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OCR for page 87
ACTION
...moving into the 21st century
Over the next two decades, the nation's schools, colleges,
and universities will undergo major transitions in their math-
ematics programs transitions that will involve fundamen-
tal changes in curricular content, in modes of instruction, in
teacher education, in professional development, in methods
of assessment, and in public attitudes. Not only will calcula-
tors and computers displace some of the computational drill
that currently dominates the curriculum, but also their pres-
ence will stimulate new approaches to understanding mathe-
matics and to solving problems. The dramatic advances that
have been made in the mathematical sciences over the past
forty years will start to be felt in the schools, in the form
of new and exciting ways to help young minds perceive and
order the universe around them.
If such transitions are to become reality, all major
components of mathematics education" curricula, teaching,
teacher education, testing, textbooks, and software must
change significantly in some reasonably coordinated man-
ner. National leadership is needed to coordinate efforts by
the primary agents for change and to garner support for them
by government, business, industry, and the public.
T ....................................
In the next decade, the United States has a
historic opportunity to revitalize mathematics
education.
Although many parts of education need improvement,
there are at this time both a particular urgency and a spe-
cial opportunity for reform of mathematics education. Since
mathematics is the foundation of science and technology,
reform is needed to prepare the more highly skilled work
force that the nation now needs. Because of emerging general
agreement within the mathematics, mathematics education,
and related professional communities on goals for mathe-
matics education and means for achieving them, there is at
this time a special opportunity for the nation to push ahead
boldly in this area of education.
87
OCR for page 88
Action
88
National Goals
Our national goal must be to make U.S. mathematics edu
cation the best in the world. Nothing less will be adequate to
fulfill American aspirations. To achieve this goal will require
significant actions that respond to a three-tiered challenge to:
· Make mathematics education effective for all Americans;
· Improve significantly students' mathematical achieve-
ment;
· Develop new curricula appropriate to the mathematical
needs of the twenty-first century.
O·· ···.· ·· ···.·· ·.·.·· -
ur national goal must be to make U.S.
mathematics education the best in the world.
American education is a loosely coupled system grounded
in state and local autonomy, although important factors
(textbooks, standardized testing, teacher education, and uni-
versity admissions requirements) have nationwide influence.
To change mathematics education in the United States, one
must influence not only teachers, but also a host of other
special interest groups that control parts of the educational
system: state and local agencies, teachers and administra-
tors, local and state school boards, colleges and universities,
textbook publishers, software developers, professional soci-
eties, test-makers, state legislators, employers, parents, and
the general public.
Actions designed to begin these transitions must be based
on a broad understanding of the total American system of
mathematics education. Unless change is based on a sys-
tematic overview of all pertinent issues and an assessment
of current programs, it will have very little chance of achiev-
ing national impact.
OCR for page 89
...moving into the 21st century
Reaching Consensus
High-quality mathematics education requires national
consensus on objectives and standards, leaving wide lati-
tude for local variation in means of implementation. With-
out common standards, different communities will move in
different directions, inevitably widening the gap in mathe-
matical power available to children raised and educated in
different circumstances. National consensus on common ob-
jectives should make possible policies that will ensure that
all students benefit equally from the opportunities provided
by mathematics.
" .-- --.--.- ----.---.-----
Duilding national consensus is the first step
in renewal of school mathematics.
Although pressure for change is high, little consensus exists
on what mathematics students ought to learn now, much
less on what they will need for the future. Lack of national
focus has created such disparities among standards that it
is difficult to discuss curricula in meaningful and productive
contexts. Teachers have received such mixed signals that
even the best of them often do not know which choices to
make in those few classes where they have some discretion
over what to teach.
The new Curriculum and Evaluation Standards for School
Mathematics, being published in early ~ 989 by the National
Council of Teachers of Mathematics (NCTM), focuses na-
tional attention on specific objectives for school mathemat-
ics. That report, the draft of which has been reviewed ex-
tensively by teachers and the public, has received widespread
support in the mathematical and educational communities.
It represents the first effort ever to establish national expec-
tations for school mathematics.
In keeping with American school traditions, the Sfanciards
report is not the result of government edict, but the product
89
OCR for page 90
Action
Why Not Just Imitate Japan?
International studies of math-
ematics and science education
show that, when compared with
students in other countries, U.S.
students do very poorly while
Japanese students do very well.
One natural response, therefore,
is to think that we could improve
our educational system by imitat-
ing Japan.
These same studies, however,
document that the social con-
text of education has a greater
influence on student performance
than does actual classroom prac-
tice. Parental attitudes, student
expectations, and teacher self-
respect are among the most sig-
nificant factors in quality educa-
tion and they depend uniquely on
culture.
Imitating others is no solution.
The United States must find a
strategy that builds on the tradi-
tions of this country, one whose
strength lies in this nation's
unique tradition of local initia-
tive and decentralized authority.
