The one topic in Geometry that brings students to their knees quicker than any other, is proofs… I love to teach proofs because I love the logic in it. I tell the students that they live in a proof world: I get out of bed (because my alarm clock is ringing), I take a shower (because I smell), I eat breakfast (because I am hungry), I stop at a red light (because it is the law AND I want to live). I am always looking for ideas on how to make geometric proofs that easy for them to understand.
I think congruent triangle proofs lead themselves to the Flow Proof method easier than any of the others. I tell the students it is a “visual” relationship. If your prove box reason has three letters then three boxes should lead into that box. The only draw back is when you use CPCTC (corresponding parts of congruent triangles are congruent)… I always get that handful of students who point out that there aren’t 5 boxes that lead into that, but I can’t make it too easy, huh?!?!
I like to use the SMARTboard when teaching these because it is easy to manipulate and move statements/reasons around. Here is a .pdf of my quick review (the first couple slides are a quick review from the previous lesson – used as a bell ringer). I let the student pass the marker around to the next student to write up a statement/reason. I also give them copies of the slides so they can work ahead or along.
I am trying some new ideas with algebraic, segment and angle proofs this year. I taught algebraic as two-column and had them work out the algebra problems as bell-ringers (showing ALL steps), then we went in and highlighted the completed steps (not their work). I had them write their work into words to the right and then we talked about how that gives us the reasons. We then did a couple algebraic proofs and from the exit slips I know they all have a greater understanding!
I am going to teach segment proofs this week and think I am going to use the “puzzle piece” idea. I tried it last year, but I need to figure out a way I can check quick just by looking at their output instead of actually making them write out the entire proof (they weren’t able to get a lot done last year).
I would love to hear if anyone has suggestions on how to teach coordinate proofs…