Wednesday, 22 February 2017

Feb PD: Peter Liljedahl

Our board has a day in February devoted to Professional Development, delivered by teachers. For 2017, our subject council brought in Dr. Peter Liljedahl from Simon Frasier University in British Columbia, to deliver the keynote. I present that here, along with some follow-up at the end; the rest of 2017's PD Day is in that separate post.


Peter started “with my last slide”, so that you could find him and/or see this presentation:

He’s based his findings on a lot of literature, and he flashed up papers noting “some of these are not so boring”. Our story starts about 13-14 years ago. Peter was asked to come in and help a middle school implement problem solving. He was a former high school teacher and PhD student at the time.

This was great. Though the first thing the middle school teacher said was she didn’t “need your glee and enthusiasm” - she wanted tasks, not a co-teacher. Peter said okay, but if he gives a task, he gets to see how it’s used. Which brings us to Jane’s Class (2003), and the first problem, one of Lewis Carroll’s: “If 6 cats can kill 6 rats in 6 minutes, how many cats are required to kill 100 rats in 50 minutes?” Peter had used it in many settings, it had gone well, he thought “this is going to be awesome”. Note “Jane” had never done problem solving before this.

Peter asked us, “What do you think happened?” (The audience is silent until someone pipes up “Like what’s happening now.”) Disaster! Peter explained it as, arms went up, and the teacher ran between students for 40 minutes, trying to push them to do it. As soon as the teacher left, they sat there, and hands went back in the air. After, Jane came to see him in the back of the room. I figured “one and done, I’m out of here” but she asked for another task. This woman’s got tenacity! Second time, disaster again. Gave her another one. After the third, she said, “I think that’s enough.”

It had been painful for everyone. Students were in pain, Jane was exhausted, and Peter was bleeding internally. He asked, “Can I just stay in class the rest of the day to watch what you normally do.” Then stayed there for 3 days. He had an epiphany.

At no point during the regular teaching had the students been expected to think. Sure, they were doing stuff, solving questions, but all the thinking had been sucked out, either through direct instruction or modelling or the like. Peter went to another math classroom and saw the same thing. He went all over the lower mainland of Vancouver and kept seeing same thing. It doesn’t matter how good texts are, or how smart a Smartboard is, or whether desks have seats attached to them versus sitting at tables. Nothing is going to matter until we get students thinking.

The person doing the thinking is the person doing the learning. Right now, the best one can hope for is good behaviour. Peter started on a quest.

He spent lots of time in classrooms. Good ones and bad ones. Came to a realization: Classrooms all over the world are more alike than they are different. It doesn’t matter if it’s Grade 2 or Grade 12. It doesn’t matter if you’re in a low socio-economic setting or a privileged private school. It doesn’t matter if we’re in Canada or Taiwan or Chile. Classrooms for the most part look the same.

Students sit in desks, usually oriented towards a teacher, who provide knowledge to those students. It’s been the same in every classroom for 100 years. Yeah, desks now have wheels and the board is white, but fundamentally, nothing has changed. Maybe it’s time to pay attention to some of the things that are taken as “non negotiable” in classroom settings. Peter started on a project. (Aside: “I have no idea what my next slide is.”)

He recruited more than 400 teachers to work with (casting about), and started with a contrarian approach. Figuring the best way to start is to just do the opposite, and see what the effect is. Students are used to sitting? Stand them up. They’re used to us answering questions? Let’s stop. They’re used to furniture in the room? Take it out. (They got calls on that one.) They’re used to us talking? Let’s not talk at all. (Aside: “That doesn’t work.”) The project always started with the contrarian approach; sometimes, it was the best option. Always, it brought them closer to what was the best way.

Peter also experimented with problems. It’s a myth that if we want students to learn through problem solving, we just find a magical book that will wash knowledge all over the student. “I don’t have that book.” He spent a year and a half on problems. Also this:
-How we give the problem. We could write/project on a board, or use a textbook, or handout. Or other ways.
-How we answer questions. We’re implicit with “learned helplessness”; being helpless is a good way to move forward.
-Room organization. Desks in rows, in pairs, in clusters, desks like trapezoids, round tables. Arranged in horseshoes, or the Ikea model, where you walk around the whole room to get to the door.
-How groups are formed. It’s February 17th; in 12 days, elementary teachers all over Canada will create new groups. “You two can’t sit next to each other.” Sometimes that’s about ability, sometimes about management... does it matter?
-Student work space. Could be desks, computers, tablets.
-Automony. Some students have none; some have more, and play in the back.
-How we give notes. Essentially, how to get them from us to students. On a board & copied, upload them online, fill in blank sheets?
-Hints and extensions. What’s the best way to provide them? Or is it everyone try this for 3 min 42 seconds, then reveal the solution and continue. Related: How we level.
-Assessment. Still playing with this, we’re probably doing it for our whole lives.


