I have been trying to shift my Math classes toward activity- / problem-based learning. We still have individual practice days, but as much as possible I want them solving new, complicated problems in groups. Two ideas that I heard about at a meeting of the OCDSB Mathematics Department Heads have really changed how I do things in class lately:

- Visibly Random Groups
- Vertical Non-Permanent Surfaces

Both ideas come from the work of Peter Liljedahl and have been gaining traction amongst OCDSB teachers lately, particularly in Mathematics classrooms.

**Visibly Random Groups (VRGs):**

Original research available here.

Every day I make random groups so that my students work with different partners each day. Students are learning from ALL of their classmates this way, getting a chance to hear different viewpoints, different strategies each day. To make these random groups, some teachers use a smartphone app such as “Shuffle Names, Dice” while others use websites such as “Team Maker”.

When I first started using VRGs in my classes, I used the Team Maker website. You paste in your class list of names & it makes however many groups you ask it to. But I would have to go through the list & delete any students who were absent. This meant the groups could only be created after the bell had rung. I wanted a system that would tell students their group for the day as they arrive so that they can sit right down & get started.

So this year I have been using a deck of cards (low-tech & old school!). Here’s how I do it. I post their bellwork assignment on the screen/board before class starts. The desks in my classroom are arranged in 8 groups of 4 desks, each with the group number hanging from the ceiling above them (which you can see if you look closely in this photo).

*For a more recent photo of my room check this post.*

I stand outside my classroom door during the travel time. As my students arrive I hand them a playing card (with a number from 1 through 8 on it) indicating which group they are sitting at that day. This method for VRG has the added bonus of giving me the chance to personally greet each student as they arrive to class as well as monitor student behaviour in the halls during transition times.

The conversations I hear between students while problem solving this year are far richer than previous years & I believe it also contributes to a positive culture of collaboration & sharing in my classroom.

Peter Liljedahl’s research shows the following benefits for VRGs:

**Vertical Non-Permanent Surfaces (VNPSs):**

*Original research available here.*

After we finish the bellwork activity to start class off, I usually present the problem or activity of the day (often done in Dan Meyer’s 3-act math style). Students solve the problem in their small groups (I try to limit each group to 3 students – which works when my class has 24 students or less). They get out of their seats & proceed to a section of blackboard or whiteboard assigned to their group in order to solve the problem together.

The vertical nature of the surface:

- gets students out of their seats which seems to activate their thinking
- allows students to see the work of other groups which gives them ideas of things to try or perhaps what not to try
- allows me as the teacher to see the work of each group at a quick glance, which prompts me to offer feedback & question their thinking as they work

The non-permanence of the surface is important too. Students seem willing to get to work faster and are willing to make mistakes because they can be so easily erased. Pencil & paper can be erased too, but there’s something about the whiteboard or chalkboard that makes students more willing to just try something. As Peter Liljedahl’s research shows in the data below, students get to work faster, they work longer, and are more engaged:

I have two walls w/ blackboards in my classroom & the third wall (which already has a DIY whiteboard for a projector screen in the middle) will be getting fully covered with DIY whiteboards in the coming week. My 4th wall is windows, although I know other teachers that get DIY whiteboards cut to size & lean them up against windows to create student work stations there as well. *(Update: I now have the 3rd wall covered end to end with whiteboards & a small “station” set up in one of the window wells on the 4th wall as well).*

The rules of working on the VNPSs in my class:

- One person has the chalk at a time.
- The person with the chalk can only write down what their partners tell them to (if they want to explain the next step, they hand the chalk to a different partner).
- The teacher can say “switch the chalk” at any point & a new partner needs to become the writer.
- I also tell them that if one person does the solving & writing without partner input, I’ll erase their work.
- No sitting down.
- No working things out on paper before using the board.

Have you tried VRGs and/or VNPSs in your classroom? Leave a comment below!

Check out some other teachers’ experiences with these ideas like Mr. Overwijk’s:

http://slamdunkmath.blogspot.ca/2014/08/vertical-non-permanent-surfaces-and.html

*Update: I wrote an article for Edutopia about the first 3 elements of the Thinking Classroom – good tasks, VRGs & VNPSs – that you can read here https://www.edutopia.org/blog/student-centered-math-class-laura-wheeler*

– Laura Wheeler (Teacher @ Ridgemont High School, OCDSB; Ottawa, ON)

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