My thoughts on vertical non-permanent surfaces

Otherwise known as whiteboards on the wall

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Once upon a time in Sweden...

Last week, I had the privilege of spending three days in Sweden. On the first day, I visited a school and watched five lessons. In three lessons, students spent a significant portion of their time - around 20 minutes - in small groups, congregating around vertical, non-permanent surfaces, otherwise known as whiteboards on a wall.

The terminology, vertical non-permanent surface, and the associated pedagogy, comes from Peter Liljedahl’s successful book, Building Thinking Classrooms in Mathematics - a book that is influencing maths pedagogy in the US, Sweden, and I am sure in many other places.

The arguments for vertical, non-permanent surfaces

Liljedahl’s reasons for recommending the use of vertical non-permanent surfaces (VNPS) can be summarised as follows:

1. Increased Collaboration:

   • VNPS encourage group work as students naturally gather around the surface to share and discuss ideas.

   • The vertical setup makes it easier for peers to see, contribute, and refine each other's work.

2. Improved Student Engagement:

   • Students find the process of writing on a whiteboard or similar surfaces less intimidating compared to writing in notebooks.

   • The impermanence reduces fear of making mistakes, encouraging risk-taking and experimentation.

3. Faster and More Dynamic Thinking:

   • The ability to erase easily encourages quick revisions, iterative thinking, and trial-and-error learning.

   • Students are more likely to "think aloud" and adjust their ideas visibly.

4. Increased Mobility and Active Participation:

   • Students are physically moving and standing, which increases energy levels and keeps them more alert.

   • Mobility helps students engage dynamically with the task and interact with peers.

5. Teacher Visibility and Assessment:

   • The teacher can quickly assess the group's progress by scanning the room, spotting misconceptions, and identifying successes without interrupting the workflow.

   • It allows for immediate feedback, either through direct intervention or prompting group discussions.

6. Equality and Accessibility:

   • VNPS level the playing field as everyone in the group has equal access to contribute. Unlike sitting arrangements, no one dominates by holding the paper or hogging space.

   • Writing on a shared surface promotes inclusivity in problem-solving.

7. Encourages Group Accountability:

   • Since the work is public, groups feel responsible for their contributions, fostering a sense of accountability.

   • Students are more likely to explain and justify their reasoning to their peers.

8. Reduces the Focus on Individual Achievement:

   • The emphasis shifts from individual correctness to collective understanding and problem-solving.

   • This aligns with the ethos of building a thinking classroom where collaboration is central.

9. Facilitates Growth in Mathematical Thinking:

   • By working together and iteratively solving problems, students are exposed to diverse approaches and strategies, enhancing their problem-solving toolkit.

   • The process prioritizes reasoning and communication over rote methods.

Three important points

This was the first time I have had the chance to see this medium of participation in action, and I have several concerns. But before we get into those, here are three important points:

1. I have a bias against group work. Despite conversations with group-work advocates such as Sammy Kempner, I have never been able to make group-work effective in my lessons. This is probably my failing as a teacher. I much prefer structured paired discussions at desks called Turn and Talks.

2. I only saw this in three lessons in one school. The teacher who accompanied me felt what I saw was representative of what happens in maths lessons across schools in Sweden, but of course, we must be aware of over-generalising from such a small sample.

3. The activities the teachers asked students to complete on the VNPS were not the “thinking” problems advocated by Liljedahl. However, this does not change my concerns or suggestions.

My concerns

1. There is a lack of individual accountability

Group work - in any form - is hard to get right. Slavin, Hurley and Chamberlin explain that when groups are rewarded based on the individual learning of each member, students are motivated to teach and assess one another, leading to increased achievement. However, when groups can get away with offloading all the work and thinking to one student, this does not happen. Perhaps you can tell from the photo at the top of this post that some students are working hard, and some students are having a chat. I asked one student sitting away from the board what was happening, and she said - pointing to her groupmate frantically writing away on the VNPS: "He is smart. Like Young Sheldon. He will do it all".

