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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 K12: What Is Still Fundamental and What Is
Not
Conference Board of the
Mathematical Sciences • 1983
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http://www.mathcurriculumcenter.org
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The Mathematical Sciences Curriculum K12: 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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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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Meeting Participants
30 participants and 2 observers representing the larger mathematical
sciences community included:
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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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
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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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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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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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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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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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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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The Role of Technology
• Computers and calculators have potential to enhance
mathematics instruction. The interplay between wordprocessing, 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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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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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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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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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. 1984 Yearbook. Reston, VA: NCTM.
Hirsch, C., & Zweng, M. (Eds.). (1985). The secondary school
mathematics curriculum. Reston, VA: NCTM.
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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. 33-49).
Washington, DC: Department of Education, Office of Research.
National Science Board. (2000). The National Science Board: A
history in highlights 1950-2000. Retrieved November 6, 2004,
from http://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, 109-123.
Shufelt, G., & Smart, J. (Eds.). (1983). The agenda in action. 1983
Yearbook. Reston, VA: NCTM.
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