These are from my classroom, and a little bit of context might be helpful:

• This is from a very strong Honors class.
• Proof, right now, means something less formal in our Geometry class than it might mean in yours’. Proof doesn’t mean “Statements/Reasons.” Proof means offering an explanation for why something is true.
• We do this because it’s just as rigorous without crushing the souls of anyone in the classroom. Look at the array and variety of reasoning going on in these proofs. By keeping things less formal, we’ve got enough breathing room to actually do some Geometric thinking.
• As the year has been going on, though, we’re getting more and more rigorous. These exercises help reveal some sloppiness in the kids reasoning. These proofs fail by their own standards of explanation. I’m thinking that I’ll be printing these out and handing them back for discussion. This is exactly what my English teachers friend does with essays.

Feel free to comment wildly here, either on my standards, some of my bulletted statements, or about any of the student work.