1.Spiraling through curriculum
The structure of most mathematics courses (or even I suspect most courses) mirrors its curriculum document. The curriculum divides the course into three or four strands, each with three or four overall expectations that are elaborated on with a half dozen or so specific expectations. Similarly, long range plans usually divide the course into a half dozen units derived from the overall expectations which are subdivided into lessons to sequentially address each of the skills required. A linear document (the curriculum) is translated to a linear teaching plan, and most of the time the system works to deliver prepared students to the next grade so long as they don’t fall off the linear skills assembly line (... or if they do so long as we can pick them up and put them back on quickly enough...)
In their tiny five minute long IGNITE talks both Mary Bourassa and Alex Overwijk referred to an alternative approach. When “spiraling” through the curriculum the linear planning model is gone. Instead, students wind their way through activities and lessons that span the curriculum. All of the overall expectations might be addressed within the first six weeks of a course, and then revisited in more depth as the course circles back again and again.
