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1 This resource was developed by CSMC faculty and doctoral students with support from the National Science Foundation under Grant No. ESI The opinions and information provided do not necessarily reflect the views of the National Science Foundation

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2 Committees and Reports that Have Influenced the Changing Mathematics Curriculum This set of PowerPoint slides is one of a series of resources produced by the Center for the Study of Mathematics Curriculum. These materials are provided to facilitate greater understanding of mathematics curriculum change and permission is granted for their educational use. The Mathematical Sciences Curriculum K- 12: What Is Still Fundamental and What Is Not Conference Board of the Mathematical Sciences 1983

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3 The Mathematical Sciences Curriculum K- 12: What Is Still Fundamental and What Is Not Conference Board of Mathematical Sciences (CBMS) A Report to the National Science Board (NSB) Commission on Precollege Education in Mathematics, Science, and Technology

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4 Background Charged by the NSB Commission on Precollege Education in Mathematics, Science, and Technology to identify the parts of mathematics considered fundamental at the elementary and secondary levels, especially in light of increasing availability of calculators and computers Meeting held September 25-26, 1982 Six position papers on the fundamentals in the school mathematics curriculum were prepared for review prior to the meeting.

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5 Meeting Participants 30 participants and 2 observers representing the larger mathematical sciences communityincluded: Henry Pollak, Chairman of the CBMS Presidents of CBMS constituent organizations Richard Anderson, Mathematical Association of America James Baldwin, American Mathematical Association of Two-Year Colleges Andrew Gleason, American Mathematical Society Seymour Parter, Society for Industrial and Applied Mathematics Stephen Willoughby, National Council of Teachers of Mathematics

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6 Additional Participants Joseph Applebaum, Society of Actuaries John Burns, SIAM Ray Collings, MATYC John Dossey, MAA, NCTM Edgar Edwards, NCTM James Fey, NSB Consultant James Gates, NCTM Mary Gray, AWM Emil Grosswald, CBMS Ray Hannapel, NSB Mary Kohlerman, NSB James Landwehr, ASA Katherine Layton, NSB Nelson Markley, CBMS Stephen Maurer, MAA Douglas McLeod, MAA, NCTM Frederick Mosteller, NSB Ivan Niven, MAA Eleanor Palais, AWM Eileen Poiani, MAA Anthony Ralston, MAA James Stasheff, AMS Marcia Sward, CBMS James Swift, ASA

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7 Position Papers Participant papers: Richard D. Anderson, An Analysis of Science and Engineering Education: Data and Information Richard D. Anderson, Precollege Teacher Training and Retraining in Light of Expected Changes in School Mathematics Richard D. Anderson, Arithmetic in the Computer/Calculator Age James Baldwin, Untitled Paper James M. Landwehr, Memo on Activities of the American Statistical Association Stephen Willoughby, Untitled Paper Non-participant papers: Henry Alder, List of Temptations to Resist Peter Hilton, The Role and Nature of Mathematics: Implications for the Teaching of Mathematics Today Stephen White, Notes on K-8 Math

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8 Working Groups Elementary and Middle School Mathematics Traditional Secondary School Mathematics Non-Traditional Secondary School Mathematics The Role of Technology Relations to Other Disciplines Teacher Supply, Education, and Re-Education

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9 Elementary and Middle School Mathematics “A principal theme of K-8 mathematics should be the development of number sense, including the effective use and understanding of number in applications as well as in other mathematical contexts” (CBMS, p. 2). Calculators and computers should be introduced into the mathematics classroom at the earliest grade practicable. They should be used to enhance the understanding of arithmetic and geometry as well as the learning of problem-solving. Substantially more emphasis should be placed on the development of skills in mental arithmetic, estimation, and approximation and substantially less be placed on paper and pencil execution of arithmetic operations. Experience with the collection and analysis of data should be provided for in the curriculum to ensure that every student becomes familiar with these important processes.

