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)

Great post. I’m definitely going to try this out – not sure how it will work mid-semester, but if it doesn’t, I will use it from the start in the spring term. Thanks for sharing.

I’d love to hear about your experience, Wendy! I was just reading Peter Liljedahl’s full research article on the topic this morning & he studies the case of a teacher that starts halfway through the semester. Despite a couple of bumps to overcome it works out for her, so I hope it will in your class too!

I’ve got a lovely new room with whiteboards all around. It’s on the agenda!

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This is used in the Modeling Physics program. It’s called whiteboarding. That chart confirms my experience with poster paper, that the students are so fearful of making visible mistakes that they take a long time to get started.

some links:

http://physicsed.buffalostate.edu/AZTEC/BP_WB/

http://modeling.asu.edu/Projects-Resources.html and look for “Discourse in the Modeling Classroom”

Thanks Robert! Glad to see that others caught on to this method much earlier … I’m just catching on now 🙂

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Hey Laura, have you actually managed to find shower board for cheap? I went to Home Depot today and the 4′ x 8′ sheet was $55.

A few years ago at Lowe’s mine was 30 $ or so

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Greating students as they enter the room is more powerful than most people think! Sets the tone.

I do this method except in a more concrete way. Students were assigned homework if not completed from the previous class and before they leave I tell them we’re going to be asking them to post their answers tomorrow. The next day I have the board space set up (3 walls of boards, back wall is all windows). Using a random number generator students are assigned one of the questions, if a student wasn’t chosen they are expected to help a friend at the board. It’s not a solo activity. Sometimes I use wheeldecide.com to generate the random names, it takes some time but it can be fun. Students are always allowed to ask for help from a friend but must write the solutions on the board. I have a cardboard cutout of a giant boulder with a magnet on the back and Indiana Jones also with a magnet on the back. I draw 5 notches in chalk between them.

I tell the students specifically what we are looking for in the solutions with regards to the success criteria, which I call keys to success. Ex. 1. Did you create and use an appropriate formula or representation? 2. Does the solution have proper math conventions and is the solution easy to follow? 3. Is theire a final answer with units when applicable? If the students met these criteria which are clearly paved out, the boulder doesn’t move. But in chalk I’ll have 5 notches and each time as a class we decide the answers don’t met the criteria the boulder get’s one step closer to Indiana Jones. When it gets to 5 wrong well, we know what happens. You can also do this with anything, a hockey puck and a goalie if your class is into hockey. A picture of a student dunking over a cutout of Kobe Bryant. Two magnets, one of Usain Bolt and the other of something else and they race to the finish line. A front jumping on lily-pads to get to it’s baby, (doesn’t make sense baby frogs are tadpoles haha but still you get the idea. It’s just something funny and random and sometimes the kids make it up, but it gets the students accountable and wanting to do there part as a class. It also makes it visible how we are doing in a class. This is really useful feedack for me as a teacher because it let’s me know if they have grasped previous content and then I can adapt during my lesson.

It also is a fun way to start the class and when I then start the next lesson I can tie what we just did into the next thing as prior knowledge.

I think your approach is better for fostering the idea of problem solving, developing resilience and getting the kids comfortable with team work. I use it much more of a rigid and accoutability fashion.

That sounds great! If you haven’t yet blogged about that process, you absolutely should.

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Thank you so much for your thorough explanation Laura! I use VNPS, not enough, and I don’t monitor them enough to see who is talking, writing, etc…Hard to be available for 30+ students at a time! I use toggle bolts and mirror hangers to hang mine.

We do what we can. I find working o building the autonomy that Liljedahl talks about helps; groups get help and extensions from other groups; there’s only 1 of me & I can’t be everywhere at once.

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Instead of using a deck of cards for random groups, I create math questions on cue cards. These questions review fractions, integers, order of operations, etc. and the answers are either 1, 2, 3, 4, 5, or 6. This corresponds with their table number. The first job of the group is to check one another’s cards to ensure everyone is in the correct group. Then, it is up to their vertical space to work on the bell work.

What a great idea. Lots of work but great ☺

Reblogged this on teaching maths with mrs rouse.

Hi Laura,

I’m a mid-life career changer just about to start teaching (we start in January in Australia) and I’m getting excited going through your blog – thanks for all the details and links in your posts – so helpful!

I had read about whiteboarding for physics and it seems natural to use it for maths. I’m also interested in random groups – I had been thinking of the idea of “home groups” to foster collaboration, but I like the benefits of the random groups too.

I don’t know that the rooms in my school are set up for VNPS, but I’m going to try!

Cheers, Bec

Hey Bec, whereabouts in Australia are you? It can be tricky in a room that isn’t set up for it, but there are options like purchasing Wipecharts, packs of 10 whiteboard “sheets” you can hang around your room. https://wipebook.com/products/wipechart And if you have to share the room, I often suggest whichever student gets the first 2, as you hand them their card ask them to put 3 or 4 desks together for group 2. I find that if we need to move desks & change the room configuration it works best if I get the students to help & make it part of our routine. Do you share a room with another teacher usually or get your own?

I just checked Pear Deck out – love the features that I love in Desmos to make learning visible!

oh yeah, Pear Deck is a game changer! (just like Desmos is too!)

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Hi,

I teach 5th grade. Should you use this framework daily? I feel like the content we learn (all decimal and fraction operations), how will students learn the number sense to solve the problem unless it’s explicitly taught? Thanks!

Hi Esther, Peter – the researcher behind it – suggests daily. I do VRG daily. I do VNPS daily in my academic classes & every other day in my applied classes so that they can have some class time to do practice problems individually – they usually won’t do them at home. I plan my activities so that they incrementally build upon the last learning. Or they have some basic strategies (like guess & check) to solve with, then after they’ve been working on the problem I’ll call them over and show them the newer more advanced skill & have them use that to solve it now. If absolutely needed I start with a super quick demo of a new skill at its most basic level. They go solve something then I ramp it up via the extension problems. Does that help?

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