Tuesday, July 24, 2012

Made4Math Geometry Proofs


Well, it's really Tuesday, but I was visiting friends in Atlanta, so I didn't get this ready in time for Monday.

I have taught Geometry for 5 years. One of the more difficult concepts to teach, I found, was the geometric proof. My textbooks never gave enough practice, and I students struggled with "the next step," or forming their logical argument.

So I came up with the following series of pages.

The first one is a fill in the blank. In order to cut down on paper usage, I plan on using the clear sheet pockets our school has and have students fill in the blanks. This allows students to concentrate on providing a reason for a step, but taking the pressure off of doing a proof on their own.

Geo Begining Proof

I then use a hands on activity to help students sort through their thinking by literally sorting through statements and reasons. You can chunk this by having students start just by sorting the statements from the reasons, justifying why for each choice. I do this in groups of 2, and make 2 sets of these on different color cardstock. This can also allow students to see how a proof doesn't have to be done in a precise order sometimes (I relate this to baking, and how I can mix the eggs, sugar and butter first, or I can mix the flour, baking powder and salt first, but I can't bake the cookies until I mix the two sets of mixtures together.)

Here is a picture of one of the proofs cut out. Please note, they are not in order, as I just put them out there for the picture:




http://www.scribd.com/doc/100971513/Geo-Proofs

The next series of sheets I use are individual proofs for students. They are fill in the blank, but they are missing either the statement or the reason. As they progress to #3, they are creating their own proof, but they are given the number of steps it may take.

http://www.scribd.com/doc/100972429/Geo-Proof-Individual-1

http://www.scribd.com/doc/100972865/Geo-Proof-Individual-2
http://www.scribd.com/doc/100972897/Geo-Proof-Individual-3

6 comments:

  1. I miss teaching Geometry! Thanks for sharing your proof idea! :)

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  2. Do you find that using these methods makes the proofs that students write on their own better? I have used fill in the blank proofs for years and find that they don't necessarily improve the proof-writing skills of my kids.

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  3. in the beginning it helped. I haven't taught Geometry in 2 years now :-( Something my district had started focusing on was justifying thinking throughout all grades, and the hope would be that by the time the students hit Geometry, they would be able to give a reason for a step. When I first started teaching, I couldn't find anything on how to teach proofs. I almost think that they could have an entire semester just dedicated to writing proofs. I don't know if that answered your question

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  4. I'm working on geometry right now in school, and sometimes I find it difficult because I'll get almost the whole proof right, but I'll get like one or two of the statements or reasons wrong or missed. I feel like these "fill in the blank" proofs would be good while introducing a concept, but that they should gradually be moved away from and developed into full-fledged, independently solved proofs.

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  5. A resource that I have found to be very effective in teaching proofs is Proof Blocks. Check it out at www.proofblocks.com. It is worth trying!

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