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10 Traditional Secondary School Mathematics “The traditional component in the secondary curriculum can be streamlined, leaving room for important new topics.” (CBMS, p. 4) Algebra—reduce time allotments to routine drill, increase emphasis on algebraic-form recognition skills and conceptual understanding; anticipate future use of computer-algebra systems Geometry—decrease emphasis on two-column proof; increase emphasis on algebraic methods in geometry, analytic geometry, and vector algebra; anticipate increased use of computer-based drawing programs Precalculus—eliminate precalculus for better students if algebra and geometry are done “right” with the concepts made clear Algorithmics—increase opportunity for students to program computers to complete routine algorithms

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11 Non-Traditional Secondary School Mathematics “There is need for substantial change in both the subject matter of and the approach to teaching in secondary school mathematics.” (CBMS, p. 5) Recommendations on content, technology, and pedagogy include: – Reduction in treatment of topics in trigonometry – Addition of discrete mathematics, data analysis and statistics, algorithmic thinking, and computer science – Incorporation of CAS and computer software for drawing and manipulating geometric objects to enhance understanding, support experimentation and discovery, and reduce need for tedious computation and manipulation Professional development support for teachers should be provided and certification requirements should be changed, as needed, to include courses in discrete mathematics, statistics, and computer science.

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12 The Role of Technology Computers and calculators have potential to enhance mathematics instruction. The interplay between word- processing, data bases, and data analysis should foster problem-solving experiences that cut across disciplines. Computers should be available in every mathematics classroom and hand calculators should be available to students on the same basis as textbooks. Access to technology is an important equity issue and every effort must be made to provide access to all sectors of society. Curricular change related to technology should be encouraged and supported at the national level. New programs should be tested extensively.

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13 Relations to Other Disciplines Optimistic about the promise for greater connections between mathematics, the physical sciences, and the social sciences due, in part, to proposed: student use of calculators and computers emphasis on number sense and estimation introduction of statistical ideas, data handling procedures, and discrete mathematics Recommended discussion with college personnel and with representatives from business to ascertain their views on the mathematical preparation of students who would be: seeking technical vocational employment after graduation going to technical or vocational schools going to college programs in the natural sciences, social sciences, and business

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14 Teacher Supply, Education, and Re-Education “... The most immediate problem is not the mathematics curriculum, but the need for more, and better qualified, mathematics teachers.” (CBMS, p. iv) Recommendations were made: to make the problem of the projected shortage of qualified mathematics teachers a national priority and to communicate the message to the public; to create incentives to attract and retain qualified mathematics teachers and several possible incentive and re-education scenarios were provided; to provide professional development programs to keep qualified teachers abreast of trends in the mathematical sciences; for the content preparation of both elementary and secondary school teachers.

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15 Significance of the Report Continued the momentum from An Agenda for Action and provided curricular vision for the future Inspired innovative curriculum materials development projects Encouraged the use of technology, K-12 Provided a foundation for the NSB report Educating Americans for the 21st Century and for A Nation at Risk Defined groundbreaking direction for curricular reform and national standards

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16 References Commission on Standards for School Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: NCTM. Conference Board of the Mathematical Sciences. (1983). The mathematical sciences curriculum K-12: What is still fundamental and what is not. Report to NSB Commission on Precollege Education in Mathematics, Science, and Technology, Washington, DC. Hansen, V., & Zweng, M. (Eds.). (1984). Computers in mathematics education Yearbook. Reston, VA: NCTM. Hirsch, C., & Zweng, M. (Eds.). (1985). The secondary school mathematics curriculum. Reston, VA: NCTM.

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17 References, cont. Kaput, J. J. (1995). Long term algebra reform: Democratizing access to big ideas. In C. Lacampagne, J. Kaput, & W. Blair (Eds.), The algebra initiative colloquium (Vol. 1, pp ). Washington, DC: Department of Education, Office of Research. National Science Board. (2000). The National Science Board: A history in highlights Retrieved November 6, 2004, from nsb50/ 1980/k12.htmlhttp://www.nsf.gov/nsb/documents/2000/nsb00215/ nsb50/ 1980/k12.html Schoen, H. L., & Hirsch, C. R. (2003). Responding to calls for change in high school mathematics: Implications for collegiate mathematics. The Mathematical Monthly, 110, Shufelt, G., & Smart, J. (Eds.). (1983). The agenda in action Yearbook. Reston, VA: NCTM.

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