for the learning of mathematics

Jérôme Proulx and  David Pimm - Vol. 28 Num. 2 (2008)
 Algebraic formulas, geometric awareness and Cavalieri's principle


This article discusses issues of geometrical awareness by means of an exploration of the concepts of area and volume drawing on a historical theorem (now-named Cavalieri's principle) due to the seventeenth-century mathematician Bonaventura Cavalieri. We draw ideas from and work through this principle to illustrate insightful geometrical awareness that can be obtained within school area and volume teaching, in contrast to a more-usual 'formulas and computations' perspective, and argue for in-depth qualitative awareness in geometry. Mathematical in essence, the article points to the fact that geometry need not only to be seen arithmetically and algebraically, but also in its own terms, that is, geometrically.


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