**ERIC Identifier:** ED335238

**Publication Date:** 1991-00-00

**Author: **Frye, Shirley M.

**Source: **ERIC Clearinghouse for
Science Mathematics and Environmental Education Columbus OH.

## Communicating the Next Message of Reform through the
Professional Standards for Teaching Mathematics. ERIC/SMEAC Mathematics
Education Digest.

To achieve the vision of a high-quality mathematics education for every
child, the National Council of Teachers of Mathematics (NCTM) has provided
leadership in the establishment of standards for the reform of teaching and
learning mathematics. These statements of what is valued were communicated first
in Curriculum and Evaluation Standards for School Mathematics (NCTM), released
in March, 1989. The companion document, Professional Standards for Teaching
Mathematics (NCTM), was presented in March, 1991. Together, these standards
reflect NCTM's long-term commitment to the reform of school mathematics.

### WHAT IS THE VISION OF TEACHING MATHEMATICS IN THE PROFESSIONAL STANDARDS?

The teaching envisioned in the Professional Standards for
Teaching Mathematics is significantly different from what many teachers
themselves have experienced as students. Woven into the fabric of these
standards are major shifts that will empower students:

*
Shift toward classrooms as mathematical communities and away from classrooms as
simply a collection of individuals.

*
Shift toward logic and mathematical evidence as verification and away from the
teacher as the sole authority for right answers.

*
Shift toward mathematical reasoning and away from mere memorization of
procedures.

*
Shift toward conjecturing, inventing, and problem solving and away from merely
emphasizing finding the correct answer.

*
Shift toward connecting mathematics, its ideas, and its applications and away
from mathematics as a body of isolated concepts.

### WHAT ARE THE FUNDAMENTAL ASSUMPTIONS THAT UNDERLIE THE NEW
VISION?

Underlying the new vision are two fundamental assumptions:

*
Teachers are the key to changing the way in which mathematics is taught and
learned.

If teachers are to create learning environments that empower students,
teachers need time and resources to develop the professional teaching skills
envisioned here. They must have ongoing professional development opportunities,
flexibility, and instructional and assessment materials that are consistent with
the Curriculum and Evaluation Standards.

*
Teachers must have long-term support and adequate resources.

This vision of teaching mathematics requires that teachers be supported,
encouraged, and rewarded by administrators, parents, and the community. This
kind of recognition and collective support will take time to develop, but it is
a principle element in effective change in the classroom environment.

### STANDARDS FOR TEACHING MATHEMATICS

All students possess the
innate power to think and reason mathematically. The standards in this section
address the specific decisions that teachers make in the classroom to foster
mathematical thinking, reasoning, and problem solving. They are based on the
following assumptions:

*
The goal of teaching mathematics is to help all students develop mathematical
power.

*
WHAT students learn is fundamentally connected with HOW they learn it.

*
All students can learn to mathematically.

*
Teaching is a complex practice and hence not reducible to recipes or
prescriptions.

The standards are organized around framework emphasizing the important
decisions that a teacher makes in teaching:

*
Setting goals and selecting mathematical tasks to help students achieve these
goals.

*
Stimulating and managing classroom discourse so that both students and teacher
are clear about what is being learned.

*
Creating an environment to support teaching and learning mathematics.

*
Analyzing student learning, the mathematical tasks, and the environment in order
to make ongoing instructional decisions.

### STANDARDS FOR THE EVALUATION OF THE TEACHING OF
MATHEMATICS

These standards are intended to help teachers attain the vision
of the Curriculum and Evaluation Standards by emphasizing the role that
evaluation can play in teachers' professional development. Accordingly, these
standards focus on how and what information should be gathered and analyzed to
help teachers improve their teaching. The standards are based on four
assumptions:

*
The goal of evaluating the teaching of mathematics is to improve teaching and
enhance professional growth.

*
All teachers can improve their teaching of mathematics.

*
What teachers learn from the evaluation process is related to how the evaluation
is conducted.