The teacher who had no furniture in their room, they learned from that. They learned “don’t do that”. Sometimes, they learned things that didn’t work, but that was because they needed to tweak it. Or have someone else try it. The project zeroed in on the things having a powerful effect. On what answers: “Does this contribute to student thinking?” Will the students think more, will they think better? Here are the results from those above points.

-Problems. With a good category of problems for the first week, afterwards, problems can come out of the textbook. But still have to think about it, ixnay on pre-teaching.

-How we give problems: Use oral vs written. We’re used to the written form, but what worked better than anything is oral. Every demographic, didn’t matter, giving problems verbally worked better every time. “To be fair, I can’t give you the problem 3x to the one half plus..." etc. etc. Some problems we can’t give verbally. Some we have to show them text or graph. But all instructions have to be verbal, it has a huge effect.

Because when instructions are textual, the first things students do is decode and read. And in a group, they read separately. But verbally, the first students do is talk to each other, even if they don’t like each other. What’s the absolute worst source for students to do problems from? The textbook. Orally was good, this ‘other method’ wasn’t bad, down here (Peter motions low) is the textbook. “Sorry to the publishers here.” It’s because textbooks have embedded an institutional norm. The assumption is you’ve been shown/read about how to do the textbook problem in advance.

-How we answer questions: There’s 3 types of questions. 1) Proximity. You’re close, the most student-ly thing I can do is ask you a question. 2) Stop thinking questions; asked so the student can stop thinking. Most popular, “is this right?”, second most popular, “is this on the test?”. 3) Keep thinking questions, clarification questions asked to get back to work. Either of first two feed into the “learned helplessness” - answer only the third type. Caveat: A hilarious thing happens in a kindergarten class if you don’t answer. They follow you, and ask the question again. One teacher had 7 kids following after her, like a conga line. So, what to do instead of answering the question? They tried all sorts of things (like turning it back, “What do you think?”). The best thing? Is to just smile at them, and then walk away. The walking away says I’m deliberately not answering.

-Room organization: The best rooms for thinking were chaotic, in disarray. De-fronting the room means that, with no discernible front, the students are more apt to engage. They don’t know where to point at. Stop anchoring their desk as being their place to think. All of a sudden, defronted, the whole space becomes something to use.

-How groups are formed: Use visibly random groups (VRG). It worked better than anything else.
-Student work space: Vertical non-permanent surfaces (VNPS). More on those in a minute.
-Autonomy: To think, we have to create autonomy. Create a space AND push them into it. We have to be ambiguous, we have to be elusive, and give them choices about what to do about this ambiguity. But also had to push the students to use this ambiguity.

-How we give notes: Don’t, at least not how we normally do it. When students were copying down what was on the board, in every class Peter studied it, more than half the class was at least one example behind. And never more than 5 students went back to their notes. (Usual number was 3 students.) Fill-in-blanks notes turned out to be WORSE, the students were paying attention, but only listening for key pieces (to fill in). They’re still working on this. Best, students write their own notes (as “Notes to my future, dumber self”).

-Hints, etc is about “Managing flow”. Level to the bottom. Four purposes of assessment.

What do all these things have to do with thinking? All are not equally powerful. If you go to school Monday and the only thing you do is not answer questions, you’re going to have a bad day - that’s a finishing item. What’s the best way to start transforming? Begin with sledghammers and chainsaws, those being: Good problems, VRG, VNPS. Framing hammers are next, then finishing tools. When we’re ready, we slide into the next set of tools. Not answering questions, that’s in the middle (along with defronting, and oral instruction).

The project found very quickly that students were most engaged when standing up and working on a whiteboard. The cynic in Peter wanted to test this, so did a controlled experiment in five different classrooms, Grades 10-11-12. He let the teacher decide what the groups would be. (Strategic grouping.) Then Peter decided which group would work on which surface. Some had a whiteboard standing, some had it on desks, some stood and worked on flip chart paper, some had that paper on desks. A control group worked in notebooks the way they normally do. Did in five different classrooms in five different schools, randomly assigning students to a surface.

Their proxies for engagement: Time to task, time to first math notation (versus deciding on a group name). Also on a score of 0 to 3 (0 if none) they measured: Amount of dissuasion, eagerness to start, participation, persistence, knowledge mobility, and non-linearity of work (was it messy; shows real thinking, not copying). “The thinking process is messy.” They averaged scores for groups of same type.

