other questions, correct each other, and give each other clues. They knew which
combinations they still needed to work on and discussed ways to learn more dif-
ficult combinations by using combinations they already knew. I wanted Heather’s
group to acquire these skills and play the game with a clear purpose and strategy.
Gaining Entry into the Mathematics
Based on what I heard and saw in Heather’s group, it was clear that I needed to revis-
it the reasons for playing the game and the mathematical concepts they were supposed
to be learning. The following day, I gathered Heather’s group together as the other stu-
dents played the game in pairs. I began by asking the group if they remembered what
they did yesterday with the Factor Pair game. As they demonstrated how to play the
game, I asked what they were learning. I was not surprised when they couldn’t answer.
At this point, I reviewed what it feels like to be stuck in a problem and what we might
need to do to become “un-stuck.” In other content areas, the class had worked on
reflecting on their learning using the following prompts based on the Thinking
Dispositions from the Artful Thinking Program (Richhart, Turner, and Hadar 2008):
REASONING
What do you think is going on? What are your reasons? What makes you say that?QUESTIONING AND INVESTIGATING
What would you like to find out? What do you think you know? What ques-
tions or puzzles do you have? What might you need to explore?OBSERVING AND DESCRIBING
What do you notice?COMPARING AND CONNECTING
How does it connect to other things you know about?Getting “Un-Stuck”4 x 6
6 x 4
(^424)
Figure 19–1.Array card with factor pairs on the front and product and one dimension
or factor on the back.