*
Because teaching is complex, the evaluation of teaching is complex.

The consistent theme is that the major purpose of evaluation is the
improvement of teaching. The standards give guidance to teachers seeking
self-improvement, to colleagues mentoring others, and to supervisors and others
who are involved in the evaluation of teaching.

### STANDARDS FOR THE PROFESSIONAL DEVELOPMENT OF TEACHERS OF
MATHEMATICS

These standards address the pre-service and continuing education
of teachers of mathematics at the K-12 levels. They apply to introductory
programs that prepare teachers of mathematics and various continuing education
activities. They are based on the following assumptions:

*
Teachers are influenced by the teaching they see and experience.

*
Learning to teach is a process of integration.

*
The education of teachers of mathematics is an ongoing process.

*
There are level-specific needs in the education of teachers of mathematics.

These teaching standards provide essential guidance to colleges,
universities, and schools; state departments and provincial ministries of
education; public and private schools; and all who are part of the preparation
and professional development of teachers. These standards address:

*
Modeling good mathematics teaching.

*
Knowing mathematics and school mathematics.

*
Knowing students as learners of mathematics.

*
Knowing mathematical pedagogy.

*
Developing as a teacher of mathematics.

*
Teachers' roles in professional development.

### STANDARDS FOR THE SUPPORT AND DEVELOPMENT OF MATHEMATICS
TEACHERS AND TEACHING

These standards spell out the responsibilities of those who make
decisions that affect teaching mathematics. The environment in which teachers
teach is as important to their success as the environment in which students
learn is to theirs. The standards identify the groups that must play a
supportive role in achieving effective mathematics education:

*
Policymakers in government, business, and industry.

*
Schools and school systems, including administrators and board members.

*
Administrators in colleges and universities.

*
Leaders in professional organizations.

Annotated vignettes are used to elaborate the visions of teaching, evaluation
of teaching, and professional development. The narratives are meant to be like
video clips to provide brief vivid glimpses into diverse settings to animate the
standards. The vignettes present identifiable classroom situations that enable
teachers to visualize other teachers in action and to examine a range of
approaches that they might take in all aspects of their own work, from posing
problems to students to analyzing their own performance. The vignettes, which
display vividly the richness of mathematical learning, were gathered from actual
experiences of educators with students from diverse cultural, linguistic, and
socioeconomic backgrounds.

### NEXT STEP

Dialogue on school reform is taking place on many
fronts. In local areas, individual schools, districts, and universities are
approaching change in different ways and taking steps in different sequences.
Various combinations of ideas and strategies will provide many alternatives to
achieve the goals of reforming mathematics teaching and learning. The common
characteristics will be the long-term commitment and the cooperative efforts of
all teachers, administrators, parents, other educators, and policymakers. All
who have responsibility for any part of the support and development of
mathematics teachers and teaching are challenged to use these standards as a
basis for discussion that leads to actions for making changes to meet the goal
of a high-quality mathematics education for every child. As the standards remind
us: We must be impatient enough to take action, but patient enough to sustain
our efforts until we see results.

### REFERENCES

Mathematical Association of America. (1991). A
call for change: Recommendations for the mathematical preparation of teachers of
mathematics. Washington, DC: Author.

National Research Council, Mathematical Sciences Education Board. (1990).
Reshaping school mathematics: A philosophy and framework for curriculum.
Washington, DC: National Academy Press.

National Council of Teachers of Mathematics. (1991). Curriculum and
evaluation standards for school mathematics. Reston, VA: Author.

National Research Council. (1989). Everybody counts, a report to the nation
on the future of mathematics education. Washington, DC: National Academy Press.

Resnick, L. B. (1987). Educating and learning to think. Washington, DC:
National Academy Press.

Steen, L. A. (Ed.) (1990). On the shoulders of giants: New approaches to
numeracy. Washington, DC: National Academy Press.

Thurston, W. P. (1990, September). Mathematical education. Notices of the
American Mathematical Society. 37,844-850.