Groupwork on the Ground and in the Sky

Today was the first day of a five-day workshop with Karen O’Connell and Jess Griffin called Designing Effective Groupwork in Mathematics. As I’ve spent a year doing my M.Ed in cerebral mode, it was refreshing to talk with teachers about the nuts and bolts of how this might look in a classroom – the practical implementation of it all. I wanted to share here some of my initial take-aways and questions I still have.

I’m also planning to use this space to share my thoughts as my group and I move through the design of a groupworthy task. Watch this space! Your comments and feedback and questions are totally appreciated during this time as they always are!

Setting and Reactions

Karen and Jess have both been complex instruction (CI) practioners for a number of years and have a tremendous amount of experience to offer. In our opening activity, Jess led us through an origami box making task, with us in the role of students in groups of 4. The tables were cleared (KEY move), the task was introduced, roles (two of the many descriptions of roles: way one and way two) were introduced and explained (groupings were randomly assigned by the teachers), and a list of the abilities needed to complete the task successfully was presented. This was a key moment which I had been reading about – the first of two CI treatments called the multiple abilities treatment –  but seeing it in action stated with conviction while playing the role of student really hit home for me:

“Take a look at this list of abilities. There are quite a number of them that are needed to do this task. What are you bringing to your table? No one has all of these abilities, but each of you has at least one of them to offer.”

While doing the task, I immediately found myself with a role (resource monitor – and I love ticking lists and asking questions!), and ways to contribute to the task. I also found myself earnestly supporting others where I could, or being more verbal about my appreciation of other’s work.

As we were all doing the activity, Karen and Jess circulated, encouraging us to continue using “because” statements and asking good questions – like a coach, pointing out when a student is on the right track – while encouraging the group to recognize when a member was struggling with an idea or needed a voice. Yes, they were helping to move the math along, but they were also helping to move the talk along – talk which thereby facilitated the math moving along. This is the second of two CI treatments called assigning competence. Also incredibly key.

The task culminated in our making a “stand-alone” 1 page demonstration of our strategy and our prediction (for what the volume of a box made from a 20-inch sided square piece of paper might be given the four other boxes we had made, measured and analyzed). This was interesting – we couldn’t tell people about it. When showed to the class, no comments were allowed. Our paper explanations had to “stand alone” – and be understood just as they were. What a simple yet powerful idea as a way of presenting finished mathematics products to the class.


I already wrote about a number of “take-aways” throughout the “play-by-play” of the task, above. Here are some more.

There are some incredibly simple tweaks that Karen and Jess made to the task to encourage us to interact. First, there were four different sized pieces of paper (ergo, we needed to make 4 boxes), but only two task sheets and not enough cm cubes and beans to each have a sufficient supply for estimation. Thus we needed to share these latter two resources. The simple act of giving each student a task sheet or enough cubes for each student to work with might have kept us from talking until later in the task. In addition, the folding instructions (to move paper–>box) were naturally tough for some to follow, resulting in many group members needing help with others offering it.

One of our group members, Cameron, pointed out that the resource manager’s job had one crucial addition – to ask the teacher questions. Huge. Other group members were dependent on them as the way to communicate their questions to the teacher, thus the resource manager remained important throughout the duration of the task. Not including this has a student get resources, then (possibly) back right out of the task – “that’s it! Job done!” In addition, it implied that the teacher was just one of the many resources available in the room. Not the resource, but just one of them. A powerful implication. Instead of an “ask someone at your table then ask the teacher” rule, which could imply “don’t bother me” or “the teacher might be more useful (or more important) than the students,” we have a strong subtle implication of the equalized value of all in the room. Epic.

What strikes home most powerfully after today, however, is the self-similarity that is necessary for this kind of teaching to really be successful. We have all heard and likely agree that teachers must model for students what they want them to learn, yet we have all seen how teaching can sometimes be a bit lonely – whether self-imposed or not. The classroom door shuts, literally and figuratively. However, if we want our students to collaborate, must we not also collaborate? Must not our department meetings not be times for us to share things we are doing in our classrooms and get feedback? Must we not design tasks with our teaching partners to gain multiple perspectives on an activity in preparation for presenting it to students? Teaching is an incredibly creative profession, and creativity needs expression to be moulded, to evolve, to improve. (Many of you are likely already thinking the word “time!” over and over again in your heads. I recognize the practical and am indulging in a bit of optimism here 🙂 )

Questions Still Niggling

I have a TON of them, but my top 2 are:

1) How does CI look in a class with english language learners (ELLs)? CI is language (as in language of the classroom) heavy. Students are expected to talk in groups, to record findings understandably for others, to report their own learning in individual reports throughout units. How can we keep ELLs from losing status in the face of the great challenge they may appear to pose to their group members? How can they succeed and contribute?

2) CI works beautifully for exploratory tasks like the origami task. But CI practitioners readily admit we can’t do those all year long. How does CI look for more abstract and calculation based concepts like algebra, logic, functions, and the like? How could the teaching of this look different and be more engaging?

On From Here

Our task this week is to design a groupworthy task in a group of 3-5 people on a math topic – a task that we will then “micro-teach” during a 20 minute session. Fitting, especially considering my comments about self-similarity. As Lotan (2003) says: the creation of a groupworthy task is itself a groupworthy task. My group is pumped and ready for action! We have challenged ourselves to come up with a groupworthy way of involving students in learning algebra concepts connected with completing the square. Wish us luck!

Resources from Today

The book we are reading for this course is Smarter Together: Collaboration and Equity in the Elementary Math Classroom. Written by practitioners and researchers of CI, it’s already reaping great rewards in our explorations.

A colleague, Kate, suggested we look at Lab Gear, a manipulative designed for teaching algebra, during our lesson design. Have a look at Henri Piccioto’s site (he’s the creator) for a summary of what it can do and some free resources for how it can change teaching.

See the Lotan (2003) article that we read today – a short and sweet summary of “look-fors” when designing (or modifying old tasks/questions to make) groupworthy tasks.