I started spiraling my grade 10 applied math class a number of years ago and have written daily blog posts for the course twice. The second time, which starts here, also contains links to all the resources I have used.
Every time I teach this course, I tweak and adjust based on the group I have. This semester I have decided to give homework that supports the spiraled approach I take with this course. I am creating one double-sided page of homework per week. Each homework set contains a little of what we are doing in class that week, along with previously learned topics so that students stay on top of the material. So far I am pleased with how it is going.
Here is the link to my Google sheet. There is a column with links which is where you can get the homework sets if you are interested. They are PDFs as I know some people have trouble seeing equations I create using MathType. If you would like the Word files, feel free to send me an email. There are also tabs for the last couple of years so that you can see an overview of what each cycle looks like.
This semester I taught two sections of grade 10 academic math, both of which I spiralled. Although I have taught this course for many years, this was my second time spiralling it. I blogged my way though last year's journey, starting here. I thought it might be worth sharing what I did this time around as the changes resulted from my reflections the first time through the course.
The one big change was doing more quadratics earlier in the course. About half the course is quadratics so I tried to devote about half of each cycle to quadratics. We factored starting in cycle 1; the rationale being that factoring doesn't always stick so multiple exposures to it (and lots of practice) should help students better retain how to factor.
Cycle 1:
Cycle 2:
Cycle 3:
Not-really-a-cycle Cycle 4:
We managed to finish the content on December 22 so when we returned from the break there was a sufficient amount of time to review each strand and have an optional test for each strand. These tests covered 9 of the 10 curriculum expectations and each expectation was optional. Each student could choose which expectation they wanted to show - some did none while others did all 9.
I modified some of the homework sets from last year, but continued to spiral the homework as well. I tailored it to include questions that I know many students needed to practice, but always kept it to one page.
I'm sure there were other differences that I cannot recall at the moment. If you have questions I would be happy to answer them in the comments.
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.
