Geometry courses can be used to teach proof, and related mathematical thinking. So can other parts of mathematics, but by tradition, geometry is used that way. There are probably some good reasons for that - like to role that the visuals and the searching for connections within diagrams can help collect and structure the pieces for proofs. These features are often suppressed when the 'proof' is written out, giving an illusion of how thinking actually works - but it does work!
Sadly, many students see only the mysteries of the formal proof, and don't 'see' the rest of the process. They become lost and feel pushed out of mathematics, which is a great loss. You will find a lot of 'help' messages on this list from students who are on 'the outside looking in' when it comes to proofs in high school.
Latin also used to be use for that purpose. When I was a high school student, Latin was one of the options for proving you were prepared for Law School, because of the precision and the thinking that went on with the grammar.
HOWEVER, I will say that proof is not the main reason why geometry should be studied. In fact, too much proof buries the important geometric thinking which is needed for a number of jobs/applications. I studied lots of proofs (even at graduate school) and only later learned geometric thinking. I am glad I stuck around math long enough to also learn geometry!
I currently use geometry for a number of purposes: - with computer scientists to figure out how to locate objects in a network of moving sensors (e.g. a wireless office) (geometric control theory); - to model proteins and how they move when the function, when they fail, when a drug docks (a very geometric process); - to model when buildings fail, and what design changes would prevent that (working with structural engineers); - to workout how computers can control robot arms or other moving objects in space - a very geometric process (Computational Geometry); - to work out how to represent something like a car hood inside a computer, so it can be modified and manufactured (Computer Aided Geometric Design).
All of these involve lots of geometry - and only some proofs, seldom proofs of the type I learned in school. Sadly, some students are driven away from geometry because 'proofs' do not reflect some very effective ways of reasoning and doing geometry. Some students who miss out on the geometry of 3-D which is needed in engineering etc encounter really big problems in university, because the curriculum chose not to do 3-D (where we live) but rather to do 2-D (perhaps because it was easier to do proofs, and easier to write in elementary algebra).
There are studies that show: - students can get worse at 3-D geometric thinking as they go from grade 7 to 9 to 11. Distracting pieces, not connected to making sense (or using the senses). - they can get better if they are giving suitable exercises and practice in 3-D geometric reasoning (not to be confused with proofs).
We owe students a chance to experience the breadth and depth of geometric thinking. Proof is not the essential part of that, any more than proof is the essential part of algebra.
On 24-Jan-05, at 9:23 PM, david wrote:
I am a software engineer and I got into the field because of Geometry. When I was in H.S. I learned how to do proofs, and I thought they were fun because it was like doing a puzzle. You had some 'game pieces' to play with that you put in the correct order to solve the puzzle.
The next year in H.S. I took computer programming, and found doing proofs and programming computers to be very similar. The 'game pieces' were different, but the concept was the same. So, I'd say that a 'software engineer' is a job that uses geometry. Do I ever use the Pythagoras Theorem in my job? No. Do I use the skills I learned in Geometry 'prooving' the Pythagoras Theorem? You betcha.
Are there other fields that use geometry in the same way? Sure. Lawyers need to make arguements and write legal documents in the same way that you learn to do 'proofs' in Geometry. They simply have a different set of 'game pieces'. The same applies to virtually any of the sciences or any job that relies heavily on logic.
For me, geometry wasn't about learning about circles, lines, and angles and stuff. It was about learning how to think. Geometry taught me to think in a very specific manner than I had before. This is what I think geometry REALLY is all about.
BTW, this answer to your question is also an answer to some of the educators out there who ask why they should teach proofs or if geometry should still be taught in H.S.