solidifying. The mathematics community welcomes the focus on excellence in K-8 mathematics education that will be generated by the national test.
The MSEB has contributed several reports raising issues about mathematics education and standards in mathematics education, including The Preparation of Teachers of Mathematics: Considerations and Challenges, A Letter Report (National Research Council [NRC], 1996b), Everybody Counts (NRC, 1989), Reshaping School Mathematics (NRC, 1990), Measuring What Counts (NRC, 1993c), and Measuring Up (NRC, 1993b). The standards prepared by the National Council of Teachers of Mathematics—the Curriculum and Evaluation Standards for School Mathematics (National Council of Teachers of Mathematics [NCTM], 1989), the Professional Standards for Teaching Mathematics (NCTM, 1991), and the Assessment Standards for School Mathematics (NCTM, 1995)—constitute “widely accepted ^{1} , challenging national standards in mathematics,” and have been endorsed and promoted by the MSEB (NRC, 1989; NRC, 1993a).
The MSEB has not been asked to make comments directly about the proposed national test in mathematics. Nonetheless, the very existence of the Working Group coincides with the President’s intention of having a voluntary eighth grade test. The action plan and strategies to be developed by the Working Group seem to be intended as the mechanisms for achieving excellence in mathematics education that will work in concert with the national test. Thus our recommendations are not generic recommendations about the improvement of mathematics education. Rather, they are recommendations that reflect the government’s intention to institute a test, and to use that test as an occasion for improving mathematics education. Following the recommendations, we discuss the underlying considerations about the context in which the action strategy will be developed and undertaken.
This report begins with a set of overarching recommendations. Then, within the four specific areas under consideration by the Working Group, we provide recommendations, as requested, for the action strategy.
Construct and sustain a Federal effort that brings together, in a coherent framework for decision-making, the various National Science Foundation and U.S. Department of Education programs that will significantly influence K-8 mathematics education.
^{1} |
The Third International Mathematics and Science Study (TIMSS) found that 95% of US teachers were either “very aware” or “aware” of current ideas about teaching and learning mathematics; 75% felt their teaching was in accord with current ideas. Weiss et al. (1994) find 56% of secondary school teachers aware of the NCTM Standards (Office of Educational Research and Improvement [OERI], 1997). |
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solidifying. The mathematics community welcomes the focus on excellence in K-8 mathematics education that will be generated by the national test.
The MSEB has contributed several reports raising issues about mathematics education and standards in mathematics education, including The Preparation of Teachers of Mathematics: Considerations and Challenges, A Letter Report (National Research Council [NRC], 1996b), Everybody Counts (NRC, 1989), Reshaping School Mathematics (NRC, 1990), Measuring What Counts (NRC, 1993c), and Measuring Up (NRC, 1993b). The standards prepared by the National Council of Teachers of Mathematics—the Curriculum and Evaluation Standards for School Mathematics (National Council of Teachers of Mathematics [NCTM], 1989), the Professional Standards for Teaching Mathematics (NCTM, 1991), and the Assessment Standards for School Mathematics (NCTM, 1995)—constitute “widely accepted 1 , challenging national standards in mathematics,” and have been endorsed and promoted by the MSEB (NRC, 1989; NRC, 1993a).
The MSEB has not been asked to make comments directly about the proposed national test in mathematics. Nonetheless, the very existence of the Working Group coincides with the President’s intention of having a voluntary eighth grade test. The action plan and strategies to be developed by the Working Group seem to be intended as the mechanisms for achieving excellence in mathematics education that will work in concert with the national test. Thus our recommendations are not generic recommendations about the improvement of mathematics education. Rather, they are recommendations that reflect the government’s intention to institute a test, and to use that test as an occasion for improving mathematics education. Following the recommendations, we discuss the underlying considerations about the context in which the action strategy will be developed and undertaken.
RECOMMENDATIONS
This report begins with a set of overarching recommendations. Then, within the four specific areas under consideration by the Working Group, we provide recommendations, as requested, for the action strategy.
Overarching Recommendations
Construct and sustain a Federal effort that brings together, in a coherent framework for decision-making, the various National Science Foundation and U.S. Department of Education programs that will significantly influence K-8 mathematics education.
1
The Third International Mathematics and Science Study (TIMSS) found that 95% of US teachers were either “very aware” or “aware” of current ideas about teaching and learning mathematics; 75% felt their teaching was in accord with current ideas. Weiss et al. (1994) find 56% of secondary school teachers aware of the NCTM Standards (Office of Educational Research and Improvement [OERI], 1997).
