Everybody Counts A Report to the Nation on the Future of Mathematics Education (1989) / Chapter Skim
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MATHEMATICS
MATHEMATICS
Pages 31-42
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From page 31... ...
The cycle from data to deduction to application recurs everywhere mathematics is used, from everyday household tasks such as planning a long automobile trip to major management problems such as scheduling airline traffic or managing investment portfolios. The process of "doing" mathematics is far more than just calculation or deduction; it involves observation of patterns, testing of conjectures, and estimation of results.
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From page 32... ...
The ability to compare loans, to calculate risks, to figure unit prices, to understand scale drawings, and to appreciate the effects of various rates of inflation brings immediate real benefit. This kind of basic applied mathematics is one objective of universal elementary education.
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From page 33... ...
· Leisure- disposition to enjoy mathematical and logical challenges. The popularity of games of strategy, puzzles, lotteries, and sport wagers reveals a deep vein of amateur mathematics lying just beneath the public's surface indifference.
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From page 34... ...
Postwar government investment in mathematics, fueled by Sputnik, accelerated growth in both education and research Then the development of electronic computing moved mathematics toward an algorithmic perspective even as it provided mathematicians with a powerful too! for exploring patterns and testing conjectures.
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From page 35... ...
in 1960, at a time when theoretical physics was the central jewel in the crown of applied mathematics, Eugene Wigner wrote about the "unreasonable effectiveness" of mathematics in the natural sciences: "The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve." Theoretical physics has continued to adopt (and occasionally invent) increasingly abstract mathematical models as the foundation for current theories.
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From page 36... ...
Indeed, just as computers afford new opportunities for mathematics, so also it is mathematics that makes computers incredibly elective. Mathematics provides abstract models for natural phenomena as well as algorithms for implementing these models in computer languages.
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From page 37... ...
Robotics design, for instance, often encounters limits imposed not by engineering details, but by incomplete understanding of how geometry controls the degrees of freedom of robot motions. Models of weather forecasting consistently reveal uncertainties that suggest intrinsically chaotic behavior.
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From page 38... ...
Present educational practice for mathematics requires approximately 1,500,000 elementary school teachers, 200,000 high school teachers, and 40,000 college and university teachers. Mathematics education takes place in each of 16,000 public school districts, in another 25,000 private schools, in 1,300 community colleges, 1,500 colleges, 400 comprehensive universities, and 200 research universities.
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From page 39... ...
Not only do all the sciences depend on strong undergraduate mathematics, but also all students who prepare to teach mathematics acquire attitudes about mathematics, styles of teaching, and knowledge of content from their undergraduate experience. No reform of mathematics education is possible unless it begins with revitalization of undergraduate mathematics in both curriculum and teaching style.
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From page 40... ...
40 dergraduate mathematics teaching. To administrators worried about tight budgets, mathematics departments are often the best bargains on campus, but to students seeking stimulation and opportunity, mathematics departments are often the Rip Van Winkle of the academic community.
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From page 41... ...
This challenge provides a great opportunity. With approximately 50 percent of school teachers leaving every seven years, it is feasible to make significant changes in the way school mathematics is taught simply by transforming undergraduate mathematics to reflect the new expectations for mathematics.
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