Monday, March 9, 2009

Geometric Proofs

I believe hands down the toughest subject for students is proofs. There are a few reasons why that is the case. Number one, proofs tend to be taught very early in a geometry course. There is no way around it, but it causes students some problems. You have to teach proofs in order to work with theorems in a Geometry course, yet you teach proofs before students know a lot of definitions, postulates and theorems. The subject seems to come out of nowhere for students and causes some stress.

I want to give everyone a few websites that students can refer too while working with proofs. Hopefully this extra information will help students transition their thinking from Algebra to Geometry and especially geometric proofs.

Sparknotes have a great set of pages that can really help students. The website includes a table of contents that is very thorough.

Proofs for Dummies is another good website that seems to be affiliated with the popular books.

Another great website is How to Write Proofs. Again, there is a comprehensive table of contents that includes direct proof, proof by contradiction, counterexamples, just to name a few.

The Library of Math has a huge collection of proofs that students can use as a reference. Sometimes students need a few examples to see how proofs are constructed.

If anyone has any other websites to share I would love to see them. I have written and taught Geometry and this is always a difficult subject for me to explain to students well. Share your experiences in the classroom as well. I know I will learn a lot.


VCC Sunday Treats said...

Thank you for posting these websites. I did not find them on my own last year. I will share them with other teachers and new math teachers.

I am thinking of giving out some jigsaw puzzles to introduce proofs. The pieces represent the info you already know but they have to look at each piece to see if it helps to get to the 'proof'. Maybe they would have to write about how they got the puzzle solved - their strategy. Maybe I could switch a piece in a couple of puzzles so their 'proof' doesn't work. The picture could be the 'proof'.

Holly said...

Thank you. I am trying to tutor a geometry student and finding that it is much more trying than I expected. I know the subject matter, but have not tried teaching it before. I am finding that it is much more difficult to explain than any other math course material.

Patricia C Vener said...

I am about to tutor my nephew on doing proofs and am so glad your site and the links you provide came right up in my search. As a person whose perspective is that of a physicist, proofs have always been the least fun aspect of geometry for me. I don't want to let that bias have too much of an influence when I am introducing the topic to anyone else.