Displaying similar documents to “Didactical Analysis - a Plan for Consideration”

Dogmas and the changing images of foundations

José Ferreirós (2005)

Philosophia Scientiae

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We offer a critical review of several different conceptions of the activity of foundational research, from the time of Gauss to the present. These are (1) the traditional image, guiding Gauss, Dedekind, Frege and others, that sees in the search for more adequate basic systems a logical excavation of structures, (2) the program to find sound formal systems for so-called classical mathematics that can be proved consistent, usually associated with the name of Hilbert, and (3) the historicist...

Mathematical practice and naturalist epistemology : structures with potential for interaction

Bart Van Kerkhove, Jean Paul Van Bendegem (2005)

Philosophia Scientiae

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In current philosophical research, there is a rather one-sided focus on the foundations of proof. A full picture of mathematical practice should however additionally involve considerations about various methodological aspects. A number of these is identified, from large-scale to small-scale ones. After that, naturalism, a philosophical school concerned with scientific practice, is looked at, as far as the translations of its epistemic principles to mathematics is concerned. Finally,...

Mathematics and Morality on the Cusp of Modernity

Peter Dear (2001)

Revue d'histoire des mathématiques

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This note suggests that a fruitful way of investigating the history of mathematics lies in consideration of its pedagogical purposes. As a general illustration of the directions that such an approach might take, the paper discusses early-modern arguments for the practical utility of mathematics and its capacity to inculcate good habits of thought, as well as the appearance of new uses for mathematical training in the later eighteenth and early nineteenth centuries that served the purpose...