I am very interested to hear more about how you or your district implements any intervention for mathematics.— Mark Chubb (@MarkChubb3) February 16, 2019

I would love to know your answers to some of the final reflection questions as well:https://t.co/iwhzqIvNsN#iteachmath #MTBoS #mathchat #satchat #elemmathchat

Mark asks some great questions about groupings, specifically focusing on issues of equity, identity, and experience vs achievement gaps. I would highly recommend going to read his post, where he details his recommendation for a progression between Tier 1 (all students), Tier 2 (small groups), and Tier 3 (individual students) instruction.

These are questions near and dear to my heart. My school, like many, has tried a variety of approaches to groupings over the years. As a school that targets gifted learners whose needs were not being met, we see huge ranges in students' experience in Math that make purely heterogeneous groupings challenging. However, as Mark points out, the danger of groupings, especially ones that are static, holistic, and that lead to diverging learning and opportunities, are manifold. This year, we have piloted a model in our 5th and 6th grade Math classes that has tried to walk the fine line between the benefits of some groupings, while trying to avoid some of the negative effects of groupings discussed above.

**Flexible groupings model**

Our model relies on the fact that for 5th and 6th grade, students have Math at one of two distinct times every day they meet. That means that there are several same grade Math classes scheduled at the same time. The other component of our schedule that makes flexible groupings easier is that these Math classes are happening in classrooms next to each other and two of the rooms share a retractable wall that can be moved out of the way to create a large shared space.

We started the year with all students who were taking Math at that time in the large shared space, working in random, heterogeneous groups that we mixed up every day. All three Math teachers for that grade were present so that students could get to know the entire teaching team and vice versa. The first unit for both of these grades focuses on Mathematical habits of mind so problems are rich and low-floor/high-ceiling and don't have specific content objectives. Students were able to work with a variety of peers and we were able to gather a great deal of data of how students approach new problems, collaborate and communicate, and write down and process their thinking. We then moved into content-based units, which all followed a similar pattern:

**Key features of our model -- student-facing**

- Students start each new unit in random, heterogeneous small groups within a large shared space with multiple teachers, working on open tasks that introduce some of the new concepts.
- At the same time, students complete a take-home pre-assessment that looks at their prerequisite knowledge, as well as knowledge of the concepts and skills to be taught in the upcoming unit.
- Teachers create new groupings based on the pre-assessment and observational data of students' learning strengths and needs.
- Students move into their new groups, which last for two-three weeks.
- There is some student choice built into each grouping - as we review and prepare for an assessment, students select what and how they would like to review and are regrouped based on this choice.
- Students are assessed on their understanding of content for this grouping cycle and are given feedback and opportunity for individual revision, intervention, and/or extensions.
- These unit assessments and pre-assessments are used to drive groupings for the next cycle.
- Most homework assignments are the same for all groups and are differentiated by giving students choice over which problems to work on.
- Students regularly reflect on their needs, choice of homework problems, and how they are working in different groupings and settings.
- Units that are more project-based (we have three large units like this during the year) are done entirely in heterogeneous groups.

**Key features of our model -- teacher-facing**

- Teachers who share a common pool of students use a shared spreadsheet to track observations/feedback on classwork, homework, assessments, and projects. This is really important in order to know how students are doing as they move through different groups and work with different teachers. We spend time as a team discussing what we think is important to include in our notes and what our notes reveal about different students' needs.
- Each grade level team meets twice per week to discuss lesson plans, how students will be grouped that week, students we are concerned or wondering about, how we're giving feedback, and all the other little things that need to be aligned when co-teaching.

**Benefits of flexible groupings**

Students and families have been really positive about this implementation. It has many of the benefits of both heterogeneous and homogeneous groupings and has ameliorated a lot of the issues we have seen in the past with groups forming a fixed mindset about their abilities and trajectory. Especially in our project-based units, we see students working productively with a greater variety of peers and having a better understanding of themselves as learners. It supports a philosophy of meeting students where they are and the idea that different students have different mathematical strengths and areas that need more support.

**Questions and next steps**

I would like to see more heterogeneous mixing within a unit rather than just at the start when the unit is being launched. There should be other opportunities for rich, low-floor high-ceiling tasks that many different students can access and work on together. At the same time, I would also like to see more differentiated materials used for intervention/re-teaching/practice. We currently give students access to a spreadsheet of practice problems and guided notes, but don't have fine-tuned intervention and reteaching strategies or problem sets. I would also like to see more spiral review built in to the curriculum so that students who are still working on concepts can continue with the rest of the grade, but continue to revisit material.

The biggest question that I have is whether this model can continue into the higher grades. In 7th and 8th grade, we have traditionally broken students up into two tracks that had different curricula and that resulted in different placement in high school math classes. Our high school math classes are not grouped or tracked, but students can start at different points in the sequence of classes, which is another way of trying to avoid homogeneous, fixed groups, but is very different and operates on the assumption that students of different grade levels can take Math together. This is really different from our middle school model, where the entire schedule for a student is driven by their grade level. I'm very curious to hear how others (both middle and high school) are solving this issue and whether anyone has been able to make flexible groupings work for higher grades.