Took some time this weekend to update my Thinking Classroom sketchnote to the contain the now 14 elements as outlined by Peter Liljedahl:

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

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Took some time this weekend to update my Thinking Classroom sketchnote to the contain the now 14 elements as outlined by Peter Liljedahl:

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

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I spent Friday at the OAME annual Leadership Conference. It was a great day of learning more about Peter Liljedahl’s Thinking Classroom framework as well as on the topic of leadership & what it looks like.

Peter Liljedahl was the keynote speaker. He outlined the (now) 14 elements of his Thinking Classroom framework for us. I had previously sketchnoted about the 11 elements he previously outlined so today I just added the 3 new elements to today’s sketchnote of his keynote:

Next we were broken up by panel & experience level w/ Thinking Classroom. I attended the secondary intermediate/advanced session led by Al Overwijk & Jimmy Pai. We were visibly random separated into groups of 3 and given a vertical non-permanent surface to work on the problem of decomposing the number 25 into numbers that summed to 25 and finding the set of these that would generate the greatest product:

We also added to our boards the questions we still have about implementing the Thinking Classroom framework – what we are struggling with. It was a relief for many of us to see that other experienced educators that we respect are struggling with similar questions and strategies:

After lunch Jimmy Pai led a panel discussion on the topic of leadership. I did my best to capture a summary with this sketchnote:

After the panel were two breakout sessions for the secondary panel; one by Mary Bourassa which involved immersing ourselves as students in a round of Desmos Parabola Slalom and a session about great problems to spark learning by Kyle Pearce & Jon Orr:

It was a great day of connecting & learning. A big round of 👏applause👏 to OAME president Jill Lazarus and the team for putting the day together:

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

I had the pleasure of welcoming Peter Liljedahl to visit my classroom this past week. Peter is the brains behind the Thinking Classroom framework that I’ve been implementing in my classroom over the last few years. While he was in town this week for the OAME Leadership conference he took the time to visit some Thinking Classrooms in the area and I was lucky enough to have him come visit ours. He spent a period with my grade 10 applied students where I was running a problem-based learning task (or 3 Act Math task) to do with solving for the missing angle in a right triangle.

The two most popular elements that most people know about Peter’s Thinking Classroom framework are vertical non-permanent surfaces and visibly random groups. Another of the elements is to have students take meaningful notes after the problem-solving task; giving them time to select, organize & synthesize the ideas they want to keep in their notes. My way of doing this has been to create course packs for each of the courses I teach. Peter shared out this idea during his keynote on Friday and a number of teachers were interested in hearing more about them and seeing examples, so I figure a blog post was in order!

**What are my course packs?**

They are approximately 10 pages long (1 page per overall expectation for the course) or 5 sheets back to back. There is a box for each of the key terms or skills they need to know (I pull these from the specific expectations listed in the curriculum docs). For my applied classes I usually fill it in with worked examples of the skills, but leave the key terms blank for them to complete (see below right). For my academic classes I usually leave every box blank for students to complete (see below left). I copy & staple one for each student and hand it out at the beginning of the course.

**How do we use them?**

*A place for meaningful notes:* After each activity we do, I get my students to take out their course pack & open to whichever page matches the content we covered that day. I give them time to write their own notes based on the student work on the boards, the short notes I may have written on a board or on their boards, and I’ve also suggested mathisfun.com as a good site for definitions at their level. I also encourage them to put both images & words in every box.

*A reference document:* When groups go up to their boards to solve the day’s problem, one of the 3 members is given the role of bringing the course pack (the other 2 are responsible for scribing and calculating, respectively). Groups will often look through the worked examples if they need some help solving the day’s problem or remembering how to do something. On individual practice days, students often have their course pack out to help them with their practice problems. When students are stuck on a problem, I’ll often ask them to show me where a similar problem is in their course pack & we’ll use that as our starting point as we work together.

**Can I see some examples?**

Sure can!

