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.
I am intrigued by the big-idea activity driven approach. I’m a bit intimidated by the lack of (apparent?) structure. My recent experiment (which I will blog about soon) with a flexible class environment for grade 10 applied was a modest success, but I still have some fear in moving away from clear learning goals reached on a clear schedule. Mary is in the midst of blogging her way spiraling through the grade 10 applied course, so reading through that may answer some of my questions.
2. Build peer communication through video creation
The “achievement chart” found in the mathematics curriculum documents and Growing Success describes criteria for balanced instruction and assessment. One criterion reads: “Communication for different audiences (e.g.,peers, teachers) and purposes (e.g., to present data, justify a solution, express a mathematical argument) in oral, visual, and written forms”
I see students communicate in many ways: visually with graphical representations, descriptively with words or symbols, and even occasionally orally. I see students communicate “for a variety of purposes.” However, when I pose a question or set a task I am the audience students have in mind as they respond. Chris Papalia and Lawrence DeMello suggest asking students to create instructional videos aimed at their peers. They find this helps to build depth of understanding as students describe mathematics with more detail and creativity than in work intended for a teacher audience.
3. If MATH is the aspirin, what is the headache?
Dan Meyer has three suggestions for encouraging kids to engage in challenging mathematics. They are not to sell math as relevant to the real world, future careers, or teen life. Instead, Dan advocates for creating controversy by asking questions to stir debate, reducing the “mathiness” early on by de-emphasizing precision and orienting lessons in a way that mathematics is received as a welcome relief to a difficult situation.
Our curriculum is filled with ideas and skills that had their inception in someone’s desire to make life easier or its patterns more understandable. One reason for lack of engagement from our students is that they don’t seem to have the pains that our curriculum concepts salve. Dan’s suggestion then is to identify the “headache” and create that headache in our students. For example, we can motivate the desire for specific graphing vocabulary by asking students to describe graphs and create the desire for efficient and accurate common language. This example is the same one that caught my attention at OAME last year, and which I actually used again just this week with my grade 10 applied class. Today’s talk was a good reminder to continue this same process through other topics too.
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