Push-Back to Student-Centred Learning. #sketchnote

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:

Student centred instruction.jpeg

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)

Running VS Walking Headstart #MPM1D #MFM2P #3ActMath

A month ago or so I read a post by Mr. Hogg about his Fast Walker activity. I thought it would be a great way to introduce linear systems graphically to my combined grade 9 math class before the end of the semester. I also did this activity with my Grade 10 applied students – next semester I’ll use it as an introduction to systems graphically with them earlier in the course.

What turned out to be super awesome is that a student in my grade 9 class just won gold at OFSAA last week! So I tweaked Mr. Hogg’s activity to use Joe’s winning data in our problem. I also structured the activity to be a 3 act math task. Here’s what we did:

Act 1: Notice – Wonder – Estimate

Runner Speed (1)

What do you know / notice?Capture

What do you wonder?Capture

If you want to cross the finish line at the same time as Joe, what distance head start will you need?Capture.JPG

Act 2: Measure & Solve


Students were told they had to stay in class when taking measurements; my idea being to force them to time themselves walking over shorter distances (the length of our classroom) and then use that to model their speed for this problem given. Each student had to calculate their own head start:

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Act 3: Check & Reflect

We went out to our 400m track and students measured out their starting position. They staggered themselves according to their calculation (photo below – tried to take video but my phone battery died). Most students were around 100m before the finish line (~300m head start). We counted down & Joe started running & the class started walking. I so wish I’d gotten the video because it was awesome how close they all finished to each other!DB6mp2rXgAE8O55

I had my grade 9s graph their walk & Joe’s run on the same grid. Here are their graphs overlaid on top of each other:
Most students had the right idea, and I talked to a few with incorrect graphs individually but when I look at this overlay now I can see that I missed helping a few students correct their work 😦

We discussed which line was partial variation & which one was direct. I then introduced the language of “linear system” and “point of intersection”. My 2P class time to create an equation for each line also.

The next time I try this, I’d like to add an individual follow up question such as if you only had a 50m head start, at what distance would you & Joe meet? At what time would that be?

Here are my files for this activity (the unassociated one is the Pear Deck slideshow).

Tech Tip: Did you know you can add the same Google Doc/file to multiple folders without copying it? I didn’t until recently. It was useful for this lesson because I wanted to have it in the folder for each of the 2 classes I did the lesson with! Once you’ve clicked on the file just press Shift+Z :Capture.JPG

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

Tree Height #3ActMath #MPM2D #MFM2P

Here is a tree height 3 act math activity I do for right angled trigonometry with both my 2D & 2P classes. The screenshots below were taken from my 2P class this semester.

Act 1: Setup


Some noticings:IMG_2298

Some wonderings:IMG_2299

We do some turn & talk guesses for “too low” & “too high” then we go back to Pear Deck for our best estimate:IMG_2300

Act 2: Measure & Solve

Students downloaded a clinometer app onto one of the phones in their group.

Here are photos of last year’s group out measuring:

Up to the “vertical non-permanent surfaces” to solve in their “visibly random groups”:

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Act 3: Consolidation

This is one activity I don’t have a true act 3 for – I don’t know the actual height of this tree 😦 I led a class discussion going over the solutions from various groups. We discussed the fact that trig would not find the whole tree height & that groups needed to add the height of the person up to eye level to their value found using trig. I sent groups back to their boards to adjust their solution for this (final photos above).

The whole activity, including the Pear Deck file, can be found here.

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

#3ActMath – What is it?

I learned about a great tool this past weekend at the Ontario Summit; Adobe Spark video. A huge shoutout to Rushton Hurley for the introduction to this tool. It’s a super fast & easy way to combine photos, videos & text and narrate over top of it to create a seamless professional looking video.

I tried my hand and created one about 3ActMath lesson style. Give it a watch & let me know what you think:

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

Height VS Foot length #MFM1P/#MPM1D #3ActMath

As an introduction to Linear Relations with my combined 1D/1P grade 9 Math class we investigated height VS foot length and the guinness record holder for the tallest woman:Summary 2017.02.08 (1).jpg

I asked students to measure their height and foot length and record it on a Google Spreadsheet we had up on the projector:


What do you notice?Capture.JPG

What do you wonder?Capture.JPG

I posed this question:

Zeng Jinlian was born in 1964 in Yujiang village in the Bright Moon Commune, Hunan Province, China. She holds the record as the tallest woman. She measured 2.48 m (8 ft 1.75 in) when she died on 13 February 1982. How long were her feet?

