I attended an Escape from the Textbook! meeting last weekend. The first part of the meeting focused on the mathematics of the game of Set, and the second part launched a conversation about assessment, which will continue in future meetings. Avery Pickford took notes, and posted them on his excellent blog, “Without Geometry, Life Is Pointless“. (Great name for a blog, and the converse is true: without life, geometry is pointless!)
One issue that came up at the meeting was: what could we learn about grouping in the mathematics classroom, from our experience playing the game of Set in groups of four? If you don’t know the game, it shouldn’t be too hard to learn about it on the Web, but you do need to know one thing about Set before you read on: this is a game where participants call out as soon as they see a “set” (as defined by the rules), so there is a lot of pressure to think fast.
One participant, who did not know the game, was in a group with three much more experienced players. This was, as you might imagine, quite overwhelming, and she commented that this episode confirmed her belief that it was best to organize students in homogeneous groups. The fact that her group-mates were thoughtful and considerate (probably much more so than many students in middle or high school) really didn’t help. She would have been much happier in a group of all beginners.
While it’s easy to determine who has different levels of experience in a given game, it is not so easy to make homogeneous groups. Among beginners, some may be fast learners. Among experienced players, some may be experts. And homogeneity becomes all the more difficult to achieve in a more general situation, as almost any group-worthy mathematical task involves a range of different skills and understandings, and rewards a range of different approaches. Thus my preference for random groups, changing every couple of weeks. (I’ve written more about this for my department, and shared it on this page.)
In my group we addressed the heterogeneity by taking turns instead of just calling out “set!” This helped calm things down, and made it much easier for me to think. (Like many students, I have a hard time thinking under time pressure.) We were informal about this, so that if someone was taking a very long time to find a set, others gently notified us they had found one, and they were able to take their turn early. In fact, the generally less frenetic atmosphere made it possible for our resident expert to explain how she thought about the game, and how she helped students think about it.
As a rule, I’m not a big fan of games in the classroom, precisely because they emphasize and reinforce status inequalities among students. I much prefer puzzles, which on the one hand more closely mirror the process of doing math, and on the other hand are easier to set up in non-competitive or less-competitive formats.
But back to Set. The strongest connection with the standard curriculum is with counting, as encountered at the beginning of an introduction to probability. In particular, our group found the question “how many cards can you have and still not have a set?” quite interesting, but we ran out of time before we answered it. (It turned out to not be as hard as I thought, and I was able to figure it out later that afternoon.)