After a smashingly successful first day doing proofs in Geometry I was excited to prepare for day two!  Our Geometry classes are not tracked (leveled).  On day 1 I noticed that I had a wide range of proof writing ability.

I still wanted the students to have time to think and process the proofs as they did the day before, but I did not want to go too slowly for some students, or two quickly for others.  I wanted everyone to be able to think and to learn at their own pace.  Enter Stations.

I am a huge fan of stations for review, but I really haven’t done much at the beginning of a unit.  This worked beautifully!

I gave my students six proofs in (of course) an INB foldable.  All they had were the givens and the prove.  I had them work on them silently for 10 minutes.  After the 10 minutes, they were able to work with a friend, and move around to the stations.

At each station, I had a copy of the same proofs that were on their papers, with some “hints” added.  The “hints” were the “fill in the blank” that can help students along if they get stuck.  On the back of the picture frame I had the proof fully worked out.

I encouraged the students to try the proofs FIRST, then if they got stuck or needed a hint they could go to the station.  Or, if they finished the proof they could check their answer with the proof answer on the back of the station frame.  Many students did not WANT the hints.  I agree with them, I really hate reading how someone else has solved a proof before I have time to think about it and try it on my own.  But, I did want students to check to make sure their proofs were similar to mine.  Since they are just beginning proofs, they often leave steps out.

This activity worked so well!  Students had time to think and try to work out the proofs on their own.  They were able to move around at their own pace.  They could get a hint if needed, and check their answers.  Another great thing came out of this as there are usually a few ways to solve each proof.  I loved it when a student proved something in a different way and came to ask me about it.

We still have a long way to go, but I feel this gave them a great foundation!

** I did not provide the proofs I used here as I “borrowed” them from many sources and am not sure where they all even came from.  🙂

After a couple weeks of p, q logic proofs, we started proofs “for reals” in Geometry this week.  First, we did algebraic proofs.  The kids were not happy that they had to show all of their steps.  “But I can do this in my head!”  Yeah, right.  At least it was a pretty easy introduction to proofs.  Anywho…

After learning all about segment and angle addition postulates, we started beginning baby proofs.  The first day went really well.  I took a page from the amazing Fawn’s book and modeled my first proof lesson after her problem solving lessons.  After all, proofs are just giant problems you have to figure out.  I gave them a proof.  We wrote down our “given” and marked up our diagram.  Then, I had them “think” silently for a few minutes.  I encouraged them to write what they were thinking or to take notes, but they didn’t have to do any “work”.  I just wanted them to think about what they knew.

After those few minutes, I gave them a few minutes to talk to their group about their observations and what they were thinking.  I walked around and heard amazing things.  “Could we just add these up?”,  “Aren’t these equal?” and “I think we could use the segment addition postulate here.”  Then, we pulled it all together.  I let the students tell me (and each other) what I should do next.  The students explained their thinking to their peers and I also jumped in occasionally when needed.

Learning how to “do” proofs (how to prove something) is problem solving.  This takes time and effort.  This takes a person looking at something on their own and really trying to figure it out.  You can give a student strategies, but I don’t think you can “teach” someone how to do a proof.  They need time to figure it out on their own.  The time spent in class “thinking” and “talking” to each other before actually doing this together as a class was well worth the time.  First of all, I have freshmen, so a few of them are not doing their homework as consistently as I would like.  This means that the in-class time is the only dedicated time they will get.  Also, many of my students get frustrated on homework at home and will just quit.  I wanted them to have support when they were starting out.

The best part was when we worked as a class.  Since I gave them time to think silenty and work together, some of my students “figured” out the approach they would take.  They were excited to explain it to their peers.  Their peers are much tougher on them than I am!  Students often had to explain their reasoning in a couple of different ways.  The listeners wanted to know how and WHY their classmates are doing a certain step.  And voila, there are the proof “reasons”.

I was worried about teaching proofs, but it has been amazing so far!

Day 2 – Proof Stations!