# Elementen en principia van verhoudingen

 Tijdschrift voor reken-wiskundeonderwijs, uitgegeven door het Freudenthal Instituut, Universiteit Utrecht in de periode 1981-2013 De Nieuwe Wiskrant berichtte vooral over nieuwe ontwikkelingen op het gebied van wiskundeonderwijs in het voortgezet onderwijs, zoals de vernieuwde tweede fase, ict in het onderwijs, de nieuwe plannen voor vmbo, zelfstandig leren, toetsen en examens, de A-lympiade, de Nationale Wiskunde Dagen, e.d. Streefland, L. Nieuwe Wiskrant. Tijdschrift voor Nederlands Wiskundeonderwijs 1982 – 1(4), 32-38 In older times the ancient Greek mathematicians created the building of deductive geometry. In Euclid’s ‘Elements’ one can take cognizance of the way the building looked like at 300 B.C. Euclid’s fifth book in the ‘Elements’ contains a pure, formal, deductive theory concerning ratio and proportion. The development of the theoretical notions for ratio and proportion demanded many decades before Eudoxos — to whom this theory has been attributed — was able to take the last steps in theory building. In the sixth book of the ‘Elements’ the applications of ratiotheory, like the similarity of triangle’s have been dealt with. It is the authors concern to make the readers aware of this change of sight. Instead of justifying the theory by means of the geometrical phenomena, which served as a soil for its development, the abstract theory was premised, followed by its applications, thus neglecting its origin. There exists a parallel between the development of both mathematical and physical theory. Newton — for instance — argued in his ‘Principia’ —in accordance with the accepted ‘regulae philosophandae’ — that (repeated) experiments with respect to physical phenomena bear the main justification for related physical laws. If mathematical and physical ideas needed a meaningful soil to be derived from in history, a corresponding condition must certainly be claimed in education for the pupils. voortgezet onderwijs, [id:fi2726] Download pdf

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