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~athemaUcs' Scicncc, and Technology Lducabon: ^ Search Agenda Comae on Search ~ ~athemadcs, Science, and Schnook Education Com~s~on on Beba~or~ and Social Sciences and Education National Research Council NATIONAL ACADEMY PASS Washington' D C. 1985

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NOTICE: The project that is the subject of this report was approved by the Governing Board of the National Research Council, whose members are drawn from the councils of the National Academy of Sciences, the National Academy of Engineering, and the Institute of Medicine. The members of the committee responsible for the report were chosen for their special~competences and with regard for appropriate balance. m is report has been reviewed by a group other than the authors according to procedures approved by a Report Review Committee consisting of members of the National Academy of Sciences, m e National Academy of Engineering, and the Institute of Medicine. The National Research Council was established by the National Academy of Sciences in 1916 to associate the broad community of science and technology with the Academy's purposes of furthering knowledge and of advising the federal government. The Council operates in accordance with general policies determined by the Academy under the authority of its congressional charter of 1863, which establishes the Academy as a private, nonprofit, self-governing membership corporation. The Council has become the principal operating agency of both the National Academy of Sciences and the National Academy of Engineering in the conduct of their services to the government, the public, and the scientific and engineering communities. It is administered jointly by both Academies and the Institute of Medicine. The National Academy of Engineering and the Institute of Medicine were established in 1964 and 1970, respectively, under the charter of the National Academy of Sciences. This report was prepared with support from the National Institute of Education under contract no. 400-83-0059.

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Committee on Research in Mathematics, Science, and Technology Education JAMES G. MARCE (CHAIR), Stanford University (political science) ARNOLD B. ARONS, University of Wash, ng ton (physics) W.O. BAKER, Bell Telephone Laboratories, Inc., retired (chemistry) JEROME S. BRUNER, New School for Social Research (psychology) MICHAEL COLE, University of California, San Diego tPSychology) ALLAN M. COLLINS, Bolt Beranek and Newman Inc., Cambr idge, Mass . (communication sciences, psychology ) MARGARET B. DAVIS, University of Minnesota (biology) FREDERICK ERICKSON, Michigan State University (anthropology) ROBERT GLASER, University of Pittsburgh (education, psychology) ANDREW M. GLEASON, Harvard University (mathematics) MICHAEL A. GUILLEN, Harvard University (mathematical physics) JILL H. LARRIN, Carnegie-Mellon University (mathematics and science education) ROBERT G. LOEWY, Rensselaer Polytechnic Institute (engineering) CORA B. MARRETT, University of Wisconsin (sociology) SAMUEL J. MESSICR, Educational Testing Service, Inc., Princeton, N.J. (psychometrics) PAUL E. PETERSON, Brookings Institution, Washington, D.C. (political science) MARE TAAGEPERA, University of California, Irvine (chemistry) DAVID E. WILEY, Northwestern University (education) SENTA A. RATZEN, Study Director ROLF R. BLANK, Research Associate CAROLYN STEWART, Administrative Secretary . . .

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Contents PREFACE 1 INTRODUCTION: A BASIC ORIENTATION FOR A FOCUSED RESEARCH AGENDA 2 RESEARCH ON REASONING Developing Competence, 8 The Search for Generality in Reasoning Skills, 11 RESEARCH ON INSTRUCTION Research on Teachers, 15 Research on Curricula and Curricular Materials, 19 Research on Testing, 24 4 RESEARCH ON SETTINGS Research on Classroom Settings, 26 Research on the Political and Social Context of Mathematics and Science Education, 30 Research on the Home as a Setting for Education, 34 Research on Out-of-Classroom Settings, 36 RESEARCH ON NEW LEARNING SYSTEMS Research on Interactive Computer Software, 39 Research on Microsystems, 41 Developing a Systems Approach to Improving Mathematics and Science Education, 43 v . V11 1 s 15 26 39

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6 SUMMARY OF A RESEARCE AGENDA Research on Reasoning, 52 Research on Instruction, 53 Research on Settings, 5S Research on New Learning Systems, 58 REl?ER=CE; APPENDIXES A: Background Papers B: Biographical Sketches of Committee Members and Staff vat 51 61 85 86

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Preface This is a report to the National Institute of Education from the National Research Council Committee on Research in Mathematics, Science, and Technology Education. The report is based on a review of current work in relevant fields, several papers commissioned by the committee, and our understanding of existing knowledge and promising directions for research I see Appendix A for titles and authors and Appendix B for biographical sketches of committee members). It reflects our assessment of where we are and where we might go and outlines some strategies for extending and utilizing research to improve precol- legiate education in mathematics, science, and technology. The background for the report can be read in any con- temporary newspaper. Concerns about the quality of mathematics, science, and technology education have become commonplace in the United States. Unflattering comparisons between the performance of American youth and youth in other countries, and between the current ineffec- tiveness of schools and their traditional quality, are regular topics for journals, legislatures, and street corners. The educational system has responded by raising requirements for high school graduation, by stiffening standards for teacher certification, by developing incentives for attracting able teachers, by exploring new technologies for instruction, and by challenging the validity of the critiques. Our report neither describes nor endorses a program for educational reform. Judgments about the allocation of resources to education and their utilization are the province of political leaders and educators. Our inten- tion is simply to suggest a strategy for research and development that would provide somewhat better answers to the practical questions of educational change: How should V11

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new courses be designed and taught to ensure student achievement? What makes an effective teacher? Or a good school? How can modern information technology contribute? How can parents and the public assess the extent to which educational goals are being reached? This volume is the result of the efforts of many people. We have drawn gratefully on the assistance of our colleagues and would like to acknowledge particularly the contributions of the National Council of Teachers of Mathematics, especially Joseph Crosswhite and Sigrid Wagner, who provided an extensive bibliography and other materials on research in mathematics education, and of the National Association for Research in Science Teaching, especially David Butts. We want to thank the National Institute of Education for its support of this project and the National Science Foundation for support of the committee. We also want to express admiration and thanks to the National Research Council staff, who made our work possible. Senta Raizen, study director, made a major contribution to the substance and organization of this report. Rolf Blank, research associate, was very helpful in the later stages of its preparation. Christine McShane, editor for the Commission on Behavioral and Social Sciences and Education, added to the clarity of the report and managed its production. JAMES G. MARCH, Chair Committee on Research in Mathematics, Science, and Technology Education . . veal