Math in Motion

I always wanted to teach since kindergarten. My teacher said that I was good at helping others do math.

Daniel Muller, a relatively new teacher – 3 ½ years in the profession – teaches math at Abbotsford Traditional Secondary School. A few weeks back I had the good fortune of being able to visit his class. When I entered, what I saw intrigued me: Daniel walking around the class talking to students who were communicating in pairs, everyone working through complex math equations, everyone standing and writing their responses with erasable pens on the white boards and the windows in the class. Daniel was working through a question with them and upon completion moved them around the room to new couplings. Another question, more partner talk and more work. Everyone engaged and everyone helping each other work towards mastery. Here’s a brief video that captures a piece of the learning experience:

I found the time to sit with Daniel a week later to talk about what I had observed in his class. This is my interview with him.

Tell me about your philosophy around teaching math.

Well, first and foremost, I want to teach for learning and create critical thinkers – students who can think, work something out and develop resilience and confidence through math.

I always assumed that math was about students sitting down, taking notes, receiving time to work
in class and then writing some sort of quiz or test to check on understanding. Why would I think there was an alternative way? All of this changed when I went to a Math Conference and these beliefs were challenged. Why should I ask kids to take all of these notes when these same notes go unread by 75% of the class? Why am I teaching in a way that does not engage my students? Why do they need to sit down and take notes? And with this delivery model I really have no ability to use “in the moment” formative assessment to gauge understanding.

So how did you go about making the change in practice that led to what I saw in your class the other day.

During my practicum I was with traditional math teachers; however, they granted me the license to try whatever, whenever. I got my students to work on windows and boards – it worked ok but back then I didn’t have the classroom management skills that I have now.

I think that anyone trying this has to go in to it with the expectation of classroom chaos – it won’t be quiet. But I don’t want risks
quiet. I want a buzz, active engagement, bodies moving. From the outset, I set very clear expectations and we talk about them as a class. I tell them that it takes a lot of courage to take risks but that it takes even more to share out your thoughts and answers when you’re not 100% sure that you’re right. If there’s no trust and no respect amongst the kids then that culture of risk taking won’t be developed. In terms of discipline issues, by switching up partners between questions these issues seldom arise. If a student wants to disengage, I’m ok with that because it allows me to reflect on either my practice that led to this or reflect on the learning needs of the student at that moment. What I’m not ok with, and I’m very clear about this, is a student negatively impacting the learning of their partner.

Ok, so they’re standing up and working on the math challenges…what about the notes?

I provide the notes online if they need to access them but I don’t have them spend the class copying them down. What’s the point? I mean I can have them take these notes with me sitting at the frontof the room stating, “this is how you do this question,” but how do I know that they are actually learning? Really, why do we have kids take notes? Is there an importance attached to writing it down? I don’t think that all 30 students need to copy it down. I mean, if you want top down control than sure, you can tell kids to keep quiet and copy the numbers. I want to teach for learning so I throw up a question that they do not know the answer to – they can get started and standing up with a partner, start working critically. If I can get my students to critically think for five minutes then I have accomplished more than I would by having them copy notes for an hour.

Math in MotionSo this is why you have them standing up?

Yah, standing up is the only way that I can ensure that this is happening. I can see everyone in the
room and if they just know the basics, I can assess that immediately and I can see the progression in their learning. By standing, they can show me way more than they could sitting in their desks and taking notes. If I’m going to teach for learning then I have to see them doing the Math. For the student it’s a little more intimidating because everyone can see you.

I agree. Opening up your thought process, your draft work, to those around you can be intimidating. What do you do to ensure that this is done in a way that encourages risk taking and, to a degree, vulnerability?

That vulnerability piece is huge when you’re talking about developing critical thinkers. I tell them that failure is the vehicle to deeper understanding. I have them working in teams, never alone, so that they can help each other. They are accountable not just for their own learning but that of their partner as well. They use non-permanent markers so that they can easily erase work, take more chances and become risk takers.

And this wouldn’t happen if they were sitting down in their desks?

Well, if they’re sitting down by themselves, chances are this will not happen. When They’re at their desks, I can’t tell anything. When they’re standing and writing on the windows, I can see them work, I can see their thought processes. I see them trying to figure it out and I can gauge where they’re at; I can base my lessons on what I see and this formative assessment is guiding my practice. Are people getting this, can I move on, where are they now

There’s something about everyone moving that creates an energy. Even when they’re stuck, they’re working, they’re talking and they’re looking. They are not sitting at their desks zoning out because of frustration

So, it’s not only about the content? The “getting it” isn’t all that matters? 

