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A Practical Philosophy
Pages 7-16

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From page 7...
... .'.'.'.'.'.'.'.'.'.'.'.'.'.'.'.'. We teach mathematics to serve several very different goals that reflect the diverse roles that mathematics plays in society: · A Practical Goal: To help individuals solve problems of everyday life.
From page 8...
... Today to be mathematically literate one must be able to interpret both quantitative and spatial information in a variety of numerical, symbolic, and graphical contexts. These changes provide an unprecedented opportunity to redirect much of current elementary school mathematics to more fruitful and important areas especially to the new world of sophisticated electronic computation, As calculators and computers diminish the role of routine computation, school mathematics can focus instead on the conceptual insights and analytic skills that have always been at the heart of mathematics.
From page 9...
... Fundamental Questions To realize a new vision of school mathematics will require public acceptance of a realistic philosophy of mathematics that reflects both mathematical practice and pedagogical experience. One cannot properly constitute a framework for a mathematics curriculum unless one first adciresses two fundamental questions: · What is mathematics?
From page 10...
... Yet even as forces for change are providing new directions for mathematics eclucation, the public instinct for restoring traclitional stability remains strong. Unless the 3uiclance system for mathematics education is permanently reset to new and more appropriate gocis, it will surely steer the curriculum back to its Al path once present pressure for change abates.
From page 11...
... Laboratory work and fieldwork are not only appropriate but necessary to a full understanding of what mathemofics is ancl how it is used. Calculators ancl computers are necessary tools in this mathematics lab, but so too are sources of real data (scientific experiments, demographic clata, opinion polls)
From page 12...
... In its symbols and syntax, its vocabulary and idioms, the language of mathematics is a universal means of communication about relationships and patterns, It is a language everybody must learn to use, Knowing Mathematics If mathematics is a science and language of patterns, then to know mathematics is to investigate and express relationships among patterns: to be able to discern patterns in complex and obscure contexts; to understand and transform relations among patterns; to classify, encode, and describe patterns; to read and write in the language of patterns; and to employ knowledge of patterns for various practical purposes. To grasp The diversity of patterns-indeed, to begin to see patterns among patterns -it is necessary that the mathematics curriculum introduce and develop mathematical patterns of many different types.
From page 13...
... 1989 The Geometric Supposer is a set of software learning environments deliberately designed to change school plane geometry from a closely guided museum tour (where the guide points out certain artifacts to be "proven") to an active process of building and exploring conjectures.
From page 14...
... , this pragmatic view highlights the philosophical basis for using calculators in school mathematics: as microscopes are to biology ancl telescopes to astronomy, calculators ancl computers have become essential tools for the study of patterns. · By recognizing that practical knowledge emerges from experience with problems, this view helps explain how
From page 15...
... Present strategies for teaching need to be reversecl: students who recognize the need to apply particular concepts have a stronger conceptual basis for reconstructing their knowledge at a later time. By stressing mathematics as a language in which students express ideas, we enable students to develop a framework that can be cirawn upon in the future, when rules may have been forgotten but the structure of mathematical language remains embecicled in memory as a foundation for reconstruction.
From page 16...
... They are, however, sufficient to meet certain important criteria that any effective philosophy of mathematics education must satisfy: · They encompass new as well as traditional topics; · They provide a substantive rationale for using calculators and computers in school mathematics; · They encourage experience with genuine problems; · They stimulate exploration, use of real data, and apprenticeship learning; · They help bricige the gap between pure and applied mathematics; · They emphasize active modes of learning; · They are understandable to a broad segment of the public. The framework for mathematics education that follows from this practical philosophy provides an environment to support present efforts at curricular reform.


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