Mathematics coaches have the ability to transform the teaching and learning environments in schools. Research suggests thatteachers need opportunities to reflect on their practice并拥有知识渊博的，从事同事，他们可以在他们的工作中思考合作伙伴。我们的承诺重点介绍了支持雄心勃勃的学习和能够做高级别数学的学生的公平教学做法。教练可以与教师合作，练习倾听意图，提升学生的数学思想。
In her bookCoaching 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.
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 canfind vignettes from resources或个人经历。我们可以为教师团队创造机会，以检查和理解禁止学生因强调竞争，贫困，语言和地位的标签而禁止学生从事雄心勃勃的工作的信仰和做法。
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。“
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 bookStrength in Numbers: Collaborative Learning in Secondary Mathematics, Ilana Horn defines status as “theperception学生的学术能力和社会责任。“当教练与教师一起承认学生的想法时，他们扰乱状态问题并促进平等地位互动，并且公平参与可以增加。
Examine Student Work From an Assets-Based Perspective
看着学生工作是一种努力确保实践和提升学生数学的车辆。数学教练可以做的最重要的事情之一是使用庆祝和建立在学生的优势上的语言 - “他使用手指在被困” - 他陷入困境时分解数字，而不是关注赤字 - “他没有数字意识。”教练可以指导教师将学生定位为能力，聪明，值得理解。
- 我注意到学生X构成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?
教练与教师一起审视学生工作，using protocols to guide我们通过分析过程。我们通过描述我们看到和使用“低投票评论”的工作来彻底接地我们的评论。专注于基于证据的评论，而不是评估允许我们看到学生的优势，而不是对差距和能力做出假设。
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.