Looking at HPM through an old chestnut: Sum of the angles of a triangle
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Some teachers do not regard the computation of the sum of the angles of a triangle by using a cut-and-paste or paper-folding method as providing a proof that the sum of the angles of a triangle is equal to two right angles. Some even think that this way of working is not mathematics but more like an experiment in physics. Some see the method as no better than measurement of the angles by a protractor. The author will examine this issue in the teaching and learning of school geometry and more generally as a specific example from the perspective of HPM (History and Pedagogy of Mathematics).
Abstract
Some teachers do not regard the computation of the sum of the angles of a triangle by using a cut-and-paste or paper-folding method as providing a proof that the sum of the angles of a triangle is equal to two right angles. Some even think that this way of working is not mathematics but more like an experiment in physics. Some see the method as no better than measurement of the angles by a protractor. The author will examine this issue in the teaching and learning of school geometry and more generally as a specific example from the perspective of HPM (History and Pedagogy of Mathematics).
참고문헌 (6)
- A. C. Clairaut, "Éléments de géométrie", pp.1741~ (2006), Éditions Jacques Gabay
- J. Fauvel, "History in Mathematics Education: The ICMI Study" (2000), Kluwer Academic Publishers
- T. L. Heath, "The Thirteen Books of Euclid’s Elements" (1925), Cambridge University Press
- Yu I. Manin, "A Course in Mathematical Logic" (1977), Springer-Verlag
- M. K. Siu, "Zhi yì xíng nán (knowing is easy and doing is difficult)”or vice versa? —– A Chinese mathematician’s observation on HPM (History and Pedagogy of Mathematics) activities, in The First Sourcebook on Asian Research in Mathematics Education: China, Korea, Singapore, Japan, Malaysia and India" (2014), Information Age Publishing
- M. K. Siu, "History of mathematics in classroom teaching—Appetizer? Main course? Or dessert?", Mediterranean Journal for Research in Mathematics Education, 3(1-2), pp.5~10 (2004)