Sunday, May 8, 2016

Spiralling: Spinning Around in my Head

Perhaps my biggest take away from last week's OAME2016 conference, was the idea of spiralling the curriculum in my math classes. 

It wasn't a new concept to me - I had been following well-known Ontario spirallers Alex Overwijk and Mary Bourassa for a while now - but before this past week, I hadn't had a chance to really think how it could be applied to my classes, or how I would go about doing it.

To spiral, is basically to delinearize the curriculum. Traditionally, a unit of proportions, a unit of linear functions, a unit of graphing, and a unit of geometry might be taught in that order, with a unit test after each set of lessons on that topic. 

With spiralling, aspects of each unit (or, at least, several of the units) would be presented to the students either through lessons or inquiry-based activities. Any given task might require some basic concepts from graphing, some work with proportions AND some elementary geometry, among other topics.

Progression through the course occurs in cycles - seeing all the concepts for the first time at a basic level, revisiting them in a harder setting, and then seeing them all a third or fourth time in a yet more advanced manner, as mastery is achieved.

In a sense, we already do this in the Ontario system with math, but the cycles come around every year - with grade 10 math building on grade 9 math from the previous year, and so forth. This approach looks at building on curriculum within a single semester or school year.

What's so good about it?

There are a few advantages that seem to stand out to me right away:

  • All the material gets visited more than once. If a student doesn't quite understand a concept the first time through, they will get to see it again. It's not "done and gone" as in a linear curriculum. It might make more sense in a different setting.
  • Applications of the concepts are implicitly provided, as in the third cycle, students would actively use concepts explored earlier on in the course to solve "real-life" problems.
  • Spiralling can easily fit in with the mastery-based, self-paced learning we already have in our math classes. There would be no need to change how my class is set up, just the order in which I deliver the content.
  • In grade 9, where the students are preparing for the EQAO standardized test, spiralled curriculum ensures that everything is covered (more than once, even), and that the students are constantly reviewing concepts. There is basically no need for dedicated review - or the stress that goes along with it - going into the test.
From Mary's blog, outlining how she started spiralling, who in turn got it from Alex:

What I still have to wrap my head around:

  • Tracking what has been covered becomes trickier when you're jumping all over the curriculum (at least in the way it's laid out in curriculum documents). I would need to find a method that works for me to track both student achievement and progress through the course expectations.
  • I'm not sure how long each cycle should take. I know, from experience, how long previous units took when presented linearly. I anticipate it might be tough to plan out, time-wise, the first time through.
  • I'm a bit worried about finding good activities that naturally hit various expectations from the curriculum. So many teachers have offered to share what they have, though, and I hope to be able to take advantage of that.
  • Grade reporting might be tricky, as we are expected to report on knowledge/understanding, thinking/inquiry, communication, and application throughout the semester. If application-type problems aren't investigated until the third cycle, how will this affect grades reported early on (for progress reports or midterms)?

Alex, explaining his tracking system, in a session on spiralling at OAME2016.
Activities are across the top (running vertically) overall expectations are along the
side (running horizontally), and specific expectations are colour-coded by unit.
Thank you, Heather Lye, for the photo!

Where I'd like to use it

There is one course, that I teach regularly, that I think would be a perfect fit for this type of content delivery: MCF3M (grade 11 Functions & Applications). The course is broken down into units of quadratic functions, exponential functions, and trigonometric functions. In each, we look at the basics of the functions, then transformations of the functions and finally applications of the functions. 

If we're teaching the same concepts throughout, why not break down the walls between the "types" of functions and teach them all together? I'm looking forward to giving it a try, and collaborating with a new PLN of spirallers discovered at OAME.


  1. Thanks for a thought provoking post. I have struggled for years with implementing spiral tactics in a meaningful way. What I fear - and this may be entirely my fault for the way I spiral - is that many students have a consistent feeling that they do not need to master skills because they know that we will come back to them. I want instead for my students to feel some sense of urgency about approaching mastery as long as it is balanced by the security of knowing that (a) we'll see and think about these skills again and (b) when we do we will dig deeper. I have quite a bit of thinking to do about this. I may end up pestering Alex for insights this summer at TMC

    1. To be honest, I was wondering about this at last week's conference, too. So many students seem to only be "motivated" when a deadline is imminent. And if they know they'll just be covering it again, will that lead them to put off their learning/mastery? I'm wondering if the activities Alex et al. use address this somehow, so instead of having to explicitly learn, the learning is built-in to the task they accomplish. I'll have to do a little more digging around. Thank you for helping me think through this! I'd love to see how your classes are run.

  2. Alex still uses formal test-like (he calls them exams since they are not "units") evaluations at the end of each spiral. He finds the first spiral is the longest (and at the beginning the activities he uses are just to create his classroom norms, they do not necessarily cover content yet) but did not indicate he plans a specific length. It sounds like he is a big advocate of "just-in-time teaching". It sounds like the kids enjoy his classes so much the motivation piece isn't much of an issue. There is obviously more than one way to implement it all.