Grade 10 applied course pack

Destreamed grade 9 (applied & academic together) course pack:

Grade 10 academic course notes

Still have some questions? Hit me up in the comments below or on Twitter! Have you made some of your own? Share links to your course packs below too!

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

I’ve often said that I would hate to be a learner in my own classroom. I was a very strong student in high school. I didn’t need to be in class; if I missed class I would read the section in the book & do the homework problems & learn it myself. I made beautiful pages of copied notes from the teacher’s board and was able to understand the content as I copied. I did not enjoy group work; hated relying on partners to do their bit. I am still the first person to roll my eyes at ice breakers in a staff meeting or workshop.

And yet, my classroom is the opposite of this. I ask my students to work in groups, beginning with a getting to know you question every day since we change groups daily. I don’t give many notes, rather I give students time to summarize their new learning in their course packs. We do problem-based learning with hands-on components whenever possible. This is a far cry from the teacher notes followed by homework problems routine from my day.

But many to most of my students are not able to learn that way (although a small number of them are & would prefer a more traditional teaching style). Most can’t understand the notes they’re copying down because they’re too busy copying. *(Have you ever asked your students if they’re able to listen to the teacher while they copy notes? My students tell me straight up that they are not able). *

So over the years I have searched for strategies & pedagogical methods that would transform my classroom to be a better learning environment for my students. But my students haven’t always been eager about my methods; group work, problem solving, critical thinking, feedback separated from marks, etc. The workings of our Math classroom are so different from their experience so far that they sometimes push back. And for many teachers, this push back stops them from continuing to pursue different teaching methods. For example, I’ve had students say “you don’t teach us!”. But upon drilling down further as to what they mean, it becomes clear what they really mean, is you don’t write long, detailed notes on the board to copy down. They think that is teaching and don’t view the careful orchestration of a student-centred classroom as teaching also.

**My advice to teachers: keep trying!** Don’t let that student (or parent) push-back stop you from pursuing new & innovative teaching methods. It’s normal – it happens to all of us! But eventually students (most anyway) get past it. Alice Keeler shared this great article entitled “NAVIGATING THE BUMPY ROAD TO STUDENT-CENTERED INSTRUCTION” by Felder & Brent that likens the student push-back during student-centred teaching to the 8 stages of grief. I love sharing the article with teachers that are frustrated by students that are reacting negatively when they try to transform their classroom to a student-centred learning environment. So to make the ideas even more shareable, I put together a sketchnote version:

But I really do encourage you to read the whole article as the authors go on to explain some suggestions as to how to mitigate the push-back, such as sharing with students the reasoning behind the methods, and modelling & establishing criteria for the successful use of the critical thinking skills expected of students.

I’ll finish by including a few of the tweets from other teachers on the topic:

What push-back have you experienced in your classroom and how have you dealt with it?

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

*[update: There are now 14 elements in the Thinking Classroom framework – an updated sketchnote can be found here]*

Almost 3 years ago now, some math teachers in our school board returned from a conference with two concepts from the research of Peter Liljedahl; vertical non-permanent surfaces (VNPS) & visibly random grouping (VRG). I was blown away by these 2 strategies & implemented them in my classroom immediately after learning about them.

Peter tells a great story about a Math teacher saying upon meeting him “Oh, you’re the vertical surfaces guy!”. While he’s happy that teachers are finding benefit from implementing VNPS in their classrooms, he hopes those teachers will be inspired to go even further and delve into the 11 conditions Peter says will help us build “Thinking Classrooms”. A thinking classroom is . . .

