Voices from the #PrincipalProject Community

4 instructional coaching strategies for math teams


As a math coach and education administrator at the county level, I collaborate with leaders and teachers to support mathematics instruction across 23 districts. Every school has its own unique culture, students and staff, and when the collaboration with a school leader begins, I build their instructional leadership priorities into our plans (such as supporting English language learners, empowering students with disabilities or promoting culturally responsive teaching). But there’s one key driver of student success that I always recommend school leaders prioritize as they plan instructional coaching for their team: Prioritize students’ identity and agency in the mathematics class.

We adults may not always remember just how crucial confidence is to growth – if we hadn’t learned to see ourselves as achievers, we might not have achieved in school, and we might not have become educational leaders! That’s why, to empower students to master new math ideas, we have to first empower them to see themselves as confident, capable doers of mathematics. The math educators I support want to empower every student to see themselves as a “math person,” but they don’t always feel equipped to center student agency and identity in the way they teach math. Because of this, I work with teachers on developing instructional plans that focus on the students’ voices and strengths, as well as building up teachers’ instructional confidence. I have 4 recommendations I give to leaders and their teams:


1. Building lessons on student strengths

The first step to take when supporting a teacher’s math instruction is to focus on and leverage student strengths. As Rachel Lambert says: “Shift from planning for a hypothetical middle to the actual margins.” The teacher and I will sit down with the class roster, select a few focal students and I’ll ask, “What lessons, activities and roles have you seen each of these students connect with?” If there are students we don’t know enough about, we’ll get intentional about observing those students’ engagement during class or set up “empathy interviews” to ask them to share a little more about themselves.

Next, the teacher and I will design a lesson or an activity that will amplify students’ strengths. If we learn that one student loves decision-making opportunities, I might ask, “How can we invite this student to make decisions in a math context – and demonstrate their decision-making ability for their peers?” Because when we enable the student to experience math from a position of strength, in a leadership role, we boost both their math identity and agency, as well as their math understanding. We then replicate that experience by building more decision-making activities into lesson plans, and we create another opportunity to amplify the strengths of the next student, and the next. Ultimately, by building lessons around our students’ assets, we create a classroom culture where every student is working from their strengths, serving as a resource for their classmates and owning their own learning. This culture encourages students to see themselves and each other as mathematicians.


2. Folding in formative assessments

If I’m coaching teachers to develop a deeper understanding of their students’ progress, I always recommend building in more opportunities to simply hear from students. For example, we might plan a formative assessment activity that invites students to discuss a recent math experience in groups. As the teacher drafts guiding questions for the group or comes up with options for students to share their knowledge, we might use this question to inform our work: How will this activity move students to think independently and speak confidently about math? We can take this opportunity to leverage students’ strengths and promote their leadership, as discussed above. For example, we might decide to assign group roles. When we take our plans into the classroom, we might empower one student to lead the discussion, another to record the key points, a third to present a summary to the class and a fourth to draw the concepts on the board. Each student uses their strengths to contribute to the class’s learning, and together, their efforts produce an up-to-the-minute measure of their growth.


3. Promoting teacher confidence

Centering math lessons on student strengths and student voices might seem like a simple shift for a teacher to make, but it often doesn’t feel simple – so it’s crucial for a coach to foster confidence and provide support. Centering students’ strengths and allowing for student discourse might create a sense of “losing control.” It’s natural for educators to feel uncomfortable about “losing control” in the classroom, especially if they’re feeling concerned about covering all the material, meeting milestones for student progress or equipping students to demonstrate mastery during summative assessment periods. That’s why, as I co-plan new activities and embedded formative assessments with teachers, we plan in time for me to co-teach. We might decide I’ll teach the first part of a lesson, and they’ll walk around, observe and listen to students, and interject as needed based on the evidence being collected. Or we’ll move between student groups and observe focal students. Afterward, we always plan in time to review and reflect. When a teacher is trying a new strategy, and students are responding in different ways at different paces, and the noise level is rising, it can feel stressful. It’s important to create space for the educator to process their experience and brainstorm any shifts that could make them feel more comfortable next time. And it’s significant to point out the moments of engagement, agency and progress that students demonstrated in response to these new strategies. Those successes may seem small, but they’re a meaningful reflection of the students’ growth and success – so they’re a meaningful reflection of the teacher’s impact.


4. Encouraging teacher collaboration

Collaborative, relational learning can do so much to sustain growth for teachers, just as it can for students. For example, I recommend Lesson Study as a collaborative PD tool for teachers. It’s a powerful way for a math team to learn together, because it invites them to set their own growth criteria: Teachers choose an aspect of their students’ learning experience to study, research teaching strategies, bring those strategies into their classrooms and observe how their students respond. When teachers collaborate on work that’s meaningful to them, they develop new expertise and energy that can support their work in the classroom – and they develop leadership skills that can support schoolwide growth goals. As teacher-leaders, they can model collaborative growth for colleagues, inform instructional leadership plans and mentor new educators. That’s why instructional coaching can do so much to promote a strong math team in the long term: By empowering teachers to take risks, build collaborations and grow their expertise, we empower them to invest in their students and their school communities.


Every collaboration with a math team will look different, but our goal is always to develop the student-centric strategies (and instructional confidence) that teachers need to provide students with more and more agency in math class. As we promote students’ confidence, we promote their ability to master new math learning. Ultimately, our approach encourages students to see themselves as mathematicians – and to leverage their mathematical knowledge to shape their worlds.

Here are a few examples of the resources I recommend to teachers and leaders:

An example of an empathy interview with a student (click here for my template):


Resources for encouraging your team to explore Lesson Study:
Lesson Study Team Guides and Resources, via the California Action Network for Mathematics Excellence and Equity (CANMEE)

Collaborative Lesson Research, via Lesson Study Alliance


Lesson Study Resources via The Lesson Study Group at Mills College:


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About the Author

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Diana Ceja

Alexis Knox-Miller is the District 11 Director of Equity and Inclusion in Colorado Springs, CO. Follow her on Twitter @theelexflex Diana Ceja is the administrator of the Riverside County Office of Education Instructional Services in Riverside, CA. Follow her on Twitter @@imathination