I'm noticing that more kids are gaining confidence in looking for patterns, forming hypotheses and then seeing if they can make the hypothesis fail. The phrase that seems to be gaining ground when it comes to hypothesis testing is "wreck it"-as in "Oh, you think you have a rule? See if you can wreck it."
This diagonal problem is nice because a lot of students seem to zero in on special cases. For example, an n x n (or I just call them squares) rectangle has a diagonal that passes through n squares. There have also been some nice attempts at nailing down rules for odd x odd and even x even rectangles. We're finding that special cases don't lead us right to a general rule, but the information can be useful.
I've put together a flow chart that seems to be helpful.
Some students get caught in the Do research-->do you see a pattern?--> Do research loop others are making it to the hypothesis before being kicked back to research. All are having to come face to face with their impatience. Some are owning it.
There are a lot of mistakes being made. There's some frustration. There's arguing. There's collaboration.