Mathematics coaches have the ability to transform the teaching and learning environments in schools. Research suggests that teachers need opportunities to reflect on their practice and to have knowledgeable, engaged colleagues who can be thought partners in their work. Our commitment focuses on equitable teaching practices that support ambitious learning and position students as capable of doing high-level mathematics. Coaches can work with teachers to practice listening with intention and to elevate students’ mathematical ideas.
In her book Coaching for Equity: Conversations That Change Practice, Elena Aguilar states that it’s important for coaches to “see inequities and know what to do about them.” Beliefs about who can learn mathematics and who should have access to important mathematical work can impact the ways in which we talk about and respond to our students’ participation in math class.
Advocate for Just Practices
It’s important to allow time to notice, identify, and then reflect on our own and systemic practices that position students as competent or not. We begin by considering the ways in which students and their mathematical understandings are described during discussions with colleagues. By asking the question “Do our statements empower or disempower students?” we provide space for considering how our language is contributing to or disrupting the development of positive identities.
Vignettes (such as the one below) are a powerful way for coaches to identify, unpack, and reflect on unjust beliefs and practices.
“My kids can’t”: A grade-level team meets to discuss how their students did on the last assessment. Although there is a protocol for looking at the student work, one teacher starts the discussion by saying, “My students don’t have the necessary skills to do the work, so I couldn’t use the curriculum this year. Instead, I can only give them procedural math work, so I use a computer-based program.”
Coaches can find vignettes from resources or personal experiences. We can create opportunities for teams of teachers to examine and understand beliefs and practices that prohibit students from engaging in ambitious work due to labels that underscore race, poverty, language, and status in general as barriers.
It’s important for coaches to reflect on and unpack hidden beliefs (such as “Families in poverty don’t care about math learning”) in statements they hear and consider why the speakers might carry those beliefs. Coaches and teachers can work in partnership to identify beliefs about students’ mathematical thinking and consider equity-based coaching and teaching methods. This work “requires [us] to reflect on [our] own identity, positions, and beliefs in regards to racist and sorting-based mechanisms.”
We’ve found that the following questions are effective for engaging in discussions with teachers:
- Where and when do you/we think you/we first got these ideas or beliefs?
- How has this belief evolved for you/me/us?
- How has this belief been challenged?
- How does this idea encourage student learning?
Questions like these prompt honest, collaborative conversations about beliefs. Together, teachers and coaches can reflect and develop responses and strategies that can positively impact students’ mathematical identities. Coaches can suggest equitable teaching practices such as having cognitively demanding tasks for everyone or assigning competence to students who are considered as having low status.
In her book Strength in Numbers: Collaborative Learning in Secondary Mathematics, Ilana Horn defines status as “the perception of students’ academic ability and social desirability.” When coaches work with teachers to acknowledge students’ ideas, they disrupt status issues and foster equal status interactions, and equitable participation can increase.
Examine Student Work From an Assets-Based Perspective
Looking at student work is a vehicle for ensuring just practices and elevating students’ mathematics. One of the most important things math coaches can do is use language that celebrates and builds upon students’ strengths—“He uses his fingers to decompose numbers when he gets stuck”—rather than focusing on deficits—“He has no number sense.” Coaches can guide teachers to position students as capable, smart, and worthy of being understood.
Our comments and questions can focus on highlighting what is mathematically relevant and what teachers can use to forward a student’s or classroom’s mathematical understanding:
- I noticed student X posed a question that got at the heart of the lesson. I wonder how we could amplify that next time?
- What question could we ask your students that would reveal details about how they think?
- What kind of language should we use to ensure that all students are seen as capable?
Coaches work with teachers to examine student work, using protocols to guide us through the analysis process. We are explicit about grounding our comments in evidence by describing the work we see and using “low-inference comments.” Focusing on comments that are based on evidence and are not evaluative allows us to see student strengths and not make assumptions about gaps and ability.
When thinking about how to support a student, it’s important to identify the strengths in the student’s response, develop strategies for positioning the student as competent, and connect the student’s response to the mathematical objectives of the task. With those goals in mind, coaches and teachers can discuss how each student worked through the mathematics and the ways in which the whole class could learn from their classmates’ ideas.
The process of looking at student work includes the goal of better understanding the mathematics for ourselves and helps us to develop a lens that illuminates our students’ capabilities. The more coaches and teachers understand the depth and nuances of a task, the more we will be able to see and hear students’ ideas as important and connected. Rather than reviewing student work for grading purposes or to see how well they mimicked a particular method, we can use the opportunity to get to know our students and the ways in which they think, process, and learn.
When we operate from the belief that all students are capable of ambitious work, we will be better prepared to call on everyone to use equitable teaching practices and be advocates for change.