My Spiralling Process

Before I actually begin this post, I will link to some resources about spiralling as my intent here is not to explain what it is or its benefits. Suffice it to say that I am really enjoying teaching this way. If you have no idea what spiralling is, you could read my blog post recapping a session that I co-presented at TMC14, found here. There are also some interesting articles/blog posts found here, here, here and here.

I am often asked how I spiral (interleave) a course. Thus far, I have not had particularly insightful answers, as the only course I had spiralled prior to this semester was grade 10 applied (MFM2P). I stole everything my first time spiralling that course from Alex Overwijk, with whom I collaborated throughout that semester. I cannot thank him enough for taking the time to work with me and Sheri Walker, and for generously sharing all his resources. 

What has changed? This semester I am spiralling the grade 10 academic course (MPM2D) for the first time. I am doing this alone, but feel confident having spiralled MFM2P for the past two years (and continuing to do so), and having taught MPM2D dozens of times (so I know the content inside and out). By the end of TMC15 this past summer, I had envisioned how I could make spiralling this course work for me. Although I found it very difficult to do a lot of planning before actually being in the trenches of teaching the course, I worked out a draft of my plan. I first stated the overall curriculum expectations for the course. I then worked out what I wanted the first cycle to look like and got less and less specific with each subsequent cycle. It looked like this:

I then made a gdoc for my first cycle. Choosing which activities fit in with my goals takes a little time, but I try to make each day as meaningful as possible. I also want my students to enjoy math class so choosing good activities that will engage them is key.

Soon after the semester began, I added columns for what I actually did each day as things always take longer than planned and my plans are always flexible. I adjust what I do based on how the previous day went. Here is what that doc looks like now:

I am recording what I do each day, along with what homework I assigned. Speaking of homework, I also decided to create my own homework sets. I am doing lagging homework some days. For example, homework set 11 had one question where students had to find the equation of a line given two points, one question where they had to sketch a parabola given the equation in factored form, one question with binomial multiplications and one question where they had to solve systems of linear equations using substitution. This way the content is always fresh and students who struggled with a concept will get more opportunities to practice and improve. I try to give feedback on homework (it never counts toward the grade) several times a week, and check only for completion occasionally. I feel that this has helped me really know where each student is in the course. Lagging homework also doesn't let students "escape" any of the material. If they didn't understand something they soon learn that it's going to keep coming back and that they really do need to take advantage of some extra help. I post full solutions to all the homework after it has been handed in, allowing students to figure out some of their own errors and how to correct them.

In addition to the gdoc above, I have gone through the curriculum document and highlighted all the specific expectations that I will hit during cycle 1, and pencilled in cycle 2, 3 or 4 for each of the others. I hope to create a digital version of this at some point.

Evaluations in a spiralled course look a little different. They have multiple curriculum expectations, making them more like a little exam than a standard unit test. I mark on levels (R, 1, 2, 3, 4) by expectation. This makes it clear to each student how they are doing on each expectation. Should they get a level R, they will be given an opportunity to reassess before the next evaluation, after getting some help from me. I record results using a locally-developed program called MaMa which allows me to see progress throughout the semester. Here is a screenshot from a previous year:

The curriculum expectations are along the left and each test is a different colour, getting darker as the semester progresses.

I am also blogging my way through this course. I write a post each day where I explain what I did and reflect on how things went. I also post link to all the handouts. If you are interested in reading more, my first post for this semester can be found here. I also blogged my way through the MFM2P course last year and the one before.

Do you have questions about spiralling that I have not addressed? Please fire them my way in the comments.