reflection whiteboards

Thoughts on Thinking Classrooms

“Mathematics is equipment for thinking”

Francis Su, Mathematics for Human Flourishing, p. 110.

The sun sets around 5:30PM this time of year in my little prairie slice of paradise. Yesterday, well after dark, there was a ring of the doorbell and a package delivery: My copy of Building Thinking Classrooms by Peter Liljedahl. Over the last couple weeks, I have watched as tweeps1 sent messages of exhilaration having received their own copies. The, now familiar, orange cover adorned with the beautiful illustrations of Laura Wheeler is a welcomed sight on my Twitter feed, each time accompanied with excited messages you’d expect to hear from children anticipating a visit from the Tooth Fairy.

Honestly, holding the book felt weird. I say that as a testament to Peter’s work: It draws you into participation to the point where it feels like it’s a part of your history. In my case, that’s because this book is a part of my history. Receiving the book sponsored a sort of nostalgia, as I’m sure it did for so many who have followed the ideas as they’ve developed over the years. This feeling surprised me, because, despite the real feeling of connection to the physical copy of the book and the brand of teaching it represents:

I don’t run a Thinking Classroom.

surface area tasks whiteboards

Double House Task

Surface area is intuitive. Intuition is a natural hook into curiosity. When you think something might (or should) be the case, it begs the question, why? It just seems as though textbooks haven’t gotten wind of that.

Perusing the surface area chapter of the assigned textbook for my Grade 9 math class offers a steady diet of colourful geometric solids all mashed together (at convenient right angles) in various arrangements. Without fail, the questions ask the same thing:

Find the surface area of…

classroom structure formative assessment review unit analysis whiteboards

The Review Day: Unit Analysis and Scale Factor

There seems to be three sacred cows in mathematics education:

  • the worksheet / exercise set
  • the review day
  • the exam

It is not surprising that these three feed off one another, and make up the bulk of assessment in the typical mathematics classroom (including my own). 

Here’s my disclaimer:
While I have been known to slaughter a few of the sacred cows of the instructional process, I have lagged severely behind in my attention to assessment. I value the complexities of learning that occur when student ideas encounter perturbations, curiosities, and other conceptualizations. The type of assessment that comes out of these mathematical encounters is rich, connected, and constantly evolving. 

classroom structure whiteboards

Large Whiteboard Project

Group whiteboarding has changed how I teach mathematics. It has also changed how students operate as a community of mathematicians. 
Since ordering my first set of large whiteboards, our department has ordered four times again, and given workshops to the division’s mathematics teachers. (For a tour through my whiteboarding history, start here: mini whiteboards)
My running motto has become, 
“Whiteboards give me more than eight-and-a-half by eleven ideas”
discourse formative assessment investigation linear functions pattern reflection relations whiteboards

The Discourse Effect

This semester, I’ve been attempting to infuse my courses with more opportunities for students to collaborate while solving problems. This post is designed to examine the shift in student disposition throughout the process.

I have noticed an increased conceptual understanding almost across the board and this is reflected in the differing solutions on summative assessments. It is also nice to see their marks  grow on these unit tests. I do not believe that paper-and-pencil tests are the best venues for displaying conceptual understanding, but it is awesome when the two intertwine.

classroom structure discourse tasks whiteboards

Creating Communities of Discourse: Large Whiteboards

I have talked about individual whiteboards on this blog before. My school bought me supplies and I was loving the various classroom activities. While the grouping questions facilitated good mathematical talk between peers, I was still searching for a method to encourage more collegiality where my role could diminish to interested onlooker or curious participant. 

So I had this brilliant idea. 
Why don’t we get group-sized whiteboards created where students could work collaboratively on tasks?
assessment classroom structure formative assessment whiteboards

My Whiteboarding Framework

This year my department decided to make using whiteboards as formative assessment tools our department focus. This was nice because I had already began to experiment with the process. It just meant that:

  1. I wasn’t obligated to try yet another “thing” in my room.
  2. I would be given better materials and funding to work with.
  3. Other math teachers in my building would see the enormous benefits of the technique.
classroom structure scale tasks unit analysis whiteboards

Gummy Bear Revisited

The giant gummy bear problem has been floating around the blogosphere for a while. When I first saw it, I knew I wanted to use it. I finally have the perfect opportunity in Foundations of Mathematics 20 this year. (Saskatchewan Curriculum).
History of the Problem (As far as I know)
  • Originally presented by Dan Anderson here. Included original Vat19 video and driving question about scale.
  • Adapted by John Scammell here. Edited video and new driving question.
  • Dan Meyer provided a 3Act framework for the problem here.
  • Blair Miller adapted his own 3Act structure here.
My apologies go out to anyone else who played with or re-posted an original interpretation on the problem.