90
of the nation's mathematics teachers themselves. It leaves
much leeway for local initiative in implementation and for
teacher ownership of specific curricula. Through the Stan-
dards, parents and teachers will be able to understand in
concrete terms what a school mathematics program might
look like if it is to serve our national objectives adequately.
The ensuing public discussion on feasibility, appropriate-
ness, costs, and benefits will provide an unprecedented op-
portunity to forge national consensus on goals and objectives
for school mathematics.
National Strategy
New strategies for renewal of mathematics education must
be based on what we have learned about making changes
in the extremely decentralized U.S. system where local and
state agencies control education. Two special strengths
of American mathematics education should underpin any
movement for renewal:
· The creative efforts of many teachers, schools, and projects
around the country.
· The strength of coordinated national leadership which has
evolved within the communities of mathematicians and
mathematics educators.
Together, these resources provide an "augmented grass-
roots" mode! of curricular development, harnessing the
power of a centralized system with the flexibility and ini-
tiative of the decentralized U.S. tradition.
The objective of our national strategy must be to make
significant improvements in mathematics education on a na-
tional scale. To do this, we must first reach consensus on the
transitions required to revitalize mathematics education and
then help local educational leaders move mathematics edu-
cation through these transitions. Inevitably, this process will
lead the American public into uncharted territory, paving a
new road for mathematics education that balances national
goals with local jurisdiction.
OCR for page 91
...moving into the 21st century
R. . . . . . . . . . . . . . . . . . . . . . . . . . . . · . . . . .
eform of mathematics education requires
voluntary local implementation of common
national standards.
The key to success is voluntary acceptance of a common
framework to guide local choices:
· National Standards. School mathematics programs across
the nation should share a common philosophy and frame-
work, a universal set of interrelated concepts and methods,
held together by a simple workable philosophy, yet flexi-
ble enough to allow for local and regional variations. In
a highly mobile society, the basic framework should be
transportable and adaptable.
· Local ·mp;lementation. Changes in mathematics curricula
must be proposed and undertaken freely by those who bear
direct responsibility for curricula in the schools. A deep
sense of identification with those changes must be devel-
oped within the entire community. In particular, teach-
ers and parents need to be involved in adaptation and
decision-making in a thorough and comprehensive way.
Implementation will require more than good will and
community dialogue; it will need professional leadership of
teachers operating in a transformed school environment. No
one should underestimate the complexity of the challenge;
elective reform will be truly difficult to accomplish. Few
teachers in today's schools have the authority or resources
necessary to carry out this agenda. But as schools evolve
from a mode} with teachers as hired hands to one in which
teachers function as professional educators, schools should
welcome the challenge to implement national standards for
mathematics education.
Support Structures
In order for this strategy to work, the United States must
develop new national support structures to help states and
91
OCR for page 92
Action
92
localities promote excellence in mathematics education for
all students. These structures must assure appropriate con-
sistency among the nation's many different school districts,
yet encourage a sense of local ownership by allowing adap-
tation to local preferences.
important parts of this national structure are in place al-
ready, while other parts will emerge in coming months and
years. Professional organizations (the National Council of
Teachers of Mathematics, the American Mathematical So-
ciety, the Mathematical Association of America, the Soci-
ety of Industrial and Applied Mathematics, the American
Statistical Association, the Conference Board of the Mathe-
matical Sciences) are actively engaged in projects that seek
to improve the teaching of mathematics. Related actions of
other groups such as the National Congress of Parents and
Teachers, the National Governors' Association, the National
School Boards Association, and the American Association
for the Advancement of Science will ensure a vigorous na-
tional dialogue, which is a necessary prerequisite to national
consensus.
As schools are not the sole source of America's problems in
mathematics education, neither can they be the sole vehicle
for renewal. Informal, nonschool-based undertakings that
support school-based mathematics education can be found
in clubs, churches, and scouting. Community organizations
electively complement schools, reaching youth- especially
minorities who find school uninspiring. Being outside the
formal public structures, community organizations offer a
testing ground to validate the power of innovative or uncon-
ventional ideas.
Building national consensus requires
effective national leadership.
To stimulate informed debate about curricular change, the
Mathematical Sciences Education Board is preparing two re-
ports on concepts and principles of mathematics suitable
OCR for page 93
...moving into the 21st century
for the education of students who will work in the twenty-
first century. One, a statement of philosophy and curricu-
lar frameworks, provides a general structure that can guide
curriculum development for the future. The other, on ma-
jor strands of mathematical thought, is intended to stim-
ulate creative development of new curricula that embody
a broader interpretation of mathematics. These strands-
chance, change, shape, quantity, dimension are examples
of deep ideas of mathematics that could become organizing
principles for some future mathematics curriculum.
These actions of many different groups representing
mathematicians, scientists, educators, and administrators-
will form the basis of a national consensus for new directions
in mathematics education.
