Does problem-based learning mean students need to forget everything they knew about how to act in math class?
By Max Ray-Riek
As a teacher, and then as a coach and teacher-educator, I’ve been thinking for a long time about the shifts teachers need to make when using a problem-based curriculum like the IM Math curricula. Recently, though, I’ve gotten to be in classrooms not as a coach or a teacher, but just to observe. Sitting with the students, experiencing math class from their perspective, I’ve been reflecting a lot on the demands placed on them as learners in a problem-based setting.
There are lots of ways to organize a math class, and lots of ways to describe that organization. One way that math classes sometimes look is often called “Gradual Release of Responsibility” or I Do-We Do-You Do.
As I sat in classrooms, I started asking myself, “What are the messages about when and how to participate that come with this kind of teaching?”
- Wait to participate until you know what to do.
- The teacher starts the work by explaining, the student starts by waiting and listening.
- Wait for the teacher to evaluate or restate other students’ ideas, in case they’re wrong.
- Another student’s statement is valuable if they understood what the teacher said better than you did.
- Don’t answer unless you think you know what you’re supposed to say or do.
These aren’t the messages teachers are explicitly telling kids. Teachers can value mistakes, prompt kids to ask questions and engage in rough-draft thinking, and encourage kids to try problems even when they’re not sure what to do. But if every learning opportunity starts—by design of the curriculum—with all the information kids need to get started if they just listen and understand it the first time they hear it, kids notice what it takes to be “good” at math. They notice that some people seem to always know how to get started, seem to always know the answer that doesn’t get questioned or corrected, and seem to always be able to explain the method just like the teacher does and so get called on to help a friend. They learn that while they might make mistakes, not everyone does and those people seem to get good grades and get looked up to in math.
What happens when kids who’ve been socialized in this kind of classroom come into a math class that uses a problem-based approach? The IM curriculum is designed for conversations that look more like this:
The expectation is that students will be given problems that they have enough mathematical knowledge to approach, but that they will need to play, try ideas, and pursue dead-ends as they figure out how to make progress. This process of playing and persevering requires things like sharing ideas that might be wrong, listening to peers’ ideas and evaluating them for yourself, and comparing your ideas to other people’s. How do students who’ve been socialized for almost the exact opposite ways of behaving get comfortable in a problem-based class, and how can the teacher support kids to try on new ways of behaving . . . ways that might initially involve a lot more social risks?
In the IM curriculum, we put a lot of work into three areas that seem to help students shift how they participate in math class:
- an invitation to the mathematics
- concrete representations
- explicit classroom norms
In the next three posts in this series, I’ll dive into each of these topics and share a little bit more about how they can help students make the transition from other ways of behaving in math class, to becoming part of a problem-solving community of learners.
I’d invite you to start by getting curious about the hidden messages students have learned, up until now, about how to behave in math class. Try noticing (or asking your students about) whether they believe:
- that it’s better to raise your hand if you know what to do than if you’re not sure yet
- that what the teacher says is more important to listen to than what other students say
- that if you’re good at math, you’ll already know how to do all the problems when the teacher tells you to begin
Then you might wonder about whether those student beliefs will serve them well in a problem-based curriculum, in which they learn by trying problems collaboratively and comparing their ideas with their peers.
Max Ray-Riek is the Director of 6-12 Professional Development at Illustrative Mathematics and worked as a writer on the high school curriculum. Before coming to Illustrative Mathematics, Max worked for The Math Forum, focusing on fostering problem solving and making student thinking the center of math class. He is the lead author of Powerful Problem Solving: Activities for Sense Making with the Math Practices. Max is a former secondary mathematics teacher (and before that, preschool teacher) who finds the art and discipline of valuing each student’s ideas, and supporting all students to see themselves as people who can listen, connect, and act mathematically, to be the hardest, most rewarding, and most important work in the world. Max lives in Philadelphia with his wife, with whom he fosters puppies who will grow up to be trained to be service dogs.