“a classroom that is not only conducive to thinking but also occasions thinking, a space that is inhabited by thinking individuals as well as individuals thinking collectively, learning together, and constructing knowledge and understanding through activity and discussion” (Liljedahl, 2016)

In his chapter titled “Building thinking classrooms: Conditions for problem solving” Peter outlines 11 practices teachers can adopt in order to build a Thinking Classroom. Actually, I think that chapter proposes 9 of them, and Peter has an upcoming chapter to be released that details all 11 practices that his most recent research has unveiled. Here is my sketchnote summary of those practices:

Building a thinking classroom:

- Begin with problems/tasks
- Visibly random groups
- Vertical non-permanent surfaces
- Oral instructions
- Defront the room
- Answer “keep thinking” questions
- Build autonomy
- Hints & extensions to maintain flow
- Level to the bottom
- Student-created notes
- Assessment

That last one is the one I am the least clear about what it entails. I heard Peter say in a talk that it would take him another 3 hour session just to cover that piece alone. I’m hoping that the more I explore his publications, the more I’ll learn about what he proposes for assessment as I am keen to get away from tests & make my assessment match my classroom time.

For more of my posts on Peter’s Thinking Classrooms work, click here.

Peter’s Thinking Classroom research can be found here.

He provides some “good problems” so you can start with the 1st step, here.

You can watch a 1-hour archived webinar by Peter on the topic here.

*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*

*[update: There are now 14 elements in the Thinking Classroom framework – an updated sketchnote can be found here]*

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

A few years ago I started using visibly random groups & vertical non-permanent surfaces in my Math classroom. I got so excited about these strategies when some colleagues brought them back from a PD they had attended and immediately changed my classroom routines & setup. These strategies come out of a body of research by Peter Liljedahl on the Thinking Classroom.

Peter came to Ottawa last week for our Math PD day. He keynoted our event as well as offered workshops, both beginner & advanced, on how to apply his research findings in our classrooms. I tell everyone I can about how much Peter’s research has changed my classroom for the better, and so after his recent visit I decided to work on sketchnoting & sharing his research.

Here are my first two sketchnotes:

**Visibly random groupings:**

**Studenting behaviours around homework & studenting behaviours in the “now you try one” teaching model:**

Stay tuned for more sketchnotes about the Thinking Classroom!

*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)

A roundup of things I did differently, or that I continued to evolve with, this year in my Math classes:

**Visibly Random Groups**

Groups of 3 students sitting together. New partners & new desks every day. I used playing cards given out at random as students entered class to assign students to tables – with hanging numbers indicating which tables made which group. More details about VRGs here.

**Kahoot!**

2 to 3 days per week I used Kahoot as our bellwork. Kahoot is an interactive quiz that the kids answer using cell phones/tablets/laptops. I have created a bank of basic skill-based multiple choice questions for each of my courses and we often start class by playing 10 randomly chosen questions. Correct answers get points & the faster you answer, the more points it’s worth. The kids really love this & it’s a great way to practice basic skills.

What’s especially cool about Kahoot is that they have pre-made question banks for lots of different topics and courses, so you can play this with almost no prep work required. Julie Reulbach does a nice job of outlining her experience with Kahoot this year in a blog post here.

**Problem-based Learning**

As much as possible, I try to start with a problem to solve, instead of starting with a lesson. Sometimes this is a hands-on activity in the style of Al Overwijk & Bruce McLaurin. Sometimes it’s 3-act math in the style of Dan Meyer. Other times it’s a word problem from a textbook stripped down to make it more open (like here & here) and solved on vertical non-permanent surfaces (see next). Students always started by estimating the answer (too low, too high, best guess), collect data/measurements if needed, and then solve. And at whatever point students get stuck, or need to learn something new, that is where I go to the board for a mini-lesson before having groups return to finish solving the original problem given their new knowledge/skills.

**Vertical Non-permanent Surfaces**

In our visibly random groups of 3, we solve the problems on whiteboards & blackboards. This gets students up out of their chairs, working together, thinking. They try out different ideas because they know it’s easy to erase whatever doesn’t work. It allows me to see everyone’s work all at once and give prompt feedback on their progress. Students can also look around at other boards to get ideas if they’re stuck. More details on VNPSs here.

