I have had the pleasure of "mentoring" (which is a total misnomer...we really just learn from each other) one of our new teachers this year. She's amazing. Yesterday we were planning a probability unit together and we were trying to figure out an answer to the unit question that would drive our investigation of probability. In the process, her and I were collaborating, conjecturing and testing, investigating smaller problems, drawing diagrams, and listening closely to each other. Honestly, I don't really care if, as a class, we are successful in calculating an exact answer to this problem. I want students to come up with an answer that makes sense to them, that responds to their ways of knowing, and that is reflective of their deepening understanding of chance and probability. To quote a brilliant mentor of mine, "I guess my point is, 'solving' the unit problem will certainly be in the discussion but we'll be 'successful' moreso because students invented the solution, rather than being told." Mostly, I just want the students to have the same experience we had; the experience of playing with and doing mathematics.
I know there are "realities" in a lot of schools that make this difficult. Benchmarks, AYP, API, etc, etc. There are all sorts of measures of success and progress out there (most of which, I would argue, are false indicators of "learning"). Well, here's my vote for success/progress: