High School Geometry!

I recently found out that I am going to be teaching high school geometry this up coming school year. This will be my first time. This will also be the first time I teach high school.

At first, the best preparation I could think of was reading my old high school geometry text book and Euclid's Elements then I realized how vastly different they were. Euclid rarely dealt with the length of lines since he held himself to using an unmarked straight edge. The concept of measurement/number doesn't really appear until Book IX/X or so. He didn't measure angles. In fact, the only angles specifically named are right angles. Those two differences are huge.

I enjoy reading The Elements and working out the proofs. They are amazing demonstrations of constructive proofs! I don't really enjoy reading the high school text book but I can appreciate why there is a modern text book. The proofs, which are pleasingly elegant and logically organized, are also esoteric. They are probably hard to follow and boring to someone who hasn't studied advanced math, like high schoolers. This thought hits home even harder when I realize that the most educated of Greeks probably finished with studying The Elements. They had also probably studied Biology, Physics, Philosophy, Logic and Rhetoric before even setting out to work through it.

If Euclid isn't going to be my model, I am going to have to rethink my approach. Here are several books that I am reading to figure out what I should cover and how: Geometry in a Modern Setting, Designing Learning Environments for Developing Understanding of Geometry, Perspectives on the Teaching of Geometry for the 21st Century, Learning and Teaching Geometry, K-12. 1987 Yearbook and Geometry in the Mathematics Curriculum.