The past few years have been an exciting time in math instruction. Research on brain plasticity and mindset have caused a shift in the idea of what it means to know and do mathematics. Consequently, our district has seen a downhill trend in standardized test scores in mathematics over the last few years. This has forced us, as educators, to take an intentional look at our teaching practices.
The problems students are being asked to solve require interpretation, analysis, and resilience. We knew we had to change our instructional practice to reflect the rigor of the tasks they would be asked to solve. Yes, on the test, but ultimately as future employees and citizens of our world.
Gone are the days of I do, we do, you do. That model never allowed for enduring understanding of conceptual mathematics. It was designed to promote recall and computation and it succeeded in that. However, we now know that we are preparing students for a world that no longer requires such skills. Our charge is to develop thinkers. Problem solvers. Grit.
This offers a docatomy for many educators, one that faces off the way they were taught to teach and what research now shows as best practice.
As we began our pilot of IM K-5, our teachers were struggling with that very issue. For years, we had implemented a workshop model that followed the I do, we do, you do model and used ability grouping to differentiate content for students. Based on recent research, we had modified that model to also include whole class problem solving days, but we had lots of work to do in supporting teachers in their new roles as facilitators.
The IM curriculum was designed for much of the time to be spent with students working in heterogeneous collaborative groups and partnerships while the teacher monitored and facilitated discussions. When the pilot teachers met after implementing a few lessons in Unit 1, they discussed their struggle with what differentiation looked like in this model.
It became clear that we had had a very narrow vision of differentiation. This required us to look at differentiation in a new light; one that empowered students to be the mathematical experts in the room.
We began looking deeper at The 5 Practices for Orchestrating Mathematical Discussions to begin that shift.
Through the careful planning and monitoring of student interactions, teachers could utilize student work to connect strategies to support students at each level of their learning.
Illustrative Mathematics allowed this to become common practice due to the structure of the lessons and the ample opportunities for formative assessment.
IM has structured the teacher support materials to offer possible student solutions for each of the warm ups and activities as a means for teachers to begin planning for what strategies they might want to call attention to. This was an invaluable support for teachers as many might not have been able to generate all possible solutions on their own.
Monitor, Select, Sequence, Connect
During the warm up and activities, students are encouraged to approach the concept in multiple ways. The teacher monitors by watching students approach the problem and recording strategies.
The teacher can then select which strategies she/he feels need to be highlighted based on instructional goals. These goals might differ from day to day.
For instance, one day the teacher might choose student work to highlight because it provides other students a structure for keeping track of their work.
For example, in a first grade classroom where students are working on combining two collections, many students might be recreating the collections by drawing strawberries when they are part of the scenario. A teacher might have a student show a piece of work that has drawn a literal interpretation of strawberries and then after show a piece of work that a student drew circles to represent strawberries (Sequence). She/he might ask connecting questions like, “what is the same about these two representations? What is different? Which do you think was more efficient?” (Connect)
Or in the same scenario, a student has drawn random circles on the paper while another student draws five on top and three on the bottom to show the two collections. Or perhaps, a student used different colors for the two collections. A teacher might say, “show me the five in the first collection. How about the three in the second collection. How do I know which collection I am looking at? How does that support me in finding a solution?”
One of the greatest struggles voiced by teachers in shifting to a role of facilitator is having the right questions to ask. We use this monitoring sheet that includes a place to note possible questions you might ask to connect strategies or dig deeper into student understanding.
I truly believe that problem based resources, like Illustrative Mathematics, have the potential to not only support students in developing enduring understanding of mathematical ideas, but also to develop the capacity of teachers in becoming expert facilitators of student learning.