Productive Struggle in Mathematics
By Sarah Burns, UChicago STEM Education Curriculum Developer
“Productive struggle” is a phrase we hear a lot in the math world these days: kids should be doing it and teachers should be facilitating it. This idea of learning from challenge — from not knowing exactly how to solve a problem, from trying an approach that doesn’t ultimately work, and from collaborating with others to figure out what to do next — is one we have always embraced in our work. But we know that it is challenging to provide opportunities for students to “productively struggle” and to support students so that struggle remains productive, rather than becoming unproductive and demoralizing. (Yes, there is such a thing as “unproductive struggle”!) This is especially true in classrooms with limited time and wide-ranging student skill levels (virtually all classrooms we engage with), and in a larger educational context that often seems to value correct answers and speed over slower learning from exploration and mistakes.
In our work with teachers and students, we have found that using thoughtful, purposeful questioning and promoting rich math conversations are powerful strategies for promoting productive struggle. We have also found that collaborating with a colleague — a coach, fellow teacher, mentor, or administrator — to plan, observe, and offer feedback on lessons is an effective way to develop these questioning and discourse strategies. There are three natural points at which the assistance of a colleague can be particularly helpful, especially for lessons that center on high cognitive demand tasks designed to promote productive struggle.
Before the lesson
While preparing to teach the lesson, it is helpful to consider both the task and teacher expectations through the lens of supporting productive struggle. Questions a teacher might discuss with a colleague before teaching the lesson include:
- What are the mathematical goals of the lesson? How does this task support those goals and allow opportunities for students to engage with productive struggle?
- What are different ways your students might approach the task? What background knowledge do that have? What might they struggle with?
- How will you ensure that students understand the task without suggesting a particular approach or otherwise over-scaffolding?
- What questions might you ask students who struggle? What other supports can you give them without reducing cognitive demand?
- How will you provide opportunities for students to share their thinking and explain or justify their ideas?
During the lesson
Having a second set of eyes in the room to observe gives teachers an opportunity to get timely feedback about their own teaching practices and about their students’ learning. It’s important that both the teacher and the collaborator view this not as an evaluation, but as an opportunity to grow professionally. During the lesson, the colleague can take notes about the issues that were discussed during the planning session, with a focus on how the teacher supported productive struggle and how students responded. Some specific things that a colleague might note during the lesson include:
- Which students seem productively engaged in the task? Which seem less engaged? How can you tell?
- How does the teacher respond to students when they struggle? To those who finish quickly or easily?
- What hints or modifications are offered? To whom? Why?
- How does the teacher encourage student-to-student discussion?
- What questions does the teacher ask, and of whom?
After the lesson
Just as we hope students’ reflections on their work promote their growth as learners, debriefing a lesson after its implementation affords teachers the opportunity to reflect on how well they promoted and supported productive struggle. A post-lesson discussion can include questions like:
- Which students engaged in productive struggle during this lesson? What strategies and behaviors did they exhibit?
- Which students did not engage in productive struggle? What behaviors did they exhibit?
- What modifications did you make to support your students? Why did you make those modifications?
- If you could implement the task again, what would you do differently? What would you keep the same? Why?
There are many tools that can support teachers and their colleagues as they work together to plan, observe, and debrief lessons that focus on engaging students in productive struggle. You can find one of our favorites here. Our experience is that tools like these can help both teachers and their collaborators focus their conversations, promote collective reflection, and support professional growth.
Sarah Burns, with Ellen Dairyko, Andy Isaacs, and Debbie Leslie
Sarah, Ellen, Andy, and Debbie all work at UChicago STEM Education, a center devoted to research and development that aims to support high quality STEM instruction and learning for all students. Sarah can be reached at firstname.lastname@example.org