Over the past year I have had a number of opportunities to work with teachers who have been using Investigations for many years but are new to Investigations 3. Keith’s blog about “the size of the chairs” and respecting “the knowledge and experiences brought to the learning situation” struck a chord with me. It doesn’t matter the age of the learners, my beliefs about how people learn best is the same. I am, however, thinking a lot about the best way to facilitate professional development with teachers who have extensive experience with Investigations. My instincts are that I should “go deeper,” but sometimes I’m not sure what that should look like. What have I learned over the past year, doing professional development with a variety of groups of teachers at a variety of grade-levels, all of whom have had quite bit of experience with Investigations? The examples below reflect how my thinking — and what I did with teachers — evolved over the year.
One thing I noticed about myself as I began this work, was that I packed a lot into my sessions. In much the same way teachers feel pressure to “cover” content, when facilitating a unit workshop, I tried to get to as much of the mathematics as possible in the unit we focused on. While I tried to dig deeper into the mathematics of the unit, participants were already pretty familiar with the activities we worked on, felt familiar with the math ideas, and knew how their students interacted with the curriculum. Looking back, I also realize that I mostly asked questions that I thought I already knew the answers to. While I tried to dig deeper — into the math of the activities and into student understanding — maybe I didn’t dig deep enough or maybe, because the participants felt they knew the content of the unit well, they didn’t recognize it. I think none of us felt very satisfied.
This experience led me to think differently as I planned and led a session on fractions with 3rd grade teachers. We began by reading a Teacher Note about making meaning for fractions, and then used the information about the mathematics to discuss what that looks like in a classroom of 8 and 9 years olds. The teachers and I each shared stories that either showed evidence of students making sense of fractions or revealed misunderstandings students had. We then spent some time looking at how students would work with fractions on a number line, a piece of new content in Investigations 3. I also planned a significant chunk of time for participants to discuss how students might engage with this work based on their experience. The teachers’ thoughts brought up new ideas for me, about how working with fractions on a number line might be different for students than working with an area model. While this session was still pretty packed, I felt that it was more focused on building on the teachers’ experiences with 3rd graders, fractions, and the Investigations curriculum.
Planning a session with Keith Cochran, for a group of fifth grade teachers who wanted to discuss the U.S. standard algorithm for multiplication, pushed me even further. After much discussion, Keith and I planned nearly a whole hour on the multiplication algorithm! We began the session by talking some about how the algorithm is approached in Investigations 3. Then, together with the teachers, we looked at a piece of work in which a student made some mistakes in using the algorithm. We discussed what was challenging about solving multiplication problems with 3-digit numbers (or larger!) using the algorithm or, really, any method at all. Mostly, I listened to what the teachers had to say about their experience teaching the multiplication algorithm in the classroom. This conversation, combined with what I already know about multiplication and the algorithm, made me think about multiplication with larger numbers and about the algorithm in new ways. (Keith and I are hoping to write a blog about our ponderings on the U.S. algorithm for multiplication with larger numbers in the fall. Stay tuned!) And I think the teachers found it a useful conversation. It felt like a group of people using their varied experience and expertise to learn from each other.
So, as I head into the summer season of leading professional development, I am trying to keep what I have learned this past year at the forefront of my mind: make clear my respect for teachers’ experience and build off of it; pack less into a session and discuss more; ask questions that I don’t have the answers to; be curious about and leave plenty of space for teachers’ voices, ideas, and experiences; expect to help teachers move forward in their learning but also expect to learn new things myself. My goal is to continue to dig deeper. Not just with the math in the sessions I lead, but also with my own learning, as a facilitator of professional development.