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Curriculum and Evaluation and Professional Standards for Teaching Math-
ematics (NCTM, 1989, 1991).
Responsibility for public education in the United States is a state and lo-
cal function, with day-to-day decisions about curriculum and teaching under
the control of over 16,000 local school districts. Some of those districts are
quite large, with substantial supervisory staffs attending to the quality of in-
struction in each discipline at each level of schooling. But most are quite
small, with limited resources to support curricular innovation or teacher pro-
fessional development. Therefore, the complex array of advice from the
mathematical, psychological, and educational research communities tends to
have only modest impact on local decisions. There is no national curricu-
lum. In fact, in most school systems, curriculum development involves only
selection of text materials from the offerings of, generally cautious, com-
mercial publishers. That selection is made with strong influence by class-
room teachers whose decision criteria are shaped primarily by personal ex-
perience in the classroom.
The difficulty of stimulating major reform in the curriculum or teaching
of school mathematics has always been a frustration to national professional
leaders. The history of American mathematics education in this century is
marked by sporadic advisory reports from concerned professional organiza-
tions. The recommendations in those reports tend to spur activity at the sur-
face of the profession, but seldom have the innovations been broad and per-
manent (NACOME, 1975). However, in the last decade, concern about the
quality of mathematics and science education has been an issue in state and
national political debates. The need for national leadership in reform has
gradually overcome the natural American antipathy toward ideas like a na-
tional curriculum or national assessments of educational achievement. In
this context, the National Council of Teachers of Mathematics undertook
two projects to develop professional standards for curriculum, evaluation,
and teaching that could guide schools and teachers across the country.
The NCTM Standards, published in two volumes (NCTM, 1989, 1991),
provide recommendations on three fundamental questions: What mathemat-
ics is most important for students to learn? What is the most effective way
to teach that mathematics? How should the effects of mathematics teaching
JAMES T. FEY

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be assessed? The processes and products of those standard-setting efforts
give interesting insights into the ways that mathematical ideas are trans-
formed into school curricula in a loosely structured system with many dif-
ferent interested parties.
First, membership on the committees to draft standards did not include a
single academic mathematician or psychologist active at the research fron-
tiers of mathematics or its teaching and learning. The various subcommit-
tees were made up of outstanding classroom teachers, local and state school
system supervisors, and university teacher educators. While each working
group included members with broad understanding of mathematics and con-
temporary research on student learning, that knowledge was applied to de-
sign of school mathematics programs with additional insight gained from
years of classroom experience.
The Standards' emphasis on a practitioner's perspective explains a second
noteworthy feature of the proposals – the recognition that it is virtually im-
possible to separate the mathematical content of a curriculum from the
learning experiences by which students acquire understanding and skill in
that content. At each level (K-4, 5-8, 9-12) of schooling, the Standards rec-
ommend important broad mathematical goals (though not so much detail as
a syllabus for a national examination might require). But each recom-
mended content topic is elaborated by discussion that includes illustrations
of appropriate instructional approaches.
While the Standards' documents are clearly influenced by contemporary
ideas in mathematics (e.g., attention to stochastics and discrete mathemat-
ics) and research on learning and teaching (e.g., emphasis on connections
and active student construction of knowledge), that influence is transformed
into recommendations clearly related to the classroom. In the Curriculum
and Evaluation Standards, recommendations about discrete mathematics
topics are accompanied by examples of practical situations modeled well by
matrices, graphs, and difference equations. In the Professional Teaching
Standards, each recommendation is accompanied by several vignettes of
typical classrooms in action embodying the recommended practices.
The NCTM Standards' projects represent a fundamentally new approach
to the task of reforming American mathematics education and, in the pro-
cess, the transformation of new knowledge about mathematics and its
learning into school curricula and teaching. While previous reform propos-
als have often been drafted by groups dominated by research mathemati-
cians, frequently with the imprimatur of a policy-making group like the
College Entrance Examination Board, the Standards' projects were a grass-
roots operation led by mathematics educators with strong connections to the
mathematical, psychological, and educational research communities, but
also with credible knowledge and connections in school practice. Their
work was not strongly theory-driven, and their recommendations are not