I’m reading Jo Boaler’s most recent book, Mathematical Mindsets. She presents a compelling vision of what mathematics teaching can be, and I’m learning a great deal. At the same time, I wonder about the ways that Boaler talks about change in mathematics classrooms. One passage struck me.
In a chapter on tracking, Boaler describes a school that made two of the changes she recommends: de-tracking classes, and providing students with low floor, high ceiling tasks:
At the end of the first week of teaching the new classes, grouped for a growth mindset, one teacher exclaimed in amazement that after he gave out one task, astudent who “would have been in the bottom group” was the first to solve it. Over time the teachers continued to be surprised and pleased by the different creative methods shown by different students from across the achievement range. The teachers were thrilled with how well students responded to the de-tracking and with how disciplinary issues, which they had feared would increase, disappeared almost overnight. This was interesting to me, as the teachers had been quite worried about de-tracking and whether the students would work well together. They discovered that when they gave open tasks, all students were interested, challenged, and supported. Over time the stduents they thought of as low-achieving started working at higher levels, and the classroom was not divided into students who could and students who could not; it was a place full of excited students learning together and helping each other (p. 117).
I worked at a school that de-tracked students, and where I tried to implement low floor, high ceiling tasks. I didn’t feel particularly successful. I had some idea of my goals, and I had some tools to move in that direction, but I didn’t have the skill to use those tools effectively and actually make a difference for students.
The narrative that Boaler provides here is important to validate these two practices, which I really believe in. But I think the narrative also sends a message that they are practices which can change a culture of mathematics alone. That’s not my experience. De-tracking students requires concerted effort and systems to ensure the success of previously low-achieving students and make sure they get the support they need. Low floor, high ceiling tasks require deliberate pedagogy to create spaces where students are willing to take risks, ideas are shared productively, and tasks are used as opportunities for instruction.
I’m being tough on Boaler here. It’s an excellent book, and she does outline strategies for making these ideas work. She is particularly articulate about structures for group work and valuing multiple dimensions of mathematical thinking. But she also offers a narrative that I think oversimplifies what it means to transform a culture of mathematics in a school. I’m interested in structural changes that alter the way mathematics is practices and perceived. I’m much more interested in thinking about the pedagogy that supports those structural changes, and how teachers can develop that pedagogy in a deliberate way to make sure they are supporting all students.