Since the onset of my career, I have been keenly interested in how students work together in the contexts of school. We know that students (and humans in general… actually animals in general) form collectives to accomplish elaborate tasks. These traffic jams of human interaction transcend individuality to the point where the level of activity is so dense that groups begin to synchronize into a sort of group mind. However, we have a school system built on individuality and (unfortunately) competition, and triggering these collective structures is extremely difficult in part because students know that, when push comes to shove, they will be weighed and measured as an individual.
My first experience with Visibly Random Grouping (VRG)1 was as a sophomore teacher. I had a Grade 10 class filled with very distinct cliques of students. When we worked in groups, I could never get them to think outside of their comfort zone. It was like the class was filled with clones. One day, a band trip left one student stranded and I told him he could choose a random group. When he couldn’t make up his mind, I decided that I would put everyone in a random group to make it less awkward for him. The result was more interaction, and eventually this became our go to grouping method. It didn’t have this mainstream name at the time, but had the same effect in my classroom. It has since become an important piece of my practice.
VRGs are a part of most class periods I teach. Students are accustomed to working with each other, and we no longer see it as novel. It sponsors novel thinking, but it does not feel unnatural–it is just part of how we function together. However, for a long time I ignored the fundamental dictums of good assessment:
- Assess what you value
- Assessment should match instruction
I value collaborative problem solving and have given groups assessments, but I have never actually shifted the groupings in the midst of an assessment. Last week, my Grade 9s wrote a “Shrinking Unit Assessment” to complete their unit on equations.
The Process:
My curriculum indicates that students should solve linear equations with variables in the numerator, with variables on both sides of the equality, that include fractions, that contain distributions, and that include variables in the denominator. My class contains 23 students, and so I decided on the following progression:
- Question 1 would be completed as an entire class
- Question 2 would be completed in groups of approximately 10 (class split in half)
- Question 3 would be completed in groups of approximately 5
- Questions 4 and 5 would be completed in groups of three (or four if necessary)
- Questions 6 and 7 would be completed in pairs
- Questions 8, 9 and 10 would be completed alone
I chose a sample of 10 questions that I felt covered the curricular requirements (linked here). While a traditional assessment might organize these on a continuum of perceived difficulty (starting with the simplest), I tried to organize them so that the types of equations were spread out across the assessment in order to provide students with exemplars completed in larger groups that they could refer to when solving questions in their smaller groups.
Each student was given a exam paper (linked here), which was almost entirely blank. It served to structure their work and made my perusal of the assessment much easier. Questions were presented one at a time, and groups were encouraged to keep their collaborative noise within their group. Several reminders needed to be issued as debates broke out. This rule was not in place for the first question, where the students were free to talk as an entire class. When it was time to re-group, students were given 30 seconds to find each other and settle in a space in the room. Each grouping was random; after six groupings, I asked if there were people who hadn’t worked together, and no hands were raised. (This is not surprising given that the first few groupings were so large). Timing was flexible, but I was conscious of getting to the individual questions at the end. (We ended up skipping question number 8 because of time).
The Results:
I was impressed with how immediately engaged students were with the process. When the first question was written, I stood back against a cabinet, and a brief pause was soon filled with a flurry of activity:
- “Okay guys. We should move a term with a variable”
- “Left or right”
- “I like left”
- “Will it be positive?”
- “Then add or subtract”
- “Is anyone drawing balance scales?”
- “Should we do a check?”
- “The check worked for me. Anyone else?”
- “Yup, me too”
Satisfied, they were regrouped and set to work on the next challenge. It was very interesting to see the social roles emerge as the groups changed. Some students were vocal leaders in the larger groups, but became small-scale coaches when working in groups of 5. Other students began connecting students together by organizing checks or asking if they did the same “moves”. The less confident were able to find support. They didn’t blindly copy down the responses, because they knew full well that individual questions were coming. On a couple of occasions, students asked me to delay a regrouping, because they were still working through an explanation. Students also used any extra time to look back on previous questions with their new group mates. The structure sponsored more error analysis than I was anticipating. In those moments, I found it tough to initiate a new grouping. (I guess this is as close to a win-win as you can get when giving a math exam).
One global affordance worth mentioning is that I did not need to be the source of knowledge in the room. I only answered a single question during the entire process. Not only did the groupings promote student agency, it provided me the rare opportunity to circulate and just listen to the problems students were posing. This rich source of observational data added to the validity of the assessment. It was as though the assessment doubled in potency.
Some Warnings:
- We work in VRGs often. Using the structure for assessment but not for instruction would result in the same oversight mentioned at the onset of this post–assessment would not align with instruction.
- Grouping strategies (such as VRGs) do not automatically result in effective thinking. Rather, it is an excellent way to provide opportunity for a high density of thinking to occur due to the suppression of certain obstacles that exist in many classrooms. Thinking is a product of opportunity. Where students think (classroom set-up) and with whom they think (grouping strategies) provide certain benefits, but ultimately, students need to know that thinking is permitted and preferred. Throughout the unit, we focused on “legal moves” that maintained the balance signalled by the equation. Moves all provided us with something, but there was no optimum pathway through a problem. This was evident in the discussion during the assessment. Some always wanted to collect like terms, some wanted to move variables to the left, some wanted to eliminate fractions, some wanted to find common denominators, etc. If we had focused on the “correct” way to solve an equation, no grouping structure would have sponsored these discussions; it is impossible to entertain debate when you are not permitted to deviate from that which is mandated.
- Even though the questions were solved in VRGs, they still provided the identical constraints as if they were given to students in isolation. That is, the social dynamics that emerge from this grouping structure provide certain opportunity, but do not change the opportunities offered by the problems themselves. Combining a novel grouping structure with problems that encourage a variety of avenues for thought might result in an even more potent combination (see here for a possibility).
I love this structure because of the variety of opportunity it provided for students. Many teachers are worried about the accountability of a group exam, but the individual questions at the end of the assessment helped to mitigate that worry. It resulted in the emergence of social roles, and it instigated good discussion and impromptu error analysis. On top of that, it provided a plethora of both written and verbal information of student understanding. Ultimately, the structure asks students to act in a variety of ways and react to a variety of situations, and I believe that thinking and learning move forward on the back of these imbalances.
NatBanting
- The term (as far as I know) was coined by Dr. Peter Liljedahl. It is now a cornerstone piece in his Thinking Classroom model. Read an introductory paper here.