Keisha has been a math coach for three years and is looking forward to the new school year. She is excited about working with the teachers she has been mentoring as well as building relationships with the new teachers. She wants to make sure that coaching gets off to a good start. In reflecting on her past coaching work, she realizes there were times when she did too much of the talking (and the thinking?) and times when the focus of the coaching conversations was not on issues central to student learning. She wants this year to be different and wonders how to make a shift in both the focus and engagement of her coach-teacher conversations.
Can you relate to how Keisha is feeling? Both issues that she has identified are ones that most coaches struggle with at some point: How do you get teachers to do more of the talking and thinking and, at that same time, ensure that you are talking about issues that matters most in terms of student learning?
When I have counseled coaches who are working with teachers on improving mathematics discussions in classroom, I have encouraged them to focus on the 19 challenges that teachers face in implementing the Five Practices for Orchestrating Productive Mathematics Discussions, 2e (Smith & Stein, 2018). These challenges, described in The Five Practices in Practice series (Smith & Sherin, 2019) identify aspects of orchestrating discussions that teachers have struggled with and specify what the challenge entails. Take for example the challenges associated with Practice 0 (the foundation of the Five Practices), specifying learning goals and choosing a high-level task that aligns with those goals. The four challenges associate with this practice, along with a description of the challenge, are shown in Figure 1.
Figure 1. The challenges associated with Practice 0.
| GOALS AND TASKS | CHALLENGES | DESCRIPTION |
| 1. Identifying learning goals | Goal needs to focus on what students will learn as a result of engaging in the task, not on what students will do. Clarity on goals sets the stage for everything else. | |
| 2. Identifying a doing-mathematics task | While doing-mathematics tasks provide the greatest opportunities for student learning, they are not readily available in some textbooks. Teachers may need to adapt an existing task, find a task in another resource, or create a task. | |
| 3. Ensuring alignment between task and goals | Even with learning goals specified, teachers may select a task that does not allow students to make progress on those particular goals. | |
| 4. Launching a task to ensure student access | Teachers need to provide access to the context and the mathematics in the launch but not so much that the mathematical demands are reduced and key ideas are given away. |
As a coach you can begin by providing teachers with a list of all 19 challenges, asking them to identify a few that they have struggled with and to briefly explain how the challenge has played out in their own classroom, and explaining that these challenges will be the focus of their conversations. In so doing, you as a coach have taken a big step in changing the nature of the conversations you will have with teachers.
Framing coaching around teacher-identified challenges has several advantages:
- When focused on challenges (particularly these challenges if productive mathematics discussion is your goal), you ensure your coaching conversations will focus on things that matters most to supporting the learning of each and every student.
- Having teachers identify specific challenges that they face gives them a key role in determining the focus of their time spent with you, allowing them to feel empowered, invested, and committed to instructional improvement.
- Organizing your work around challenges allows for deeper and more specific coaching conversations and can be powerful catalysts for teacher learning.
The teacher-identified challenges provide the grist for what coaches and teachers will talk about during the pre- and post- lesson conferences that bookend the teaching of a lesson.
The goal of these conversations is to help teachers think deeply about their practices and make decisions to ensure that all students have the opportunity to learn mathematics with understanding through participating in rich mathematical discussions.
But the question still remains regarding how to get teachers to do more of the thinking and talking during these conferences. One way to accomplish this is to use the inquiry routine, which is comprised of 4 moves:
- invite
- rehearse
- suggest
- generalize
The first move is Invite the teacher to explain what they might do (in a pre-lesson conference) or could have done (in a post-lesson conference) to resolve a specific challenge that is under discussion. The second move is to Rehearse how a teaching action would play out in the classroom by considering possible student responses or reactions. The third coaching move is to Suggest specific ideas for a teacher’s consideration. If the teacher is not making any progress towards a resolution of the challenge, you can make suggestions to help move the teacher forward and ask the teacher to consider the impact of the suggestion on students. The final move is to Generalize specific actions that a teacher decides to use in one lesson to deal with a challenge so that they can consider how the actions can apply across different lessons.
Coach Jesse, who has used in inquiry routine in her work, reflects on what she sees as the value of these approach:
First, it brings the teacher’s voice into the conversation. I get the teacher’s ideas out there, which is helpful for me because then I’m not making assumptions about what they understand or don’t understand. Then, I think the rehearse [move] supports teachers in thinking about students. So, “What might we ask this student?” or “What might the student do, if we did this?” I think it gives teachers some practice. I think the suggest [move] is useful when the teacher’s not sure, “Here are some things to try so you’re not just struggling to figure it out.” Then the generalization… “Why is this important in general?” I think helps teachers carry a practice from lesson to lesson and not see it specific only to this particular lesson. (Smith, Yurekli, & Stein, 2025, p.103)
Can the challenges and inquiry routine help you in your coaching? You can learn about these strategies and more in our new book Coaching the 5 Practices: Supporting Mathematics Teachers in Orchestrating Productive Discussions, co-authored with Bilge Yurekli and Mary Kay Stein. Think about a conversation regarding a mathematics lesson that you had with one of your teachers. This conversation could have been about planning for an upcoming lesson or a discussion on a completed lesson. Reflect on the conversation. Do you think you built the conversation on the teacher’s thinking? Did the conversation stay focused on supporting student learning?