Leadership
Real change requires action by everyone involved in math-
ematics education. Current efforts to forge national consen-
sus will not in themselves transform what happens in schools
or colleges. Change in the institutions of education must
come about as the result of intensive debate within each in-
stitution. There is plenty of work for everyone:
STUDENTS:
Study mathematics every school year.
Discover the mathematics that is all around us.
Use mathematics in other classes and in daily life.
Study a broad variety of mathematical subjects.
1 EACHERS:
Talk with each other about mathematics.
Examine current practice and debate new proposals.
Engage students actively in the process of learning.
PARENTS:
Demand that schools meet the new NCTM Standards.
Encourage children to continue studying mathematics.
Support teachers who seek curricular improvements.
Expect homework to be more than routine computation.
93
OCR for page 94
Action
94
PRINCIPALS:
Provide opportunities for teachers to work together.
Become educated on issues in mathematics education.
Support innovation.
Encourage paired teaching in elementary school.
SUPERINTENDENTS:
Stimulate public discussion of mathematics education.
Provide resources for curricular innovation.
Support a climate of change.
SCHOOL BOARDS:
Establish appropriate standards for mathematics.
Align assessment with curricular goals.
Support innovation and professional development.
CoMMuN~TY ORGAN~zAT~oNs:
Enrich mathematical opportunities for all students.
Support local efforts to improve mathematics education.
Explain to the public the need for change.
STATE SCHOOL OFFICERS:
Promote adoption of NCTM's Standards.
Encourage use of elementary mathematics specialists.
Speak out publicly about mathematics education.
Stress assessment of higher-order thinking.
Co~EGE AND UN~vERs~TY FAcu~TY:
Make introductory courses attractive and effective.
Restore integrity to the undergraduate program.
Lecture less; try other teaching methods.
Link scholarship to teaching.
Co~EGE AND UN~vERs~TY ADM~N~sTRAToRs:
Reward curricular innovation and good teaching.
Recognize that mathematics classes need computer labs.
Diminish reliance on underprepared, part-time faculty.
Emphasize and improve teacher education.
Business AND INDUSTRY:
Encourage students to study mathematics and science.
Do not steal good teachers by hiring them away.
Support local efforts to secure funds for education.
Support strong continuing education, not remediation.
Provide internship opportunities for teachers.
OCR for page 95
...moring into the 21st century
STATE LEGISLATORS:
Work with school leaders to support effective programs.
Recognize that mathematics education is an investment.
Resist pressures for simplistic cures.
GOVERNORS:
Provide resources to encourage change.
Demand new standards for mathematics education.
Lead the public to make wise choices among priorities.
Create enrichment programs for able students.
CONGRESS:
Stress education as an essential investment.
Support mathematics education at all levels.
Reward effective programs.
THE PRESIDENT:
Meet with state governors to affirm the national agenda.
Focus public attention on mathematics education.
Stress education as crucial to national security.
Taking Action
Once vigorous dialogue and grass-roots actions begin forg-
ing national consensus on goals for school mathematics, sev-
eral important national objectives must be addressed:
· Establish new standards for school mathematics.
· Upgrade the teaching profession.
· Make assessment responsive to future needs.
· Strengthen collegiate mathematics.
The first of these will emerge, with sufficient effort, follow-
ing public dialogue about the NCTM Standards. The second
is currently being advocated through the work of the Na-
tional Board for Professional Teaching Standards. The third,
assessment, may require a new, cooperative, national mecha-
nism to unlock the stranglehold that state and national test-
ing programs largely secret have on today's classrooms.
Finally, strengthening college and university mathematics-
including specific attention to those who become teachers,
how they teach, and what they teach is the primary task of
the National Research Council's Committee on the Mathe-
matical Sciences in the Year 2000 (MS 2000~.
95
OCR for page 96
Action
"Children are the future.
Everythi1'g we dFo is for
them and everything that
will be done will be done
by them."
Clay Morgan
96
l
Efforts to change must proceed steadily for many years,
on many levels simultaneously, with broad involvement of
all constituencies at each stage. First comes serious discus-
sion; then, compromise and consensus; finally, action and
change. Even as different groups work to improve curricu-
lar standards, the teaching profession, assessment practices,
and collegiate mathematics, other groups must help focus
the diverse efforts of business, industry, government, volun-
teer organizations, and educational organizations on com-
mon objectives. As there is no royal road to geometry, so
there are no quick fixes for mathematics education.
Both for reasons of international competitiveness and sci-
entific leadership, the United States must move quickly to
improve the state of mathematics education. It takes a gen-
eration to complete the mathematical education of a single
individual. The first high school graduates of the next cen-
tury entered elementary school in 1988. No longer can we
afford to sit idly by while our children move through school
without receiving mathematical preparation appropriate for
the twenty-first century.
The challenges are clear. The choices are before us. It is
time to act.
Representative terms from entire chapter:
school mathematics
