The Bay Area Circle for Teachers is hosting a week-long workshop, and I got to do a math circle there this morning. I decided to do the Spot It analysis again. I had a group of 6 teachers, ranging from a 2nd/3rd grade teacher to high school teachers. They were all eager and persistent, and we'd did lots of good thinking together.
They played the game in pairs, and one pair started analyzing it before everyone was even done playing the game. I'd guess more than half the time was spent with participants working in pairs, with us working as one group together the rest of the time. I provided cards for them to make their own decks (half-size, 2"x3", fun colors, from Office Depot), which some of them used. Yesterday I was working on organizing those quotes from Bob that all involve keeping the discussion in the hands of the participants, so I was well-prepared when one person asked, "Does ___ work?", to reply, "That's an interesting question," and wrote her question on the board.
One person made a deck with 3 symbols - actually, we called them objects today - per card. A few made decks with 4 objects per card. We put a table on the board with 4 columns: # of cards, # of objects per card, # of objects total, total # of appearances of each object. We said a proper deck would have each card matching each other cards once, and found two different decks for 4 objects per card. Our smaller deck had 5 cards, 10 objects, each appearing twice. Our bigger deck had 13 cards, 13 objects, each appearing 4 times. We looked at whether our smaller deck was minimal (the smallest possible deck for cards with 4 objects per card) and whether our bigger deck was maximal. We wondered whether there were any proper decks with sizes between 5 and 13 cards (for 4 objects per card).
I recently heard the phrase Noticing and Wondering, and used it to start the Math Teachers at Play post. (Unfortunately, I don't remember where I heard it.) I'm loving it as a framework. Just two words. Just two simple questions: What do you notice? What do you wonder? I asked that today.
We had about 2 1/2 hours, and figured out some good relationships. We did not answer the question of 'How did they do that?' (How did the company that makes Spot It manage to create 55 cards, with 8 pictures on each one, with every pair of cards having exactly one match.) But we made some significant progress toward that goal, and it was exciting to see the thinking the participants did. I'd love to run a 6-week math circle starting from this game.