What are the conditions that inspire teachers to take on problem based instruction?
This isn’t a story about how you can determine when a teacher — novice or experienced — may be interested in problem-based instruction. This isn’t even a story about why problem-based instruction is better than any other kind of math instruction. This is a story about fourth grade teacher Claire*, and her students. This is a story about a shift in instructional practice that allowed everyone to engage with new ideas. This is a story about how Claire explored issues of equity and identity in her classroom while also going deeper with the mathematics than in previous years.
It will be told in five parts.
This is part one: the beginning.
Subsequent parts will be published at 4:00pm EST for the rest of the week. On Tuesday, Wednesday, and Thursday, I will share experiences from the lessons, and on Friday I will share reflections.
So… let’s get started.
Fourth grade teacher Claire has been teaching at my school for a few years now. When I’ve visited her classroom, it’s clear to me that classroom culture matters to her. She’s been working to create more student-centered experiences, which includes multi-sensory experiences as well as helping students consolidate and synthesize their own learning.She thinks about the learning experience for the individual students in her classroom — making content accessible and also challenging. She enjoys facilitating classroom discussion, and she’s been working to incorporate discourse moves (e.g. from Talk Moves: turn & talk, asking another student to restate, asking students to critique the reasoning of others, etc.).
Claire is deeply concerned about issues around equity in her classroom (and in the school), and often initiates conversation about these issues. Claire is multi-racial, and feels comfortable discussing race with students and adults.
As we were starting up our partnership last spring, Claire was looking for a new structure for her math block, something to make the experience feel more cohesive while also addressing the needs of individual students. We talked a little about centers and workshop. I also floated the idea of a structure for problem-based learning — something consistent that would allow students to readily engage in sensemaking, and for Claire to focus on listening and responding to students. Claire was on board with trying it.
Here’s one problem-based lesson structure, from the Illustrative Mathematics K-12 curricula.
originally published on the Illustrative Mathematics blog – “Designing Coherent Learning Experiences K-12,” by Kristin Gray, May 8, 2019.
It is important to note that this is not the only lesson structure that allows for problem-based learning, but it’s a good one. This structure also did not feel like much of a stretch for Claire. She had already experimented with number sense warm ups, like Number Talks, and she believed in letting students wrestle with problems as often as possible. With that in place, it was time to talk about the mathematical content for the upcoming unit.
Next on deck for content: symmetry (CCSS 4.G.3)
The first step in planning out problem based structure is planning out the intended learning goals, and identifying quality tasks that will help us tell the story to get there. Claire and I arranged to meet together after school to discuss.
“There was a really hard problem on our state test a few years ago,” Claire told me. When reviewing the scores, she had been surprised to see that a question that her students struggled with had been about symmetry — a minor standard that her students had done well with in class .
Claire continued: “I could see that the greatest number of lines of symmetry is a circle, so the shape that’s the closest to the circle would be the one with the greatest number of lines of symmetry. But my students were used to cutting out shapes and folding them. They couldn’t cut out the items on the state test.”
“Cutting out and folding shapes is a great entry point,” I continued. “How can we help them build towards this idea that there are other features and attributes of a shape that can help us…”
A switch went off in my brain. In fourth grade, most of the geometry work centers on identifying attributes of figures and using these attributes to classify them. I was thrilled to see that the tasks available for free from Illustrative Mathematics.org matched this learning goal! (These tasks are from back before IM was writing coherent curriculum, when the main feature of the site was to illustrate the content standards. These tasks do not come from the upcoming IM K-5 Math curriculum.)
According to William McCallum, a lead author of the Common Core State Standards and president of Illustrative Mathematics:
Problem-based instruction means believing all students can solve problems on their own and giving them a chance to try.
– William McCallum, “What Is Problem Based Instruction?”
published on the Illustrative Mathematics blog on February 19, 2019
Thus, we were looking to find tasks that:
- Have multiple entry points and pathways to a solution
- Allow us to incorporate familiar instructional routines (e.g. notice/wonder) that promote structured discourse
- Help us to implement the “five practices for equity based instruction” from The Impact of Identity in K-8 Mathematics: Rethinking Equity-Based Practices by Julia Aguirre, Karen Mayfield-Ingram, Danny Martin (NCTM 2013)
- Going deep with mathematics
- Leveraging multiple mathematical competencies
- Affirming mathematics learners’ identities
- Challenging spaces of marginality
- Drawing on multiple resources of knowledge
Claire and I will share the sequence of lessons here — how we implemented the tasks, and how we started to think about equity in the classroom through the tasks. We’re at the start of our journey implementing problem-based learning in Claire’s classroom, and the start of our shared conversations about equity — and we’re excited to continue!
*In my blog, I use pseudonyms for all students, and most adults. ‘Claire’ helped choose her pseudonym.