1) Students ask mathematical questions (that in turn drive their learning)
2) Students and teachers seem happy to be in class and proud of their contributions
3) Students and teachers relate what they learn to what they already know (in math and in their lived experience) and to what they want to know more about/do better (in math and in their lived experience)
4) Students and teachers collaborate to learn and make sure everyone is learning
5) Students and teachers communicate their ideas fluently out loud and in writing
6) Students solve novel problems with a variety of strategies, tools, and representations
7) Students and teachers ask not just “am I right?” but “how do I know?”
8) Students and teachers ask, “what other math/patterns/generalizations can I discover from this?”
9) Students and teachers ask, “what are we learning about? what’s the big idea? what do we need to practice to get better?”

What’s missing? What’s superfluous/not fundamental? How do you know that your classroom looks like you want it to? How does this relate to what you assess?

Working on this problem:

100 people are in a room. In the next room, there are 100 identical boxes. Each box contains one person’s name (and each person’s name is in exactly one box). One at a time, each person can go into the box room and open up to 50 boxes. Then, they must return the box room to its original state (no re-ordering boxes, no marking boxes in any way). They leave the room and don’t communicate with anyone else. Individually, each person is asked, “which box had your name.” Fabulous riches are showered down on the group if all 100 people answer correctly. Are there strategies they can use to improve the odds that they answer right?