Oct 23 2008
Geometric Generalisations (A response)
I have read Nico’s blog about the benefits and use of utilising geometry software within a classroom. I agree with him that these are an ideal chance to get the students to construct their own knowledge.
Nico talks about the dynamic nature of such constructions i.e. “when constructing the bisector of an angle, dragging the arms of the angle and therefore changing it don’t change the fact that the bisector still divides it in 2 equal angles”. I just wanted to mention that this has been a researched benefit of such software. The dynamic nature allows students to see the generalisations of a construction. Or if you like, it aids the student in seeing that a property doesn’t just hold for one example, rather it holds in all cases (Kissane, 2002). This overcomes the problem of a student questioning the validity of a proof, as it shows that the property holds in more than one instant.
Within our curriculum, I see this as particularly useful in the area of circle constructions where a large number of difficult constructions are necessary. For example, the image below shows a construction which the students could generate to construct their own knowledge that the angle in a semicircle is a right angle.
Kissane, B (2003). Using Technology in the best possible ways. Reflections. 27(1). 2-11.
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[...] the software is not limited to functions and co-ordinate geometry, as Matthew points out in his blog it could be particularly useful for circle geometry, and I would suggest also some trigonometry, [...]