Thursday, July 11, 2013

Collaboration Literacy — essential skills in mathematical learning groups (i.e., shared mathematical thinking)

It has long been clear to me that there are important skills of interdependence that I value in mathematical group work, but I have always been dissatisfied with the assumptions inherent in the existing models. My dissatisfaction always stems from conflicts with some of my deepest-held values about collaboration and about learning about collaboration.

Sam's post on Participation Quizzes was the first model I ever heard about that felt harmonious with what I know about healthy collaboration. I love the idea of using formative assessment of a group's collaborative interactions as a lens for viewing the mathematical learning that was going on. But I also know myself well enough as a teacher to know that I need a clearer, more explicit framework in my head so I can be both clear and intentional about the skills I am cultivating and encouraging.

Fawn's epic and brilliant deconstruction of successful in-class activities the other day referenced a touchstone work that I too really value: Malcolm Swan's Improving Learning in Mathematics manifesto. This time through, though, I was struck by four skill areas for group work that Swan touches on but does not develop.

These, I have realized, form the basis of a set of group work skills I could envision developing into a rubric for participation quizzes as well as a set of foundational "collaboration literacy" skills I could wrap my mind and heart around.

Here are the four skill areas I am thinking about for the collaboration skills rubric, along with my early commentary and thoughts:

  • SHARING SKILLS — in other words, developing a sense of inclusiveness as a member of a mathematical learning group. These skills include: demonstrating patience when others have difficulty putting their ideas into words; allowing others adequate time to express their own ideas; not moving on until everyone understands; and actively making sure that everyone understands why or how a piece of shared thinking/reasoning is so
  • PARTICIPATING SKILLS — developing your own agency as a math learner (i.e., making your own personal contributions to the group's shared thinking). Skills include: overcoming shyness to share your thinking with the group; managing your desire to take the microphone more than your share of the time; genuinely "showing up" with your own unique insights and gifts as a thinker; encouraging and supporting others as they speak their ideas, confusion, or questions.
  • LISTENING SKILLS — developing your own openness as a collaborator. Skills here include: listening actively and deeply; not simply waiting for your turn to talk; making eye contact with those who are speaking; asking clarifying questions; disagreeing respectfully; and agreeing and extending others' thinking.
  • EXPLORATORY TALK SKILLS — developing your voice as a math learner and as a member of a learning group. The phrase "exploratory talk" comes from Swan's discussion (page 37), and I think it encapsulates the qualities we are looking for when we ask students to collaborate to develop a shared understanding. These are areas where I believe The Math Forum's work really shines. Skills here include: noticing and wondering; extracting information and a question; paraphrasing or rephrasing; acting out a problem; plus making explicit transitions from one topic to the next and preventing transitions from occurring until the whole group is ready to move on. 
I envision self-assessment and peer assessment being vital parts of the process in addition to teacher assessments of individuals and groups.

I am particularly excited about ways to integrate thinking from restorative practices into this framework for mathematical learning groups because I believe they hold a lot of promise for improving the quality of student interaction.

I hope there will be a vigorous discussion in the comments!


  1. Ug, lost my 1st draft at comments. Mostly wanted to say, love it. But not yet ready for "vigorous discussion." That is, I think it is very on point, and don't see a place to deconstruct, to wonder...

    Maybe some commenters will ask and/or contribute "what is missing?"

    Further: What are the skills that would be particular to a group of students engaged in activity we, as observer, might call mathematical?

    1. This comment has been removed by the author.

    2. I always figure, there's no time or place to deconstruct or wonder than the present. I've been deconstructing in place since the 80s. ;)

      I think there is a really big — and troubling — gap in the ways in which we cultivate the social, emotional, and interpersonal skills that are a huge, unspoken part of all activity that we might call mathematical. Not attending to these areas does not mean that they are not at play in the classroom. In fact, I would argue that the more we try to ignore them, the more insistently they raise their voices and demand that we pay attention to them.

      Basically, I see a huge instantiation of the return of the repressed in these areas — both textually and psychosocially.

      I tried to sketch out below some of the ways in which I find listening in mathematical contexts to be an extremely underdeveloped — and consequently stunted — skill set in a mathematically collaborative context. I don't see how a learner can be empowered if s/he does not receive support and guidance in using the skill sets required for refined auditory processing. That is why they are an explicit part of ELA pedagogy. From what I've learned from @jybuell, it's one of the hottest, richest, and most fertile area of science pedagogy right now.

      I guess in part, I am calling on myself to give my math students the same advantages I gave my ELA students!

      - Elizabeth (@cheesemonkeysf)

  2. I was wondering if writing SUPER LIKE! vigorously counted as vigorous discussion (note that I typed that with great vigor and aplomb, finger raised several inches off the keyboard and pounding quite fiercely to add to the vigor).

    But then Brian (Bryan?) asked this gem: What are the skills that would be particular to a group of students engaged in activity we, as observer, might call mathematical?

    It reminds me of the 3 dimensions of accountable talk: accountable to community (nailed!), accountable to rigor, and accountable to knowledge. I have trouble keeping the last two straight (is that because I'm not knowledgeable about them or because I'm not rigorous in describing the two precisely?). I wonder if there are certain kinds of being accountable that are specifically mathematical?

    I'd also say the exploratory talk skills are the most specifically mathematical, though there are listening skills like asking to go back to shared agreement/definitions/given is deeply mathematical, as is insisting on rigor, precision, or logic. I wonder if there is a specific exploratory talk skill around accountable calculation -- for example, using labels, units, or names of quantities in calculations so others can follow the connections between your calculation and the problem scenario, when appropriate/possible?

