Wednesday, February 20, 2013

Day 98: Intro to Proofs

Part of the revamped curriculum I created was to find a better way to teach/use proofs. In the textbook my school uses, proofs are started in Ch. 3 amid a random assortment of other information (such as solving a system of linear equations algebraically), and they're not heavily emphasized as the book progresses. I don't see the point in starting them out so early, because there are not a lot of applicable skills so early in the course, so any proofs would be so short to be almost pointless. 

All I really want out of proofs is for my students to get the idea that they need to be able to justify their reasoning with other concepts we've leaned in the course. Hearing a student say "that angle is 90 degrees because it looks like it is" is one of those things that makes me die a little each time I hear it. 

With the short week and the Unit 6 Assessment on Friday, I wasn't sure what else to do, so I created a handout with 4 very basic proofs involving triangle congruence. In my now 5 attempts at teaching proofs, this was probably the best go at it I've had. Students really did seem to appreciate what was possible with proofs as well as the structure and sequence of it. 

My hope is that moving forward, I can really push hard on using proofs to test true understanding of the content. Instead of memorizing that parallelograms have congruent opposite angles, can you prove WHY that must be true? In my opinion, the former is a MUCH better test of learning than the latter. 

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