By Victor J. Katz
There's a lengthy culture of referring to the background of arithmetic to its educating, and more and more this has prolonged all through mathematical schooling. This quantity brings jointly articles from popular figures during this zone, and offers many insights, either particularly instances and in generality, into how the heritage of arithmetic can locate program within the instructing of arithmetic itself. Educators in any respect degrees, and mathematicians drawn to the background in their topic, will locate a lot of curiosity during this ebook.
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Additional info for Using History to Teach Mathematics: An International Perspective (New Mathematical Library)
Sample text
In retrospect, it is perti nent to remark that whereas the idea of variability had been banned from Greek mathematics because it led to Zeno's paradoxes, it was precisely this concept which, revived in the later Middle Ages and represented geometrically, led in the seventeenth century to the calculus. Nevertheless, as the culmination of almost two centuries of discussion on the basis of the new analysis, the very aspect which had led to its rise was in a sense again excluded from mathemat ics with the so-called 'static' theory of the variable which Weierstrass cIeveloped.
This century saw the wide dissemination and serious study of Euclid's Elements and of the works of Archimedes. Tak ing pride of place in this revival of geometric research were Archimedean themes, in particular the calculus of areas and volumes of geometrical figures and of their centers of mass. This sector expanded very rapidly, and maintained its lead ership for most of the following century. The calculation of areas and volumes was one of the main problems of the early years of the seventeenth century, while the method of exhaustion was the only technique handed on by the an cients.
Under which historical conditions? The traditional idea that the development of mathematics is purely cumu lative is largely out-of-date. Teachers must remain aware of the inherent relativity of knowledge, and of the fact that, in the long run, providing students with an adequate view of how science builds up knowledge is more valuable than the mere acquisition of facts (von Glasersfeld, 1991). Yet there is a growing debate concerning the role of the history of mathematics in mathematics education.