First, some background.

I have been incorporating the essential elements of a Thinking Classroom in all of my Math classes for the past few years, but most notably in my high school class, where the focus on content and pressures to teach to the test are greater. This year, just like last, I had students read and reflect on Thinking Classrooms and we discussed why most of our time together is spent working on problems in random groups, sharing out ideas and conclusions, and using these to synthesize and summarize learning from the bottom up rather than top down via teacher-led instruction. Students initially seemed bought in and supportive of this type of classroom environment. We set up class norms and discussed the use of group roles, how to step up/step back in group environments, and how to be a skeptical peer and give respectful pushback on ideas.

Several weeks into the semester, however, I started noticing a troubling pattern - some students were disengaging from their collaborative work and seemed very hesitant in sharing their thinking within either small groups or the larger class. Then, I started to hear two different complaints from students - some were feeling that their work during class was unproductive because their groups moved too fast and they were feeling increasingly anxious and uncertain about their mathematical understanding and abilities. They were feeling unprepared to do problems independently on homework assignments or assessments and wanted more teacher guidance and structure, as well as more opportunities to go at their own pace and understand ideas more fully. Other students raised the opposite issue - they felt that the pace of the class was too slow, that they were doing too many problems that they already knew how to do or could figure out quickly and wanted more challenging and deeper problems, both during class and on homework assignments.

**When group work goes wrong:**

In reflecting on these issues and why they were coming up this year, I realized that we had actually made quite a large change to the Math program without making any changes to our curriculum or pedagogy. This was the first year that we had decided to mix all grades taking a particular Math course - Math had been the only discipline at the Upper School in which students were separated out by grade level. In the past, 9th and 10th graders taking Math 3 (students who had accelerated the normal sequence) were in different sections from 11th graders taking the class (students who were on grade level in terms of their progress through the sequence). This year really was different in terms of prior math experiences, expectations, and desire for challenge/acceleration for students in the same class and the normal groupwork structures were not sufficient to bring together students with such varying backgrounds and approaches.

My next step was to look for feedback from colleagues as well as the Twitter math teacher community. Some suggestions that I implemented that seemed to make a difference:

- Taking a break from random groups to help students regain their trust that the class would meet their needs; doing some work in pairs designed to foster productive collaboration; allowing students choice as to who to work with while also asking them to work with different students at times; being explicit when the goal of a task was to build collaborative skills
- Structuring activities so there was time at the start for individual exploration before asking students to share their thinking with others thus giving more processing time for students who worked more slowly; circulating and helping some students get started; building more optional challenge into tasks for students who worked very quickly or who had already had prior experience with a topic; creating tasks that could be approached with a greater variety of methods and building more writing into tasks so that different ways of thinking mathematically could be valued
- Meeting students where they were to regain trust and buy-in; this included at times splitting the class into two groups (students chose which group to join) - a more free-form exploratory group with more open and challenging problems and a more structured group where students would get some problems to activate prior knowledge and smaller, more concrete problems that would build over time to greater generalization and abstraction and more teacher guidance and reassurance that they were on the right track
- Noticing struggling students' successes and highlighting them publicly; selecting which students would share their thinking to make sure that different voices could be heard over time
- Make sure to leave time for synthesis and practice problems (at different levels) during class - this helped address student concerns that they were leaving class with lots of questions and feeling unsettled about the concepts they had explored that day
- Giving students more feedback during class about their understanding of a topic rather than relying more heavily on groupwork and self-assessment for students to know how they were doing and what might be helpful next steps
- Providing more problems at different levels and helping students navigate which problems might be more helpful for them to do during/after a particular lesson - here is an example of a tiered homework problem set.
- Providing more textbook resources - explicitly linking textbook sections to problem sets for students who wanted more references and examples

We are considering sorting students for next semester by grade level to decrease the heterogeneity of classes - while these strategies have alleviated the issues significantly, it does seem that productive collaboration and exploration is challenged when students in a class are so spread out. Despite these strategies, for example, it usually doesn't make sense for students who have worked quickly and deeply and have figured out challenging extensions to share their ideas with the whole class, most of whom have not even tried these problems. As a result, the class sometimes lacks cohesion and feeling like a true community. Additionally, the amount of work required to run a class with this much differentiation is really, really high. I'm essentially designing at least two different classes, creating both lesson plans and homework assignments that can reach the full spread of student interest and background, and giving individual and frequent feedback to students or small groups of students into which the class has fragmented. This is not really tenable for the whole year given my other preps and teaching responsibilities. However, breaking up students by grade level seems to run counter to our values of equitable access to challenging mathematics for all students and means that Math classes are essentially different from all other classes at the Upper School.

I would welcome any feedback or suggestions that others have around this issue - what strategies have worked for you in working with very heterogeneous groups?

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