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Instructional Systems Design Project =**Geometric Proofs** =

Geometric Proofs...I would venture to say most people, myself included, have horrible memories of learning geometric proofs in high school. I can remember staring blankly at my teacher in 9th grade thinking, "I have no clue what you are talking about." Now, I very often get these same blank stares at me as I am teaching the dreaded second half of Chapter 4.

There has got to be a better way to help my students understand them. I can remember thinking in college (I LOVED my geometry class), this is not that difficult, what was so hard about proofs in high school? Geometric proofs are all about making connections and making a logical "argument" to prove a statement true.

There is a definite need to teach students how to understand geometric proofs in a way where they are confident in their approach and that they have reached a logical conclusion. I believe that the main problem is due to a lack of knowledge as well as a poor attitude towards proofs. For the knowledge aspect, proofs are brand new. No previous math teacher has ever required such a thought process. For the most part math up to this point has required following a specific process...there was no need to "think outside the box." Also up to this point in mathematics there is typically one right answer or approach to solving a problem. Now, we have no numbers, no symbols, just WORDS and application of geometric theorems, postulates, and definitions! As for the attitude, it comes from friends or siblings who have taken geometry previously an been unsuccessful in mastering proofs. Students sometimes have their minds made up before they even get started that proofs are impossible and they aren't even going to waste their time trying.

The most challenging part about my instruction will be to help students overcome their fear of proofs and start with a brand new I-CAN-do-this attitude. Once I help the students to overcome the overall intimidation of proofs, the instruction itself will be easier. Teaching proofs is never easy, but with a more motivated crowd, the response will hopefully make the instruction less burdensome.

I will evaluate my students in a few different ways. I will include a group assessment where students will complete some proofs in groups. This helps with confidence as they are able pool their knowledge and come up with a correct proof with the assistance of one another. At the end of the unit, I will also evaluate my students individually in a more formative assessment situation. I am also thinking about including a piece where they create their own situation that another student has to prove. (I'm still working out the logistics of how that would actually work.)