Spiraling through the curriculum

Have you heard about Dan Meyer's 3 act approach to math education? The 3 act idea is not an exclusive idea to Dan.  There have been other three-part lesson concepts.  In Ontario, where I reside, the idea of a three-part lesson has been frequenting the professional learning community.  It has been backed by a lot of research.  I have continued to try this since I started teaching, and I have been finding a lot of success both on the front of understanding and engagement.  (Of course, the activities that I've tried are not perfect yet, but hopefully I'll continue to improve it!)

Two people in my school board had recently started structuring the activities differently (one of whom have been trying to blog occasionally).  They called it "spiraling through the curriculum.  The idea is that they would go through the curriculum entirely more than once.  Everything is activity driven.  Everything is student driven.  Mathematical concepts are not only natural consequences of the activities - the students want, need, and enjoy learning about them.  While there are similarities, note that this is not exactly the same as Jerome Bruner's concept of a "spiral curriculum."  Bruner's spiral curriculum involves continually returning to big ideas throughout the development of a student across the grade levels.  The type of spiraling that I am talking about is a bit different because topics, strands, and expectations are revisited repeatedly within the same course.  In a way, it's a tighter spiral.

In my mind, this type of spiraling is made possible due to the structure of our current curriculum where courses are driven by strands (like major topics) and overall expectations within each strand.  (Of course, I do not claim to know about how other countries in the world are structuring their curriculum.  Which is why I am eager to find out more about other countries like Singapore.)  Unfortunately not all teachers are teaching through expectations, big ideas, or activities just yet, but that's not a topic that I want to discuss at the moment.

Let me give you an example of spiraling.  Here are the strands and overall expectations in the Ontario (Canada) grade 10 applied curriculum:

The idea is that we would not introduce "topics."  Instead, we drive the classes through activities.  Activities would sometimes be short, and contained within a few classes.  Other times, the activities could span a week.  The concepts would come naturally out of the activities.  Every expectation is hit multiple times.  The first few activities may only scratch the surface (i.e. only the main concepts are introduced, and no formulas or specific calculation processes).  Then later on the activities become more extensive, because the students would have learned more about what they can do!

This upcoming year I plan on teaching classes completely through activities using the spiraling idea.  I imagine that the core of my classes are still the same (i.e. group-oriented, activity driven), but the difference would lie in how I structure the activities.  Assessment and evaluation would also be different, which would be an interesting task.  I have a lot of ideas for new assessment and evaluation methods which I am sure I will elaborate on in the future.

Note: The reason that I emphasized the differences between Bruner's spiral curriculum, and the spiraling that I plan on doing is because I do understand and recognize the debate around spiral curriculum and mastery curriculum.  The spiraling here addresses different aspects of what I want to achieve in the classroom.  In the future I will talk about portfolios for mathematical processes that I also plan on implementing this year.

Note 2: Another important distinction to make is that these 2 teachers are also promoting doing everything through these activities.  The chalk and talk portion is minimized, and exclusive to act 2 or consolidation.