A question I ask in all lessons I watch is: How easy would it be for a student to hide a lack of effort or a lack of understanding? In the VNPS phase of these three lessons, I think it would be very easy.

Of course, you can take steps to reduce this from occurring. You can assign students roles, you can actively monitor them, you can ask the student in a group who is least likely to know the answer and hold the group accountable if they don’t. But this is hard to do.

Just because something is hard does not mean we should not do it. But we must be sure our efforts will be worth it. And with such group work, whether at VNPS or done around a desk, I am not sure they are.

2. It is very easy for students to copy other groups

One of the stated advantages of VNPS is that student work is visible to the teacher. However, this means it is also visible to other groups.

Here are the boards of two groups who were next to each other:

Notice their answers are identical. Now, this could have been a coincidence. But more likely, it is because one lad from the group on the left kept walking over to the other group, having a look at their board, and then writing down what they had done on his board.

Optimists may classify this behaviour as collaboration. Maybe he was just checking his answer and would have written the same regardless if he had seen the other group’s board. Or, maybe he learned something valuable from the other group’s board.

I am a grumpy old cynic these days. I think he was just copying.

3. It takes a long time

I am obsessed with how time is spent in lessons. Every teacher's decision has an opportunity cost, as that time can not be spent doing something else. So, if we dedicate significant time in lessons to something, we must ensure that time is well spent.

In one lesson, students spent 23 minutes at the VNPS working on 10 questions about circles. The teacher then spent another 8 minutes choosing members of different groups to talk through their solutions.

As I will explain below, I think we could achieve the same outcome in half the time, thus giving us 15 minutes to use as we please - to give the students some more challenging problems to solve or some retrieval practice.

4. I don’t trust the measures of effectiveness

Warning: More of my biases are incoming…

I had an opportunity to share my concerns with some of the teachers. Whilst they agreed that it took a lot of time and that maybe some students were not putting in as much effort as others, there were two things I was missing:

1. Students like this way of working

2. The benefits of collaboration and teamwork make it worthwhile

The first is easy to deal with. Students like a lot of things, but that does not mean they are good for their learning. Students prefer to revise by rereading and highlighting, whereas we know practice testing and self-explanation are more effective strategies. It reminds me of when one teacher in a school in England told me she doesn’t use mini-whiteboards because her students don’t like them. Why don’t they like them, I asked. Because they have to think more, she replied, with no sense of irony.

The second concern is more difficult. I am sure students are developing skills such as collaborating and working in a team through working at VNPS. I just have no way of measuring this, and I think students can get similar benefits in a shorter timeframe (see below). And I’ll be honest - and I know this won’t sit right with people - I value subject knowledge and academic achievement more than this.

So, what would I do?

Listen, what do I know? I am making wild generalisations and suggestions based on having seen three lessons using a medium that I have a natural bias against.

However, having outlined my concerns, it only feels right to suggest some alternatives.

First, if you want to stick with the VNPS and overall structure of the lesson, then I think giving each student a copy of the worksheet at their desks and allowing them, say, 5 minutes of individual silent thinking time before asking them to form a group at the boards would help. That way, each student will bring something with them. In the current structure, the quicker students in each group will always dominate while the others try to catch up.

Second, I think the 4-2 approach may work better:

1. Give each student a copy of the worksheet.

2. Give them 4 minutes to work on it individually and in silence, writing their answers and working on a mini-whiteboard

3. Then, give students 2 minutes to collaborate with their partners. Ask them to physically put their mini-whiteboards between them as a frame of reference and a catalyst for discussion. Remind them to compare answers and methods, and challenge each other where they find disagreement.

4. Repeat this cycle

5. Then, strategically call upon pairs to talk through answers to key questions. Ask for pairs where they still disagree on an answer or where one person has changed their mind.

This takes less time, allows each student to see what they can do independently, ensures they both have thinking time to contribute more to the discussion, and still offers the benefits of collaboration.

I don’t think the Swedish students would like this. But I think they would learn more.

What do you agree with, and what have I missed?

Let me know in the comments below!

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Thanks so much for reading and have a great week!

Craig