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.
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.
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.
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