Check this out for a 'new' teaching idea for presenting geometric proofs:
|Euclid's proof of the equal angles in an isosceles triangle |
(the famous Pons Asinorum), as presented by Oliver Byrne in 1847.
Image from the Oliver Byrne image project at the University of British Columbia
This comes from the amazing 1847 Oliver Byrne version of Euclid's Elements. I'm thinking a page or two from this image library will make for a great exploration activity with my Year 9 class currently learning about geometric proofs and congruent triangles.
Of particular interest to modern educators is Oliver Byrne's introduction where he argues:
"Illustration, if it does not shorten the time of the study, will at least make it more agreeable. This work has a greater aim than mere illustration ; we do not introduce colours for the purpose of entertainment, or to amuse by certain combinations of tint and form, but to assist the mind in its researches after truth, to increase the facilities of instruction, and to diffuse permanent knowledge." (Byrne, 1847, p vii)
and continues with a decidedly modern take on how using visual imagery aids memory retention and understanding. I love how he denies this is merely a form of entertainment - anticipating the charge of "mathotainment" sometimes cast on alternative teaching approaches today.