    Finally, Bryan's quote about seeing "a place to deconstruct, to wonder..." also made me wonder if there is a Reflective Talk Skills area we could add? That moment (extended moment?) when we compare & contrast approaches, sniff out things like efficiency, portability, repeatability, when we think about how what we did could be extended, applied, or better understood? One deep, important part of math is as soon as we solve a problem, we try to either make a new tool, or bring the answer under another layer of scrutiny, and the disposition to do that as well as the skills to extend problems and compare and contrast multiple approaches and to move towards generalization are skills that are about ways of talking and sharing. That said, I don't think these are September communication skills!

    Thanks for this, Elizabeth -- I want to share it with everyone! Retweeting it was only a first step.


    1. Max – SUPER-LIKE backatcha! :)

      Thanks so much for engaging. I love the Reflective Talk Skills idea.

      Also, I wonder if the exploratory talk skills aren't simply the most developed mathematical skills rather than the most specifically mathematical. After all, as you said in one of your Ignite talks, listening TO students (rather than FOR the "right answer") is a difficult practice even for us trained adults. Imagine how hard it is for young adolescents!

      If it's difficult for us adults, it's a fair bet that it will be a challenge for adolescent learners. I have noticed that my middle school students find it very challenging both to listen (i.e., to attend auditorily) and to hear (i.e., to receive and understand) during collaborative work. I wonder if this is not exacerbated by the fact that naturally auditory learners are the smallest percentage of any group, making this the most challenging skill area that occurs in the least developed processing center.

      This discrepancy makes me wonder, why do we not explicitly coach students in deep listening practices?

      By the same token, the participating skills I am trying to identify and cultivate are social and emotional skills that support exploratory and reflective talk practices. Both the reserved learners and the microphone-grabbers have natural tendencies that need to be noticed and loosened in order to help the group achieve an optimal level of exploratory talk.

      By turning these areas into areas of shared group responsibility, I think it may be possible to raise the level of shared mathematical thinking and reflecting in the group work in my classroom. One thing I noticed this past year was that, when I called this kind of thing out, I heard a lot more shared responsibility for meeting these group expectations.

      For example, during Barbie Bungee, on my worksheet (which contained its own rubric), groups were asked to make sure to write down at least one noticing and one wondering from each learner in the group. I was thrilled to hear my kids following up with each other as they constructed the poster, "J — what was your noticing again?"

      I realized this morning that what I valued about this was that Student D was asking Student J to press the "rewind" button on their prior conversation. She remembered having HEARD J's noticing, but she couldn't remember exactly what it had been.

      But that is OK — it's why we take notes and write our thoughts down as we work.

      When J replied, D immediately said, "Oh, yeah! I remember that you noticed that!"

      These are the social underpinnings of the mathematical conversation that, when deficient (or absent), really impoverish the mathematical learning. That's why I am thinking explicitly about ways to build a rubric that can support the development of these essentially mathematical habits.

      Can you say more about what impressions/noticings/wonderings you have about the idea of Reflective Talk Skills?

      - Elizabeth (@cheesemonkeysf)

  3. One commenter asks, "What's missing?" What I can suggest is a class discussion of what the behaviors you want to elicit look like and sound like in a T-chart. Then follow it up with a few Socratic Circles where one group of students is in the inner circle working on a task and individual members of the outer circle observe specific, assigned behaviors. When the task is complete the outer circle debriefs.

    I need make this rubric math specific, but I've have a lot of success with it in lit/la/ss. (see page 3)

    As the year progresses and students improve their discussion techniques, eventually I'll want to capture one group on video and use it as a exemplar. I wish I did that last year but I ran out of time.

    I haven't read Malcolm Swan's work, but the collaboration literacy skills found in group work are similar to what I know as Complex Instruction. For the entire year last year our district's professional development was dedicated to designing group worthy tasks that elicit the behaviors you describe. I've written about it here

    What is also worth noting is that every student in the group must recognize all contributions are valued. Students who have "low academic status" must have access to the problem; that's why the task needs to be carefully crafted. There's also individual and group accountability where patience and all the other behaviors you describe are practiced and developed.

    I truly appreciate your contribution to the dialogue. Fawn wrote two great posts on problem solving and you are attending to the details of group dynamics and mathematical conversations.

    I look forward to learning what others have to say!


    1. Oops! Looks like I have two of the same links. The Complex instruction link is here:

    2. Hi Mary, Thanks for your thoughtful responses! I am indeed familiar with Complex Instruction; I just have problems with some of its assumptions, which is why I guess I am building my own model based on assumptions I can get behind. There are ways in which I find CI to be a too-blunt instrument for meaningful inclusion and interaction. On the one hand, I love the fact that CI gives a structure for meaningful interaction, and I especially love the "assigning competence" section at the end of the problem-solving session. On the other hand, I find the roles they use very rigid: I have experienced that students interpret them (mistakenly, but understandably) as permission to be mere "passengers" when their role is not explicitly called for.

      I am particularly interested in ways that restorative practices (including circle practice) could be used as a foundation for clearly communicating that all members of the group have an important role to play, even when their ostensibly assigned "role" might not be at center stage. I also like how it balances out everybody's responsibility to "notice" and "wonder" and contribute at the same level throughout the activity.

      In response to your following comment, I'm not sure what the Liebster Award is. Can you please explain a little more what this means?

      Thanks again for engaging!

      - Elizabeth (@cheesemonkeysf)

  4. On a different note, I know you're a seasoned blogger, but I'm acknowledging your work with the Liebster Award. Feel free to play along, or not.