Washington--Three leading national mathematics organizations are to release reports this week outlining their visions of the best practices for effectively preparing teachers to meet the needs of a society that aspires to be mathematically literate.
A conviction that math teachers are “gate-keepers to the future” underlies the reports by the National Council of Teachers of Mathematics, the Mathematical Association of America, and the Mathematical Sciences Education Board, an arm of the National Research Council.
The groups planned to concurrently release blueprints for effective mathematics teaching at a press conference here.
Although all three documents call for improvements in instruction in precollegiate math, the NCTM document may have the most immediate impact on public-school instruction because it aims to enhance the efforts of current math teachers.
The MAA report, by contrast, concentrates on upgrading the quality of the teaching force of the future.
“Professional Standard for Teaching Mathematics,” the NCTM’s 196-page prescription for improving classroom teaching, presents 55 vignettes that illustrate outstanding math instruction.
The report also contains 24 standards that outline the support, training, and evaluation methods needed to promote good teaching.
The recommendations are designed to help “create classrooms that recognize students and teachers as thinkers, doers, investigators, and problem solvers,” Iris Carl, president of the math teachers’ group, said.
The NCTM document is a companion piece to the organization’s 1989 report, “Curriculum and Evaluation Standards for School Mathematics,” which called for a “transformation” in the way that success in math is defined. (See Education Week, March 22, 1989.)
The MAA’s document, “A Call for Change: Recommendations for the Mathematical Preparation of Teachers of Mathematics,” outlines proposals for improving college instruction in the subject and for enhancing the preparation of teachers.
The MSEB planned to release a statement outlining the actions that need to be taken to incorporate the standards developed by the other two groups into the efforts for achieving the national education goals set by President Bush and the governors.
Collectively, the three documents are designed to serve as guidelines to help move teachers away from what Ms. Carl called “shopkeeper arithmetic” and toward inquiry-based math teaching.
“We’re changing the teaching practices of the past into new approaches for the future,” Ms. Carl said.
The National Council of Teachers of Mathematics document provides a framework to “broaden and deepen” the reforms called for in the organization’s curriculum-standards publication, which argued that math instruction should move away from paper-and-pencil drills to embrace such technologies as calculators and computers to solve problems.
The curriculum report also suggested that courses should employ actual problems, rather than those contrived for a textbook.
The new NCTM report calls for five shifts in the environment of math classrooms. It suggests movement toward the following goals:
Classrooms as mathematical communities, rather than as concentrations of individual learners;
Reliance on logic and mathematical evidence, rather than the teacher, as verification of students’ findings;
Development of mathematical reasoning;
Emphasis on conjecturing, inventing, and problem-solving instead of “mechanistic answer finding"; and
Connecting mathematical concepts with “real world” applications.
The NCTM report is divided into several sections that lay out in detail the characteristics it says should be shared by effective mathematics teachers.
The section on standards for teaching mathematics, for example, argues that the “nature of the mathematical task posed and what is expected of students are critical aspects against which to judge the effectiveness of the lesson.”
The section on standards for evaluating math performance argues that teachers themselves must be an integral part of the evaluation process and take an active role in it.
The report also includes a section on the “responsibilities” of various forces in education--including policymakers, schools, colleges and universities, and professional organizations--to provide adequate support for teachers as they embark on innovative teaching programs.
The document assumes that teachers are the “key figures” in effective reform of current educational practices because they have the most immediate contact with students.
Ms. Carl added that while the report lays out in considerable detail the desirable outcomes of math reform for teachers, it should be seen as a catalyst for ongoing improvements in methodology, not an end in itself.
“We’re hoping that everyone will realize that change is not an event,” she said.
But, she pointed out, the practices suggested in the report are not necessarily novel or untested.
“Thirty percent of teachers out there are doing these things now,” she said.
The organization hopes to press for wider adoption of its strategies through a series of awareness campaigns targeted at teachers, parents, and community leaders.
The Mathematical Association of America report argues that the changes called for in the professional-standards report will have a lasting effect on math instruction only if collegiate training also undergoes a transformation.
“The content of collegiate-level courses must reflect the changes in emphases and content of the emerging school curriculum and the rapidly broadening scope of mathematics itself,” it argues.
It notes, however, that current certification requirements, particularly for elementary- and middle-school teachers, “fall far short” of such goals.
The report lays out some of the characteristics that the MAA believes should be shared by the “ideal” math teachers of the 1990’s.
The qualities include:
Ability to communicate mathematical ideas with ease and clarity;
Ability to organize and analyze information, solve problems readily, and construct logical arguments;
Knowledge of math deeper than that required by the particular course being taught;
Enjoyment of math and an appreciation of its “power and beauty";
Understanding of how math “permeates our lives"; and
Ability to routinely use technology in the learning, teaching, and doing of mathematics.
The report describes how each of those characteristics can be developed at various levels of the educational process, and also how those emphases may vary among teachers at different grade levels.
