We’ve been fortunate enough to have an article published in the February 2012 issue of the Mathematics Teacher, “Geometry in Medias Res”. We teach Geometry in a fairly unusual way, we think, so we decided to write about it and see what people thought about our approach.
One of our main ideas is that we want students to encounter interesting problems on the first day. So we ask them non-trivial questions right away (e.g. can every triangle be circumscribed?), and in the process of them discussing/arguing with each other, we start to develop with the kids the necessity for a standard of proof other than “it really seems like it to me!”.
There’s a lot more, but the idea is to have a more natural and intuitive introduction to the axiomatic nature of Geometry than one usually finds. We are big believers that proof is completely accessible to all levels of students, but that it has to be introduced gradually, as a way of resolving questions students have, not as a forced superstructure like the way it was often taught in the past.
If you have a chance to take a look at the article, we’d love your feedback and thoughts.