Wednesday, October 12, 2016
This year I am embarking on a new journey - I am working at a different school and have more math in my schedule than I have had since my first year of teaching. As a part of that journey our MHF 4U (Advanced Functions) course team is taking a crack at "spiralling" the course.
Over the summer I spent some time laying out the course to begin to plan. I started with the skeleton Overarching Learning Goals (OLGs) that were created last year for math to come up with OLGs for the course (I wrote about these skeleton OLGs here) so that I would have already wrapped my head around the overall themes of the course.
Then I created a new document to start the actual planning. I pulled the overall expectations (OEs) for the course and the front matter of the math curriculum (math processes (MP)) into the chart by strand and then created a new column where I put in only key words (content & skills) from those OEs and MP. From those words I looked for common themes in the skills/content that I noticed and colour coded them.
Through this process I noticed a major theme in recognizing characteristics of functions and making connections between representations of functions (numerical, graphical, and algebraic). This seemed to be the backbone of a large portion of the course so it made sense to make this into a group of expectations - and cycle 1 was born.
Here are images of that document (they are a work in progress, evolving as we work our way through the course):
Creating the other cycles became largely about noticing the layers involved in the course. I wanted to build the remainder of the course by adding on layers of difficulty, which would allow us to revisit the same concepts. You may have noticed that the second cycle adds on algebraic techniques but is still focused on the same things introduced in cycle 1. This is the purpose of spiralling - students are able to see the same things over multiple exposures to better build their understanding of the material.
Studies are showing that the use of spiralling techniques will help with long-term retention for learners. It is not necessarily about improved results within a particular course, but will help with the foundations moving forward for longer-term success. My hope is that this type of pedagogy can also help with engagement and mindset for learning in the mathematics classroom.
One of the ideas we added to this plan was to have students start and maintain a portfolio where they would put information as it is learned organized by type of function. We are also going to do part of our final 30% as a conference with students - so students have been told that maintaining their portfolio is to aid them with this conference at the end of the semester. The possibilities are exciting.