Estimate: _____ cmCapture.JPG

Students were sent in their VRG groups to their VNPS boards to solve. Here are their boards:

Since it is still early in the semester I scaffolded the activity a bit by instructing them to create a scatter plot of the data on their board to help them solve the problem. I did not however instruct them to use a line of best fit, although many groups used that strategy to help them come up with an answer. Some groups had graphs with a Height axis that went high enough to lookup Zeng’s height and find the corresponding foot length from the line of best fit. Other groups made an educated guess based on the trend the points were showing.

Each student was asked to determine her foot length based on their graph:Capture.JPG

Her real foot length was 35.5cm!

The following day students were assigned some individual practice with scatterplots on Khan Academy.

Activity materials (include a slide deck for Pear Deck) available here.

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

Flight Costs #MFM2P

I’ve done this activity once previously. I changed how I did it for this second go. I will change it again for next semester.

Here’s how it went this time …

Students were presented with this data:copy-of-lr-flight-distance-vs-cost

Students were asked:

2016.12.21 notice.JPG


The task for day 1: Determine the initial value & rate, on average, for flights with Air Canada.

Some groups went to Desmos straight away. Others needed some reminding that Desmos can be very helpful with data like this.

On day 2, groups were asked to determine the distance they could fly for $500 using their equations from the previous day. I only took a photo of one group’s board that day:2016.12.22 summary.png

I think next semester I will change this up. I think I will present the name of a city & ask students to estimate the cost of flying there. Then I’ll give them the set of data for cost & distance for multiple cities, but with the first city blanked out; perhaps allowing them to adjust their estimate if they like. We’ll do notice & wonder, and then proceed to solve for the price. I won’t specify modelling algebraically but will perhaps create a Desmos activity builder they can do to practice that in the case where they don’t use an algebraic model to solve.

Update: Find the Desmos activity builder follow-up here

Activity available here.

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

Video clip of students at work

Today while Ms. Fahmi, my student teacher, was teaching I went to take a photo of the students at their boards solving in their groups. Then realised that I should try taking some video since there are several of us in the room & I can take the time to do so (I had parents choose at the beginning of the year whether or not they were comfortable with me including photos & videos of their child in class on my professional learning network platforms)

Here is a quick (1 minute) video clip of my students working on a visual patterns 3 act math task on vertical non-permanent surfaces in their visibly random groups:

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

Student-Paced mode in @PearDeck for #3ActMath tasks

This summer Pear Deck announced the introduction of student-paced mode; the ability for the teacher to allow students to work through the slide deck at their own pace. This is a feature I enjoyed in the Desmos activities I’d been building for graphing (interesting also that Desmos introduced their teacher-paced mode around the same time that Pear Deck introduced student-paced; both platforms now offering both pacing options).

Not sure what Pear Deck is or does? Watch this quick video before reading further:

How to turn on student-paced mode:

Click the 3-dot menu icon on the bottom right of your screen while presenting your Pear Deck, and the option to turn student-paced mode on (or off later) will be there:file-DY4DfcYV8V.png

How do I use student-paced mode?

Most of the activities I do in my math class are in the style of 3 Act Math (a concept put forth by Dan Meyer).

Act 1 consists of present my students with a scenario via photo or video & asking them

  • What do you notice?
  • What do you wonder?

Then I show them the problem I’ve chosen for the day (usually it’s one that most kids write down for “what do you wonder?” since I’ve carefully selected the scenario to lend itself to asking the question I want based on our learning goal).

  • Estimate the answer: too high, too low, best guess?

Act 1 happens via Pear Deck in TEACHER-paced mode. Students are at their seats in their visibly random groups for the day assigned by playing cards. They use their own phone or a loaned chromebook (I have 6 that live in my classroom) to answer these questions on Pear Deck. We often have a quick class discussion here too about reasonable estimates and their strategies for that. I, as the teacher, am choosing when to move the slides forward for the entire group.

Act 2 consists of sending each group to their assigned vertical non-permanent surface (ie. chalkboard or whiteboard) to solve the problem. Often groups also need to do some data collection or measurement here in order to solve the problem.

At this point I have a slide with the original picture & the problem to solve written on it projected on the board while the groups are solving. The moment the first group to finish solving heads back to their seats, this is when I turn on STUDENT-paced mode. The rest of the slides will be follow up questions to reflect on their solution or to apply their thinking to extension problems. Students work on these at their own pace at their own desk.

When all groups are done and back at their seats, I lead a class discussion about the solutions from each group using the 5 practices for orchestrating productive mathematics discussions. During or after this discussion, we might also look at some of the responses to specific follow up questions on Pear Deck. If we do, I turn OFF the student-paced mode to bring everybody’s screen back to whichever one we are discussing.

Act 3 consists of checking our answer either in real life (as we did for the cup stacking activity) or by showing a video or image answer (as we did for the phone charge activity).