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Such a coherent framework will ensure that the programmatic strategies can be effectively employed and related to the test itself. The means for enacting this recommendation are complex, and we urge the Working Group to consider questions such as: Could Title I funds be specifically allocated for the preparation and hiring of mathematics specialists in elementary and middle schools? Could some portion of Eisenhower dollars be reserved for providing long-term, school-based professional development for K-8 teachers? What about Goals 2000 dollars? Might there be a new program for the development of materials for use in school-based staff development that would progress in the directions indicated by the national mathematics test? Can the efforts of the School-to-Work program be aligned with efforts to promote high standards in grades K-8? How might Title V be reconceptualized to better prepare higher education faculty for standards-based mathematics education?
Devise a long-term plan (8-10 years, offset from political cycles) of interactive development involving test redesign and strategy adjustment, with ongoing monitoring and oversight.
An important first step in such a long-term plan is immediate Federal implementation of a process by which states and districts would be able to gather, along with student test data, information about the contexts in which students are learning mathematics, information about curriculum that is in place, information about the teachers’ backgrounds and professional development activity, and information about classroom instructional practice and areas of content emphasis. It will be very difficult to interpret test results meaningfully, and to make constructive use of them, without a measure of what opportunities students have had to learn the mathematics that is being tested. Funding should be allocated to for the development of materials for the measurement of such contextual factors. Such tools could then be made available to states and districts. The report Mathematics and Science Education Around the World (NRC, 1996a) emphasizes the importance of linking contextual information to the interpretation of test scores, and methodologies for doing so are available in TIMSS (Schmidt et al., 1996; Stigler et al., in preparation), the National Assessment of Educational Progress (NAEP) and other sources. Without a federally orchestrated plan for gathering such information, using the test as any indicator of the effectiveness of various programs and approaches is impossible. Moreover, the accumulation and analysis of such data over time are essential to the process of test redesign and strategy adjustment.
Invest in a sustained agenda of basic research to better understand what mathematical thinking is, how to foster it through curricular choices and instructional practice, and how to support teachers in doing so.
The NCTM Standards call for increased focus on reasoning, problem solving, and making connections, and on mathematical processes such as conjecturing, proving, exploring, and analyzing. In addition, the reform documents recommend focus in content areas of mathematics that have not historically been part of the K-12 curriculum. The base of basic research that exists to support instructional practice and curriculum development in these areas is surprisingly meager. With the renewed attention that will be devoted to mathematics education through the national test and associated activity, the need for basic research that can guide the development and test the effectiveness of various approaches is not only timely, but critical if this
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venture is to have a measurable impact. Particularly important is funding for basic research about instructional practice and teacher learning, and about the role of technology.
Recommendations for Improving Teaching
We recommend, for the next three years, a national focus on the professional development and preparation of grades 5-8 mathematics teachers to ensure that they are adequately prepared and supported to develop student learning at high levels.
Teachers of mathematics at the middle grades traditionally have borne the unique responsibility of helping their students in the transition from the arithmetic-dominated curriculum of the elementary years to readiness for the abstraction of algebra in the secondary school. With the advent of the NCTM Standards, new state frameworks, and new state-level eighth grade assessments, as well newly developed instructional materials, the mathematical responsibilities of these teachers have increased significantly. The recommended curricular topics for the middle grades now include a much greater emphasis on patterns and functions, algebra, and areas of statistics, probability, geometry, and measurement (NCTM, 1989). If the national test follows the NAEP framework, it is likely to also reflect these emphases.
At the same time that curricular demands are increasing, many states do not require certification or specialization at the middle grades 2 . The result is often that school districts employ either elementary teachers prepared for the elementary grades (K-6 or K-8), or teachers prepared for the secondary grades 3 (7-12). Neither the elementary nor the secondary preparation has consciously taken into account either the mathematical emphases that are particular to the middle grades, with its cross-disciplinary features and applications orientation, nor the special needs of middle grades learners. Few institutions of higher education actually offer middle grades specializations in mathematics, although such programs have been developed through NSF funding (Stake et al., 1993).
Teachers’ professional development needs are substantial (Darling-Hammond & Cobb, 1995; National Center for Education Statistics [NCES], 1993). The introduction of the national test in mathematics will only heighten and intensify the need for immediate explicit focus at middle grades. A number of reports have emphasized the importance of strong and appropriate content preparation of teachers, such as the MSEB report, The Preparation of Teachers of Mathematics: Considerations and Challenges (NRC, 1996b). Introduction of the national test will make this recommendation even more critical.
To carry out this recommendation, it will be essential to:
2
Thirty-four states offer middle grades certification, although several do not have specific requirements for mathematics (CCSSO, 1996).
3
Nationally, only 63% of secondary school teachers hold a degree in the subject they teach (Education Week, January 22, 1997).