Peter put the results up. Discuss. “Someone tell me something you notice.” (Responses included “Nonpermanent seems to be performing better”; “Notebook performed well to start”). The better non-permanent scores was determined to be since “they can make mistakes”, it’s easy to erase, freeing them to risk more. The irony is, they don’t erase. But because they can, they’re quicker to start.

Mobility of knowledge sucked when they were sitting down. Hard to work between groups that way. Standing nonpermanent is better than sitting nonpermanent - but why is standing good? They’re still unpacking that. (Audience suggestions: “Because you’re on display” “Everyone can see everything equally”; Peter remarked “If your bum is numb, your brain is dumb”.) So they stopped saying “whiteboards”, because vertical mattered, and nonpermanent mattered, hence hashtag #VNPS (Vertical Non-Permanent Surfaces).

What’s it look like? Looks like this. (Peter showed a number of rooms. One was Alex Overwijk’s. One a careers class. They brought in bar tables instead of desks; the principal made the teacher call them cafe tables.)

On to VRG (Visibly Random Groups). Random groupings started to show more success over other methods. Peter went into the harshest environment he could think of, a high school in Vancouver that was racially bifurcated, 50% caucasian versus 50% asian. No wars in the parking lot, but they create their own class system. There was social stratification, but also split in two. They moved through each other, they didn’t integrate.

Peter spent 6 weeks in the room of a teacher. After 3 weeks, this is what he saw: Students became agreeable to work in any group. (Became. To start there were trades, subversions - “How is there a group of 5, really?”) Ultimately they’d decided “I can work with anybody for an hour”. He presented a story, where individuals were learning about individuals in the other racial group.

VRG means elimination of social barriers. The mobility of knowledge between students increases. A reliance on co-constructed intra- and inter- group answers increases, while a reliance on the teacher for answers decreases. Engagement in classroom tasks also increases, Peter admitting, “I didn’t expect that one”. At parent-teacher interviews, eight parents said “my son/daughter loves coming to your class”. Students became more enthusiastic about math class.

Put those together, here’s what it looks like. Peter points out, “This guy belongs to that group [over there].” While a guy in front is part of the group where “this guy” is. These are highly collaborative, active, engaging spaces. BUT “I want to emphasize something here”. What was learned goes way beyond vertical surfaces around the room. That’s just the opening act. The rest of the tools are what get at the thinking, what drive the performance and engagement.

The work continues. We’re still learning. “I’ve added two tools this year.” You can clap, we’re back to his last slide.


There were breakout sessions with Dr. Lilijedahl through the day. I didn't sign up for these, so I don't know exactly what went on - but part of the reason I didn't sign up was because I had the opportunity to attend one of Peter's sessions back in 2014 at the Canadian Mathematics Education Forum (CMEF). See this link for a full recap. Here's a TL;DR (Too long; didn't read) version, since that was a long conference:

Picture a graph, with a horizontal axis for "Skill" and a vertical one for "Challenge". You need to vary challenge as skill increases. Little skill with too great a challenge creates Anxiety. Great skill with too little a challenge creates Boredom. There is a channel between these (picture a direct variation from where they join) which creates FLOW. From research by Csikszentmihalyi (1990) there are nine items that help people experience flow.

Three of these are external, which teachers can effect: There are clear goals every step of the way. There is immediate feedback on one's actions. There is a balance between challenges and skills. The other six are internal: Attention is focussed on one's actions. Distractions are excluded from consciousness. There is no worry of failure. Self-consciousness disappears. The sense of time becomes distorted. The activity becomes satisfying in it's own right.

Managing flow is nigh impossible in a class of 30, but is achievable using smaller groups (a reason why VRG is part of the first steps). You cannot create an engaging task that hits "an expectation", because it would remove the possibility of solving the task using other options. You can merely create a problem that goes in the right direction, and see what different groups do with it.

If you were at one of the breakouts, feel free to comment with whether this relates to what was covered, and whatever else might have been said. Or simply remark on something you found interesting. You can also check out Alex Overwijk (referenced above), who has blogged about these topics as well.

As for me, I thrive on order and structure, so bombshells like this take me time to process. We'll see where it goes. I also do unconventional in a different way - for instance, my personified math comic is currently doing a derivative arc. Okay, done now, thanks for reading.


  1. Super summary. I like the funny anecdotes you remembered peter saying.

    1. Thanks so much for commenting to let me know! I actually type in some anecdotal remarks while the talk is going on, since it helps with the illusion of being there later. (I possibly missed my calling as a court stenographer.) Though it does help to have it fresh in my memory too.