Normally, in Pear Deck, there is a projected screen being shown on the board to the whole class by the teacher. The students see a “response” screen on their own device that is different than the one being projected. When in student-paced mode, the student can see both the content slide AND The student response slide on their own device. On a tablet or laptop the two screens are shown side by side when in student-paced mode:IMG_1923.PNG
When using a smaller device such as a phone or iPod, the student will see a blue bar across the bottom of the screen allowing them to toggle back and forth between the “content” & “response” screens:

Have you used student-paced mode in Pear Deck yet? Share in the comments below how you use it with your own students!

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

Pyramid SA #MFM2P #3ActMath

Not the most exciting problem, but my students were still engaged even if it wasn’t a contextualised scenario.2016.10.31 summary (1).png

Act 1:


What do you notice (facts)? What do you wonder (Qs)?
– The shape is a pyramid that has a square base.
– The area of the triangle is 1 cm square.
– What is the area of the base?
– What is the volume of the shape?
– What is the surface area of the shape?
– What is the height of the shape?
It is a triangle What is the lenght and height of the triangle
It’s a square based pyramid how many sticky notes do we need to cover the square based pyramid
It’s a Square pyramid
It’s a triangle and it has 1cm squared What are the lengths and widths of the pyramid
Its a shape. what is 10m2?
Square based pyramid, with a sticky note that reads “I cm squared) Why is there a sticky note on one of the sides?
That it is a square base pyramid What are the other lengths
There is a square based pyramid What does the 1cm^2 represent?
There is a triangle What is the value of this pyramid
what’s the area of the square based pyramid

Estimate:2016.10.31 estimate (1).JPG

Act 2:

Each group of students was given a plastic pyramid like the one in the picture. They began measuring dimensions of the pyramid and using the formula from their formula sheets in their binder. They solved the problem on their boards:

I asked the group why they thought we got different answers in different groups and they commented that some of our plastic pyramids were slightly smaller than others. I did a little direct teaching about the net of a square based pyramid and how that translates into the formula on their formula sheet:


Act 3:

I then handed out grid paper and asked the students to draw a 1 cm by 1 cm square at the top left of the page. They told me that the area was 1 cm^2 and determined that every 4 squares of our grid paper made a 1 cm^2 area.

I asked them to trace all of the faces of their pyramid onto the grid paper to create a net. Then to colour in alternative 4-square blocks to allow us to count the area in cm^2.img_1915img_1913

We counted up the area and found the answer to be 114 cm^2; right on with our calculations!


Students were assigned a “surface area” practice set of questions on Khan Academy; different ones depending on whether or not they had completed the previous set I assigned earlier in the semester.

The materials for this activity are available here.

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

Lamp post height #MFM2P #3ActMath

Last week we used similar triangles to find the height of lamp post out front of the school:2016.10.17 summary (1).png

Act 1


What do you notice about the lamppost? (FACTS) What do you wonder about the lamppost? (QUESTIONS)
The pole is taller then the person What is the height difference between to man and the lamppost
It’s a lot taller then the person how much taller is the lamppost compared to the person?
its a tall lamppost How tall is the lamppost?
The iamppost tall than the boy What height the lamppost and what the height of the boy
there’s a person beside the lamp post how much of that person does it takes to get the height of the lamp post
The lamppost is tall What is the height of the lamppost?
What’s the height of the lampost What’s the height of the lamppost
– The post is taller than the person
– The structure of the lamp post is sturdy
– How much taller is the lamppost than the person?

– How tall is the lamppost?

– How many persons will it take to reach the height of the lamppost?

The lamppost is taller than the person What is the hieght of the lamppost/person
A person is next to the lamp What’s the height of the person and lamppost?
the lamppost is tall
The lamppost is black
How tall is the lamppost
(who is that person)


Act 2

Students were shown this diagram and asked which of these lengths/heights they could physically measure:2016.10.17 diagram.JPG

Then we headed outside to measure whatever we could with metre sticks & record on a handout of the above diagram in our small groups.

We returned to class & students solved at their boards (red/orange annotations on boards are mine during the whole class discussion afterwards):

We discussed the different boards & their strategies. We grouped the boards by strategy; proportion solving vs scale factor.

Act 3

The next day I poked a hole through a foam stress ball & fed some string through it – leaving the roll of string trailing behind. We went outside & took turns trying to throw the ball over the top of the lamppost. It took a good 20+ minutes, but we got it (“we” is a strong word since my throws did not work & my student Ahmed got it over!) and the students then measured the length of string that hung down to the ground; 10.16 m was the actual height (which was fairly close to their solutions on the boards).

The rest of the day 2 class was dedicated to individual practice. Some students never completed the first practice from earlier in the semester on similar triangles, so they were assigned the basic exercise set on Khan Academy. Those that had completed that skill were assigned a more advanced exercise set involving similar triangles nested inside of one another.

Lesson materials available here.

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