**Khan Academy**

Now hold on with your booing & your hissing … Math teachers love to have a hate-on for Khan Academy. It’s not a replacement for a math teacher, and it has it’s disadvantages, but they have some good exercise sets that can be used as homework instead of problem sets from the textbook. At the beginning of the year the homework on KA was optional as I explained here, but in the 2nd semester the homework for my grade 10 academic class was mandatory and tracked daily.

The students sign up with you as their “coach”. You can set a certain exercise as homework with a due date. The site then summarizes who has and who has not finished their homework. You can also see how many problems they have attempted to solve and whether or not they got the correct answer. The advantage for the students is that if they get stuck, there is a “hint” button (which isn’t so much a hint, as the next step explained) and a link to the infamous KA-created video related to that specific problem.

**Spiralling**

Instead of teaching unit by unit, I have continued spiralling the curriculum. This means teaching every expectation in the curriculum over the first few weeks, albeit in an introductory fashion. Then we cycle through all the material for a 2nd time, delving deeper. And then again a 3rd or maybe 4th time through depending on time. Mary Bourassa has a good explanation here of spiralling.

There are a few smaller things I introduced also such as the wireless keyboard, a “tech tub” with 5 chromebooks for students to borrow when needed, posters of course expectations & mathematical processes on the walls, etc.

*For next year:*

- Make my evaluation tools match the group-work, problem-based learning we do in class.
- Work on recording the observations & conversations that can inform a student’s final grade in addition to the products they create (tests, tasks, projects, etc).
- Improve my Link Crew class that I taught for the first time last year.

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

This month I have a student teacher teaching my two grade 10 classes each morning. He’s been doing a great job trying out the spiralled curriculum & activity-based teaching approach that I use. He’s also continued using the visibly random groups (VRGs) & vertical non-permanent surfaces (VNPSs) that I have set up in my classes. Today we had a moment that really cemented for us why the VNPSs are so powerful:

A bit of background first. This year I’m teaching the primary trig ratios using trig trainers & a trig table. The trig trainer provides the sine & cosine values for a right triangle with a hypotenuse of 1. Students then use similar triangles to solve for missing information like this:

So far we had covered how to find missing sides, but not yet how to find missing angles using this method. The students had all the knowledge they needed to do so, there was nothing new to teach them besides how to apply their knowledge in a way to find a missing angle.

So yesterday my student teacher started his lesson by putting this problem on the board:

He asked the class questions about how they used the trig trainer to solve for missing sides (activating prior knowledge) to elicit ideas about similar triangles and scale factors. He then asked them how they might use the same ideas in order to solve this problem.

Crickets.

Nothing.

No answer.

There were a few awkward minutes while he waited for them to figure out how to apply their prior knowledge to this new example type. He tried rephrasing his question but they weren’t giving him anything. They weren’t willing to venture a guess out loud. He was hoping they would suggest to him the method to solve for the missing angle & he would solve it on the board for them (direct teaching).

But I suspected that if asked them to, most of the students could solve the problem based on what they’ve learned so far, even if they couldn’t verbalize how to do so (or weren’t willing to verbalize it). So from the back of the room I piped up & suggested sending the groups to their assigned vertical surface (each group has a blackboard or whiteboard space assigned to them). My student teacher obliged & sent them to their boards.

Within one or two minutes a couple of the groups were solving the problem – using the exact method that my student teacher hoped they would explain to him in the earlier discussion. The groups that didn’t figure it out right away looked at the boards of those groups that had & quickly caught on to the idea and started solving themselves also. Here is the solution from one group:

Once most groups had solved it, my student teacher asked them to return to their desks & consolidated their learning with the whole group and then assigned some practice problems.

This experience really drove it home how beneficial the vertical surfaces are. When asked to explain orally how to solve the problem, students were not able. But working on the problem at their boards, most groups solved without having to be taught how to do this specific type of problem. And those that didn’t get to the final answer were still able to see the full solution presented, and done so in multiple ways by different group.

So powerful!

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)