By L. R. Chapman (Eds.)
ISBN-10: 0080166237
ISBN-13: 9780080166230
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Aristotle's Logic was based on a codification of the rules and methods of reasoning already established on a strictly rigorous basis by the great Greek mathematicians before t VAN DER WAERDEN, B. , Science DRESDEN, A. (New York, 1963). , trans. THE NATURE OF MATHEMATICS—ANOTHER VIEW 25 him. Notwithstanding, there are many examples of problems and solutions depending upon "kinematic" and "mechanical" methods which forced their way in, despite complete incompatibility with the established proof structure.
In the present century many new fields of mathematics have developed almost overnight as a result of problems thrown up in engineering, science and technology; at the same time, probably the most sustained and determined attack of all time has been made on the foundations and structure of pure mathematics with the aim and purpose of strengthening and unifying the logical framework which holds it together. It follows from all this that, in considering the nature of mathematics, we must concern ourselves with the developing whole—not only with the formal accepted logical framework, but also with the methods of work and the thought processes of mathematicians, the connecting threads of suggestion and analogy, the language and notation through which communication is established.
Which is more important, the components of a syllabus or the power of mathematical thinking which is developed in the pupils? If we introduce modern mathematics into our schools is it because we are interested in new content and more powerful applications, or is it because we are interested in new methods and new ways of thinking about mathematics? What, in fact, are the aims and purposes of mathematics teaching? Unless we give some careful thought to such questions our teaching is likely to remain at a mediocre 21 22 MARGARET E.
The Process of Learning Mathematics by L. R. Chapman (Eds.)
by Edward
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