Look, their doing Math, they’re being creative, they’re thinking critically, they’re collaborating with a partner and
communicating their findings. It’s as much about these competencies as it is the content. They may not go on to be mathematicians, although the world can always use more of them, but they’re building skills that are going to serve them well regardless of the career or life path they choose. If I can get them to think critically think for 5 minutes then I’ve accomplished something more than ensuring all of the notes have been copied in our allotted time together.

It definitely looks like the engagement level is high; I mean it’s nothing like my own experience with high school math. Tell me a little bit about how you set it up.

Sure. Well, the docu-camera makes it easy for me to model – I’m up and moving around. When I reflect on the groupings and the purpose of this collaborative approach, I use the lens of wanting to build a sense of community. You can’t build community if you’re sitting at a desk taking notes and working in isolation. So there are many ways I initiate. I’ll hand out a deck of cards with numbers that represent spaces along the windows or boards. We’ll do rock paper scissors. I’ll ask them to take a 5 decimal long number, add it, divide by pi and those who answer correctly have to move spots. The point is that they cannot stay with the same person for more than one question – it’s about building community. I mean, it’s a small school but not all of these kids don’t hang out together. This is a chance to get to know someone you usually wouldn’t speak to and that’s important. That’s why before they start working together, they have to introduce themselves with “Hi I’m …” every time they move.

Ok, well you lost me at pi. I get what you’re saying about community and the benefits to students. But you’re always “on”. How do you assess and where do you find the time?

I remember what it was like for me in some of my math classes. The teacher would mark tests and homework while we all sat at assessour desks doing the assigned examples. I mean, how would he even know if we were “getting it”?

I don’t mark in class and I don’t have to because I’m watching and documenting the learning as it is happens.  Even if they get lost, it’s so easy to spot them because I can see all of them and all of their work, all of the time. I may not always be able to reach all of them but if I get to two it’s more than zero (which is what I’d get if they were sitting down).

I like to look at it like this: sometimes, we will spend 5 to 10 minutes on one question and then they’ll finish with a “yes, I got it!” We’re going deeper into the process and combining content with the developing skills that will be transferable in other walks of life: patience, perseverance, collaboration.

But you must mark individually at some point and give them a grade?

Oh, for sure but their grade is based solely on their tests.

Really, isn’t this a kind of all or nothing proposition?

Well no because there are no surprises.

What do you mean?

crit thinkingWell, let me explain the process from what we you saw in my class, to homework, quizzes and finally, tests. Remember, I want to teach critical thinking and not just learning the math. So what that means is that I want every student to be able to explain their own thought processes, right or wrong, and this will help them break down the sequential learning steps necessary for math mastery.

Homework is not marked – it’s a practice tool. I could make it for marks but why? They’ll just copy it. Walk in any school hallway during a break in classes and you’ll see someone copying someone else’s work. And then they submit it and as a teacher, I have no idea if they have a good understanding of what they are doing. I can’t see the way they are thinking. So the answer is simple: don’t make it worth anything and you remove the urge to cheat.

When I assign homework, I give them the questions but also the answers with the full solutions which explain how it is broken down step by step. I want them to compare their process with the established one.

From there we move into Quiz Days. These are huge, take up the whole day and it’s the only timeeinstein other than tests that they are sitting down. Again, no marks but a lot of formative assessment to find out where they are at. What happens is that they get twenty minutes to do the work (some students need the full twenty and more while others do not). After the initial twenty, I speak with them as a group and one to one. I provide them with the start to the answer and they review their work and see where they are at. In the last twenty minutes (it happens earlier for students who are more proficient), we interview one to one and we review their work:

  • Can you spot your mistake?
  • Can you come up with the right solution?
  • Can you walk me through your process?

The quizzes are used as tools for learning. Students will take their corrections and then come to me and explain it: “This is what I did wrong and this is how I approached it.”

When test day arrives, students aren’t anxious because they know where they are in relation to their learning and so do I. If I have a student who does well in everything but then bombs the test, then it allows me to go deeper into the soft skill realm: does the student have test anxiety? Do they get nervous at formal testing? With all the formative assessment we do, situations like this become really obvious.

Daniel, I have to say that I’m really impressed. Listen, would you mind if I blogged my notes about you and the experience you shared with me?

Of, for sure. I’ve never seen your blog but ok.

(Laughter on my part) Any final thoughts?

imagesWell, you know, I love math and I think it should be fun for students. I also hope that through math I can give students the confidence to try new things, to take chances, to enjoy being in school. I believe that there is something very important with the process of standing up and doing the math. I’m focusing on this as my Masters Thesis.  What I would really like is to find someone else who is teaching math and trying this stuff out. I would love to have someone, anyone, that I could bounce ideas off of and vice versa. That would be really great.

Well, Daniel, hopefully someone out there has seen my blog and will get in touch with you. I sure hope so because it would be a pretty spectacular learning opportunity for all involved.

Thanks again.