Wednesday, July 08, 2009

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?

13 comments:

intrinsicallyknotted said...

More stories about teaching! (That request isn't quite so confusing, I hope.)

Since I'll be teaching my first course next fall (calculus with precalculus), I've been contemplating various teaching methods I can use and ways to engage the students. I guess it hadn't occurred to me that group work could be so unpredictable; I would have assumed it to be a pretty reliable way to get students engaged. Given that I haven't actually taught a course before, do you think it's worth trying this method once or twice? Or do you think it might be too risky, since I may not have the experience to recognize when things aren't working?

Zeno said...

Even experienced teachers get surprised when they try different techniques because students have a wide range of personalities and react in an equally wide range of ways. Nevertheless, you can expect certain things to occur fairly reliably. Group work is typically effective in giving everyone a chance to "do well" because the team effort shores up the weaker members. However, it easier for the shy or disengaged weaker members to fall by the wayside if the groups are too big (I think 3 to 5 is the optimal number for most activities).

Also, have definite goals in mind, even if the students might wander while getting to them. Set up worksheets or projects that give a modicum of guidance without actually leading them by the nose. You want the brightest students to discern quickly where things are going and the weakest students to be able to grasp it when it's explained to them by their classmates (ideally, anyway).

Group work always takes longer than direct lecture to cover the same amount of material, but student retention can be higher because of the hands-on component. Judge accordingly, depending on how stuffed your syllabus is.

It's best to over-prepare and have things you didn't get to than to under-prepare and be left in the doldrums. But do put group work in your mix of techniques. A class can get dull if it's the same old routine every day. And it gives you a chance to interact more directly with your students as you roam about touching base with each group in sequence during the lesson.

Oded Shimon said...

Zeno, I'm wondering how well YOU would have done in a group work class, given what you said about your status during education. (As I recall, only one other person in school with a briefcase? :)

Zeno said...

Interesting question, Oded Shimon. Group work was not in vogue when I was in school as an undergraduate student. I probably would have regarded it as unnecessary, or even an imposition (since I normally didn't need the help of others to do the work). Later, though, in grad school, it didn't bother me and I was able to work well with others. Mostly.

sublunary said...

This enty was very interesting to me because I always hated group work. I was one of the shy loner kids through high school and was still terrified by other people during undergrad.

For me, the most dreaded moment in class was when the teacher/TA/professor ordered us to select our own groups. I'd get queasy just thinking about it. I was too shy to have actual friends in class, so while most students had group members in mind already, I was usually left out. Assigned groups were always a little bit less intimidating (but just a little bit).

I didn't take math in college, the clostest approximation would probably have been in chemistry class. There, group work always ended in confusion, because no one who understood what they were doing (certain TAs included) could explain it clearly to the rest of us.

I think it's funny; since college I spent 2 years getting a MA and 2 years working. Now I'm starting law school in the fall and the thought of group work still terrifies me...

Anonymous said...

The success of group work can also depend on the teacher. I had group work in two classes the same semester -- in Class A, taught by an experienced professor, even groups of seven or eight worked together really well, and we got a lot of interesting work done. In Class B, taught by a grad student, it felt like we were in kindergarten, and going over each group's results was slow, painful, and unenlightening. However, Z, it sounds like you have your act together, so I'm sure most of your students enjoy the experience. :)

Sili said...

I'm a lot like sublunary.

And I've always been lazy, so part of my beef with groupwork has been that I often had to put in more effort in order not to reflect poorly on my teammates.

I don't particularly want to teach, but so far I've had no luck finding any work, so unless something happens fast, I'll have to apply for a position at the CC where I worked in maintenance during my reconvalecense.

Poor kids.

Gary said...

I too always disliked groupwork. I've been a loner all my life, and in a group, I always feel that the other people are doing it wrong, missing the teacher's purpose.

I just finished the last class of a program I needed to complete for a teaching certificate. Yesterday we had to work in groups to make an acrostic poem from the word MOTIVATION and concepts from educational psychology, written as single words or short phrases. My group focused more heavily on the request to use short phrases than the request to use concepts from educational psychology.

Admittedly, it's not like a calculus class, it's a wishy-washy educational psychology class with a tenuous link to reality and largely pointless assignments. But one of the things I got from this class is that teachers now believe that such assignments, working in a group on something useless like an acrostic poem, increase student retention. Instead, they make the loners in the group remember the mistakes of others and the contributions they didn't get to make. Meanwhile, if the other students don't follow closely the teacher's intentions, they end up missing the goal of the lesson.

I intend to teach a science class someday (hopefully next year) and after participating in the classes for my certificate, which included numerous group-based assignments, I think that I will mainly use group-based activities when resources or complexity demands multiple people working on a task, but I won't use it for simple things like vocabulary reviews or reading articles or chapters from a textbook.

unapologetic said...

The only class I can really remember with significant group-work was my high-school (AP) physics class. I had a similar experience to Gary's, diverging from the path of the group, but with one difference: I knew they got the teacher's point, but I thought the teacher's method was misguided.

So each and every lab they'd go off with their experiment-heavy methods while I'd sit at the desks on the non-lab side of the classroom and work out a more sophisticated mathematical model that had fewer experimental inputs (and thus chances for errors to creep in). Yes, I didn't collect the reams of data the teacher expected us to, but was it my fault I got better results than everyone else in the class?

João said...

Thanks to a workgroup in Portuguese literature (Os Maias de Eça de Queiroz) I got to know a girl that became my best friend. More than twenty years later we keep that friendship and we still remember that assignment. Even though I prefer to work alone I must say things came out right that time.

Tony said...

Ironically, the only place where I enjoy group work is in mathematics. I have always found the process of math far more intriguing than the answers. The social aspect of that process has made me a much more rounded mathematician and conversations with group members forces me to practice clarity and hone my understanding. I fully intend to use as much group work as possible in my lesson plans.

Zeno said...

The social aspect of small-group work is valuable and should not be neglected in planning whether to use this technique. Especially if it's still early in the school term, small groups create an environment in which students get to know each other and build working relationships. As with any other thing, it doesn't work out that way for everyone (so no one should think of small groups as the one-size-fits-all solution to all pedagogical problems), but it does jump-start the process of making a classroom into a cooperative network of learners. To that end, I prefer group projects in which names are shared (sometimes one person in each group is charged with the task of taking names and recording each team member's initial results and setting the stage for the discussion that produces a consensus answer).

Group work is not my default mode of instruction, but it's an important part of my mix.

Anonymous said...

I often assign a group secretary; if your non-participating student is doing it wrong, and the grades of his group-members depends on what he is writing, his group members can police the situation themselves. I've had great luck exploiting peer pressure.

I feel like having individuals submit their own solutions at the end of group work can take the 'group' out of the work. On the other hand, doing it too often can take the 'work' part out for individuals, so I mix it up.