Reshaping School Mathematics A Philosophy and Framework for Curriculum (1990) / Chapter Skim
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Redesign from a Technological Perspective
Redesign from a Technological Perspective
Pages 17-26
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From page 17... ...
The image of a calculator as an inappropriate intellectua~ crutch is so deeply ingrained in many adult's minds-especially among mathematicians and scientists-that most college entrance exams do not permit calculator use. Advocates of early and unrestricted use of calculatorsincluding virtually all mathematics educators argue on the basis of student motivation, classroom realism, and needs of
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From page 18... ...
Electronic aicis like computers should be used by professionals to implement quickly anci accurately what they have aireacly learnecl, not usecl in education as an alternative to traclitional techniques for developing skill ancl unclerstanding. Despite the controversy, most mathematics educators who have studied the issues ancl the evidence have concluded that the potential benefit to mathematics education is enormous, well worth the extra effort ancl increased risk associated with venturing into uncharted territory (Wi~f, 1982; Fey, 1984; Hansen, 1984; Smith et al., 1988~.
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From page 19... ...
Thus, any reform of school mathematics must entail a major reduction in the time spent on teaching traditional arithmetic skills. Technological developments suggest strongly that even those aspects of the secondary school curriculum that are orientecl mainly to development of algebraic skills such as polynomial arithmetic no longer serve a compelling purpose.
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From page 20... ...
Often, the approximate answer is not only sufficient, but it also provides more insight than the exact answer. Moreover, the approximate answer provides a quick check on the result of any exact proceclure, whether by a hand moving a pencil or by fingers pushing buttons on a calculator, A broader curriculum stressing a variety of mathematical strategies will make it possible to teach material to students in each grade that will be useful to them no matter when they end their mathematics education, At the same time, students preparing for further study of mathematics will be stimulated by early glimpses via the power of the computer~of what lies aheacl.
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From page 21... ...
Still, enough is known now to be able to make some reasonable predictions about what is desirable and feasible for computers in schools in the year 2000: · All students should have available hand-held calculators with a functionality appropriate to their grade level. Calculators suitable for secondary school will by then have symbolic and graphics capability sufficient for all highschool level mathematics.
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From page 22... ...
The effects of calculators in school mathematics have been studied in over 100 formal investigations during the past 15 years. These studies have tested the impact of a variety of kinds of calculator use-from limited access in carefully selected situations to access for all aspects of mathematics instruction and testing.
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From page 23... ...
Indeecl, use of calcuiators can improve the average student's basic skills with paper and pencil, both in basic operations and in problem solving. Research suggests that access to calculators in a wellplannecl program of instruction is not likely to obstruct achievement of skill in traditional arithmetic proceclures.
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From page 24... ...
found that students who learned calculus with the aid of computer software developed a much deeper understanding of fundamental concepts than did students in traditional skill-oriented courses. Heid also found that her students picked up needed procedural knowledge in a short time period following careful instruction in conceptual background, and Palmiter found that her students acquired their understanding much more quickly than students in conventional courses.
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From page 25... ...
A series of articles in Eclucational Researcher (Becker, 1987; Papert, 1987; Pea, 1987b; Walker, 1987) illustrate the wide diversity of opinion on this topic, A key concern is the extent to which the development of mathematical power can be inferred from written test performance or within the limited time spans of most research studies, It has sometimes been proposed that the availability of computers would, more or less in itself, produce significant improvements in mathematical thinking, From the few attempts that have been made to measure changes in reasoning power, it is possible to conclude that such advancements cannot come from trivial technological fixes, Repeated attempts to document such change has yet to reveal a lasting effect for example, studies of the effect of Logo on planning, of the impact of Pascal on understanding of algebraic syntax, and of the cognitive impact of learning metaprinciples of programming in Basic, While these results do not necessarily imply that computers will not improve mathematical thinking, they do suggest that simplistic approaches are not likely to produce measurable improvements.
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From page 26... ...
How can school instruction provicle students with a background that will enable them to apply what they have learned in out-of-school contexts? · Instructional Uses of Technology.
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