All together now

John Donne says you'll flunk

Back when I was a teaching assistant in a university math department, Professor Joshua Stone was fortunate enough to secure my services as his sidekick in an abstract algebra class. As one of those slightly overzealous TAs, I'd sit in on the actual classes as well as holding office hours and grading exams. Stone liked to break his class up into teams and hand out projects for cooperative work and exploration. One day I was in Stone's office as he shuffled through a pile of comment forms from his students. He suddenly started chuckling and tossed one of the pieces of paper at me.

“Check it out, Zee. What are we supposed to make of that?”

I turned the sheet of paper right-side up and read the words, “More small groups!”

“It's a puzzler,” I admitted, grinning at the professor.

Stone smiled back. “Yeah. Does the student want me to give them more problems involving groups of small order, or does the student want me to break them up into small teams for group work more often? You can read it either way.”

“Or both!” I suggested.

❏

Professor Stone was a big fan of having his students work together in small groups, exploring mathematical questions and pooling their insights and resources. The success of the small-group technique, however, was anything but predictable. It was affected by the aggregate personal dynamics of each class and the weird fluctuations caused by partitioning the students into different small-group configurations. Some classes adapt happily to group work while others resist it strenuously.

So it was at the university back in those days and so it is at my community college in the present day. I've become a little more canny about breaking up my own classes into small groups, trying to balance each team to increase the likelihood of successful cooperative effort. Nevertheless, I keep running into particular students for whom this learning technique is a complete failure.

I really don't know what to do.

The pitfalls of small-group work are obvious to anyone who thinks about it for a moment. You can have a group in which one pushy student takes over and drives everything (including his or her classmates away). You can have a group in which everyone is exactly the same and nothing gets done; a kind of group paralysis ensues. (If you let groups form entirely on their own, it turns out that your weakest students have a remarkable propensity for clustering together in a kind of “reverse” brain trust.) You can have the bright student who resents the possibility (even the likelihood) of the group riding on his or her ability to do the problem—and is happy to complain to you about it at great length.

But my particular problem students are distinct from all of the above situations. They are, rather, the loners who seem unable to connect with what their classmates are doing. It seems not to matter how I set things up. I can encourage a round-table format in which each student takes a turn trying to make a contribution. They either pass or merely mumble something indistinct. I can instruct the class that each team should cross-check each answer among the team members before moving on to the next step or problem. It's to no avail. Certain students deal themselves out and end up alone and doomed—like a caravan traveler left behind in the middle of the desert.

I have two recent examples in mind. One young man was a chronic underachiever who also had difficulty getting to class on time. We did group work only a few times during the term he enrolled in my calculus class, but each instance was a crashing failure for him. I thought it might be a language barrier, although he seemed to understand me when I conversed with him. But even that excuse was swept away when he was in a team with a young woman who spoke his primary tongue and chattered away at him in that language, trying to get him to get to work through the problems with her. Even on that occasion, though, he handed in an incomplete worksheet. It was just too much trouble to transcribe what his teammates were doing. He penciled in some partial results of his own and missed the mark once again.

Every time it was the same story with him: a long period of sitting inertly while his classmates churned away, followed by some half-hearted scribbles that mostly ignored what they had been doing, and submission to the teacher of an incomplete paper.

The same class contained another student for whom group work was an exercise in futility. It didn't matter how loudly (or frequently) I declared, “Confirm your answer to part (a) with your neighbors before going on to part (b)!” The instructions didn't apply to him. He would hunch over his paper like a hungry dog with a bone, afraid that some mangy cur would snatch his prize. This student would triumphantly hand in results that bore no relationship to the right answer. The right answer that every other student in his ignored team had.

When I patiently asked him why he had not followed my instructions to verify his intermediate steps with his classmates before pushing on to the conclusion, he began to explain very defensively how he had done his work. I interrupted the flow of words and asked him again. Why had he not conferred with the other members of his team? He doggedly returned to his explanation that he knew how to do it, refusing again to answer my question. The evidence, however, contradicted his claim of competence.

These are just two of the students I never reached. And I still don't know what was going on. What will I try the next time I see their like?