Teachers of
Mathematics released their Curriculum and Evaluation Standards for School
Mathematics (1989). Contrary to what you hear today, they were widely
accepted and endorsed. This set of standards had the potential to help the
American mathematics educational community begin to address the problems
articulated throughout the 1980's.
Shortly after publication, the National Science Foundation began funding
the development of large scale, multi-grade instructional materials in
mathematics to support the realization of the NCTM Standards in the
classroom. Thirteen projects were funded. Each of the projects included
updates in content and in the context in which mathematics topics are
presented. Each also affected the role of the teacher. Each has been
through rigorous development that included design, piloting, redesign,
field-testing, redesign, and publication. This amount of careful
development and evaluation is rarely seen in textbook production.
3) These NSF projects were developed to address the crisis in mathematics
education. They did not cause the problem; they were the solution to the
problem. Their focus went beyond memorizing basic skills to include
thinking and reasoning mathematically.
4) These model curriculum programs show potential for improving school
mathematics education. When implemented as intended, research has shown a
different picture of mathematics education to be more effective. In fact,
the U.S. Dept of Education, through an act of Congress, evaluated
mathematics programs, K-12, and in 1999 found five programs that deserved
exemplary status. One of the criteria was that the program must have
evidence that it made a measurable difference in student learning. The
program had to provide evidence of gains in student understanding of
mathematics, evidence of gains in inquiry, reasoning, and problem solving
skills, evidence of improvements in course enrollments, graduation rates,
and post-secondary school attendance and evidence of improved attitudes
towards learning. Three NSF curriculum projects met all the criteria and
received exemplary awards from the U.S. Department of Education.
Another study by the American Association for the Advancement of Science
(AAAS) evaluated 24 algebra textbooks for the potential to help students
understand algebra and, once again, the NSF-funded curriculum programs
rated at the top of the list. And in 2004 the National Academy of Sciences
released a book, On Evaluating Curricular Effectiveness: Judging the
Quality of K-12 Mathematics Programs, which looked at the evaluation
studies for the thirteen NSF projects and six commercial textbooks. Based
on the 147 research studies accepted it is quite clear which curriculum
programs have promise to improve mathematics education in our country. They
are the NSF-funded curriculum projects.
5) You might be asking yourself why hasn't mathematics education improved
if we have all this promising data from these promising programs?
Let me use California as an example.
In 1997 California was developing a set of mathematics standards for K-12.
A State Board member hijacked the process. She gave the standards, which
had been developed through a public process, to a group of four
mathematicians to fix. She wanted California's standards to address just
content and content that was easily measurable by multiple-choice exams.
The NCTM standards, which the original CA standards were based on, were
banned and a new set of CA standards was adopted instead. This new set
punished students who were in secondary integrated programs and called for
Algebra 1 for all 8th grade students, even though the rest of the world,
including Singapore, teaches an integrated curriculum in 8th grade and
throughout high school. The four mathematicians and a few others called
California's standards "world class". But saying something is world class
doesn't make it so. In fact, we now have data to show these standards
haven't improved mathematics education at all. Most of California's
students have had all of their instruction based on these standards since
they were adopted almost ten years ago. Yet, if you go to the California
Department of Education's website on testing and look at the 2006 data you
will find that only 23% of students are proficient in Algebra I by the end
of high school, a gain of 2 points over four years. At the Algebra II
level, only 45% of California's students actually take the course and only
25% of those are proficient. This is a loss of four percentage points over
the last four years. (www.cde.ca.gov/ta/tg/sr/documents/yr06rel89summ.pdf)
Three years of college preparatory mathematics is required, four
recommended, for entrance into our colleges and universities, yet less than
12% of California's high school graduates now have the minimum
proficiencies expected by higher institutions. And these numbers don't even
take into account the 30% of California students who drop out of high
school. World class? Hardly. California is one state you do not want to
emulate or look to for solutions to the problems in mathematics education.
Why, then, do you read in newspapers about how terrible the mathematics
programs developed in the 1990's are and how successful California is? It
has to do with an organization called Mathematically Correct, whose
membership and funding is secret. Their goal is to have schools, districts,
and states adopt the California standards and they recommend Saxon
materials as the answer to today's problems. They are radicals, out of the
mainstream, who use fear to get their way.
I urge this panel to look at the data and make recommendations based on the
desire to improve mathematics education for all of our students. Direct
instruction of basic skills does not suffice. Moving backwards to
ineffective habits does not make sense. Our children deserve more. Thank
you.