I recently posted some photographs of my geometry students taking a team test. The idea of a team test is that the students work together to solve difficult problems, ones that may be slightly beyond their grasp at the moment. The progress made in all the classes was impressive. Here, I thought I’d share some new photos to give you a better idea of what a team test can look like, and talk about what I’ve learned by letting the students figure out for themselves how to solve the problems.
The picture that heads this post is of a very effective group. It has two 8th-graders and two 9th-graders. They came to me at the beginning of the assignment and asked if they could pull the table apart to sit closer together and work on the problem. That’s what they wanted, so I should object? And that’s how they worked…and very successfully.
Other students had different approaches. Here’s a picture of the table in front of theirs. You can see the students I just described in the background, but in this picture not all the students wanted to be seated. I’ve noticed that students like to clump together (see pictures below), and like to stand and lean. Every group is different. Compare the group in the foreground with the ones in the background. Both worked very successfully on a set of difficult problems.
In fact, there’s a good argument that we should let the students decide how they want to organize their work space. Here’s another example from the same class. While you might think that the student on the right who’s lying on the desk isn’t involved, he’s actually talking a lot, asking questions, and making contributions. This is exactly the kind of activity that I, as a teacher, want to see:
Here’s the next period at the same table. They have different postures and positions, but all were working and contributing. Posture, contrary to what I was taught in elementary school, apparently does not determine successful learning:
Other people like to sit on the table. As long as I keep the lug nuts supporting the tables tightened and there’s no physical danger to the students, I really don’t care where or how they sit, as long as they’re engaged. Here, note that two of the students are sitting on the table, one (at the right) is standing, and one is sitting and writing with his pink hoodie drawn up over his head (I usually make them take off their hats and hoodies, but engagement is engagement, and something has to give):
Sitting, standing, lying on the table, sitting on the table: does it really make a difference? As far as I’ve been able to tell, no. I’ve often thought that we start school insanely early for teenagers (10 am would be my ideal start time), but we run into transportation problems with parents (which on some level really shouldn’t be driving the discussion, but I’ve had to take my own children to school and I understand how disruptive it can be to an adult’s work day to do so).
Anyway, we see all kinds of positions. Here we have leaning, sitting, and sitting atop the desk….and they were really productive results on their tests, though they originally thought otherwise. (Americans think that if they don’t solve a problem immediately that they are somehow inferior, instead of thinking that the problem is a difficult one worthy of their best efforts.)
Finally, here’s another group with another positioning. Note the girl on the right with her head flat against the desk:
When I first saw this group, I thought that she had checked out, but in fact, as I listened and observed, it was clear that she was paying very close attention to the discussion and offering questions and suggestions on how to solve the problem. The old adage still applies: trust, but verify. When I listened to their conversation about the problems, it was everything I had hoped it would be. Heads on the desk are not an indication of a lack of interest or involvement if you really check it out. Also, I love Joshua’s lotus position atop the table, in which he apparently feels more comfortable.
I hope that it’s clear from my last few posts on this subject that students collaborating together in math is a powerful instructional technique. It’s not easy: the entropy of adolescent enthusiasm can overwhelm the enthalpy of collective action. Doh! I just made a thermodynamic analogy that probably makes no sense, so let me rephrase it: even young adolescents can learn more from working in a group than they can on their own. The problem is that they’ve been trained to work separately rather than together. The real problem of education is how to get them to the point where they realize that they are stronger and smarter together than apart. Doubtless you’ll be hearing from me more on that in the future.