Collaboration – in Math Class

So I read my friend Jay Richea’s post and decided to join in the #Peel21st Blog Hop.

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“Here’s the next instalment of #Peel21st Blog Hop. We  thought we would reflect on the 21st Century Competencies released by the Ministry which discusses the core 21st Century skills that are essential elements in modern learning. We thought these competencies could be a great way to prompt a conversation amongst the #peel21st community and afar as well. This month, it’s all about…

Collaboration: Near & Far

So my focus will be on Collaboration in Math Class.

I remember vividly spending most of my first year math undergrad in isolation, and thinking, how is everyone else handling all of this work, and understanding everything? I lived off-campus you see, and I’d head home after lectures.

Second year, I moved on-campus and discovered the marvel of study groups.  People would sit together, figuring out problems, convincing each other that their solution is the one that made the most sense, or is the most elegant. My personal success and confidence in my mathematical ability skyrocketed.  This is a skill that we far too often skip over in secondary math education.  We call it “stealing work” or “cheating”.  But my professors loved it.  They would join us in our debates.

If anyone has the opportunity, check out McMaster’s James Steward Centre for Mathematics – it’s a building with all interior walls painted in chalkboard paint.  We would stand around for hours outside of our professors office, and she or he would join us from time to time, debating about the solutions we’re trying to discover.

So the question is, how do we teach and foster collaboration in our students?  In reading Jo Boaler’s “Mathematical Mindset” recently, I’ve gotten a few ideas of how to not just have collaboration in my class, but to show students that I value it by having criteria clearly laid out for them.  I loved the two suggestions that she provided (from Carlos Cabana):


I love the fact that Carlos is open about the fact that the group needs to lean on each other in order to collaborate, that a single person cannot be successful in all of this, but together the group can.

To add to all of this awesomeness, we now have collaborative tools like GAFE, Formative, and now Desmos Activity Builder specifically for math where we need to collect data from the entire class in order to solve a problem.  Online tools allow us to create activities such as THIS one where we have to use some information from our class in order to get to discovering some math, and we can now even include information from people outside our immediate network if we push the questions further.  The possibilities are endless, but we can focus on the objective if we just keep asking ourselves the questions:

  • Do mathematicians do math in isolation?
  • What do their offices look like?
  • How do students learn best?
  • How can I best support them to believe in themselves and in their own ideas?



Who Makes Me Think – Marian Small

So I’m sure most math educators have heard of Marian Small in some way, but for me, she’s been simply transformational.  She has deeply impacted the way that I not only teach, but interact with my students.

There are so many things that I’ve learned from her, but here are a few that come to mind during my work on a daily basis:

Open Questions

Making sure that students can choose an appropriate entry point into a question.  Things like, instead of saying “Find the equation of the line through the points (2,3) and (5,7)” saying “An increasing line goes through (2,3)…what other point might it go through? What could it’s equation be?”

This question doesn’t only have multiple entry points, but it actually forces students to THINK about so much more than the slope equation and the equation of a line. It also gets students to engage with all of the terminology that we want them to engage with.

When I say the words “What might it be…” instead of “What is…” in my classes, I definitely see students become more relaxed, more at ease, and in turn, more engaged and more willing to take risks.


We often talk about being ready to give feedback to answers we want, or answers we anticipate.  Dr. Small has also talked a lot about being ready and prepared to offer feedback to thinking that you had no idea was coming…generic questions like “Oh…why do you think that is?” or “Oh…why did you think of doing it that way?”.  The other thing that Small does so well is model curiosity for students.  There is a huge importance in the tone in which we ask the question “Why would you do it that way?” It could be either a shut down question, or a feedback opening question…


This is something I haven’t actually heard her talk about, but I just see the way she models it, and having applied it in my class, it does wonders.  Instead of applying complex math terminology from the start, she uses very simple language to start, and then builds up the math vocab.  So when asking a Which One Doesn’t Belong question involving algebraic terms, she won’t say “Which expression doesn’t belong?” but she’ll say “So…like…which one of these guys doesn’t fit?”

My students have commented on the fact that this encourages them to participate, and they feel at ease.  The worries of math class doesn’t creep up on them, and they don’t feel anxious at all.  This allows me to make sure that many more of my students get the chance to be successful and to be heard.

Anyway, I’m sure I’m not doing justice to everything Dr. Small has taught me, but I want to keep my blogs short.  I’ll probably do another post on her impact in the future.  I was very happy to see Dr. Small speak again, and I got to tell her a very important truth: I use a lot of her ideas when I teach the OISE Math AQ, and the reason is that without her ideas, I don’t think I’d even be the type of teacher that gets the opportunity to teach an AQ.  So thanks again, Dr. Small 🙂