My hope for group work…and introverts


Lately I’ve been thinking about group work.

This past spring, I reached a point in a lesson where I wanted students to work together on a few tasks. Prior knowledge was there. Things were accessible. Heterogeneous groups abound. All the standard stuff. There was no reason why the kids shouldn’t have been good to go.

What did they do? They waited for me. They couldn’t get started without me but, even worse, they couldn’t even use one another to get the ball rolling. Despite being more than capable, they wanted me to feed them…again. I say again because this was a fairly common theme all year. It just took this particular lesson for it to hit me.

Realizing this, I didn’t want to lecture them on how I knew that together they could accomplish the tasks I set forth. So I sat on a desk and stared at them. The result was a bunch of concerned faces asking me why I was so quiet. I responded with silent eye contact to each and every one of them. It took a full three minutes of awkwardness before they pieced things together. Oh, he wants us to figure this stuff out. 

In the moment, I was really disappointed with them. I was borderline furious. I overplan my lessons, pour growth mindset into them all year, and live with a low floor and high ceiling. Yet why couldn’t they work together, independent of me?

It didn’t take long for me to realize that I was the culprit. This situation was a direct consequence of me neglecting to develop a culture of interdependency. Now that I think about it, my classes have been like this for years.

Next year I am determined to get out of the way. For everyone’s sake, my students must need me less. I want group work to be the norm. A successful mathematics class is dependent on communication and inquiry – both of these are byproducts of collaboration.

I’m still finalizing a structure, but thanks to a workshop by Phil Dituri, I have some tentative group norms that I’ll use next year.

  • If you have a question, ask your group before asking me.
  • If someone asks a question, do your best to help that person.
  • It is the responsibility of the group to ensure that each and every person in the group understands the task at hand.
  • If you finish and check your work, you should ask others in your group if they need help.
  • Discuss different answers and try to agree on one. You should be able to explain your group mates’ solutions as if they were your own.
  • No talking to other groups.

It will be challenging to develop these norms with students that may not understand how to work together effectively. There are strategies that will be helpful in the process, but I still may have to start with one or two at the beginning of the year and build on those.

I want my students to value collaboration and learning from one another, but there’s another aspect to this talk of group work that’s worth noting. It’s the societal belief that collaboration is the root of all things great and that everyone must collaborate in the same way. Susan Cain argues against this mantra in her book Quiet and I agree with her. She calls this the New Groupthink because it “…elevates teamwork above all else. It insists that creativity and intellectual achievement come from a gregarious place.”

This line of thinking is a huge disservice to our introverted students. I bring this up because of my own introverted tendencies, like preferring one-on-one conversations over group discussions, enjoying listening more than speaking, and leading in non-traditional ways. The need for some students to think and work in solitude is something I get. It’s how I’m most productive. Reading the book was like uncovering so much of myself.

Studies show that one third to one half of us are introverts. The class I mentioned was full of introverts and they needed a structure to work together. I hope that my system encourages collaboration and interdependency while addressing the needs of all my students, but especially my more introverted ones. My norms won’t be a saving grace since research advocates for other strategies to support introverts – such as small groups, individual think time, and supporting individual passions, all of which I could improve upon. But hopefully my group norms help to celebrate introversion and make it easier for students to rely on one another as opposed to me.



One Step, Crumple, Toss

The other day I did an activity that reminded me of both Kate Nowack’s Solve, Crumple, Toss game and Jon Orr’s Commit & Crumple activity, but it was slightly different.

I grouped students in twos and threes and gave each group one problem on a full sheet of paper. They struggled on a few concepts that we recently tested on, so the problem stemmed from those concepts. Each group completed the first step in their problem. That’s it. After, they crumpled the paper into a ball. After all the groups crumpled, I had them throw the ball at/to another group in the room. The receiving group would uncrumple the paper, check the work that’s already been done (correct it if necessary), and complete the next step in the problem. They then crumpled and tossed the paper to another group. This process continued until every problem was completed.

I like this activity for several reasons:

  • Firstly, students must put focused effort into starting a problem. Teachers, and math teachers specifically, know that the first step of a problem can often make or break a student.
  • Secondly, the bite-size chunks that they work on after each throw make long, multi-step problems easily digestible and accessible. They’re not stuck, sometimes haphazardly, on a single problem for extended periods of time. The students, without even knowing it, scaffold one another.
  • From a problem solving perspective, the idea of emphasizing the completion of one step at a time could be useful. The students themselves must decipher the procedural “steps” of a problem and also relate them to a peer’s work. This may help to develop the skill of breaking down a large problem into a series of smaller ones. I’m not completely sold on my reasoning here, but I feel there’s something meaningful on this front.
  • This activity affords kids the time to analyze and challenge each other’s work. It’s weird, but I’ve noticed, even with other activities, that students are highly engaged when analyzing a peer’s work. Maybe this is because teenagers are so judgemental of each other already, who knows.
  • On the teacher side of things, it’s never a bad thing when an activity gives you the opportunity to walk around and assess all period. It was so helpful to provide loads of individualized feedback to them on concepts they previously struggled with.
  • Lastly: who doesn’t like to throw things?! This was by far the best aspect of the lesson.

I’m still wondering about how things ended. The exit slip did show improved understanding of the concepts, which was good, but the conclusion of the activity could have been stronger. I posted the solutions for each question (they were numbered) and groups checked to see if the problem they ended with arrived at the correct answer. Most did. I also opened up a class discussion about common mistakes that were found as they checked work. That said, there still may be something better I could have done to wrap it up. Hmm.


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