As a new school year begins, teachers and leaders are already planning intervention support for students who are not currently meeting grade-level math standards. Rather than defaulting to traditional remediation practices that have produced disappointing results and failed to position students for future success, let’s cultivate the learning habits our students need to engage in rigorous mathematics and take ownership of their math learning long after they’ve left our classrooms.
Part 1 of this three-part blog describes why it is essential to grow students’ mathematical habits of thinking alongside their math content knowledge. In Part 2 and continuing here in Part 3, we outline easy-to-implement strategies to cultivate empowering math habits in all students.
Part 3: Strategic Coaching for the Habits of Mathematically Powerful People
Each time you name a strength, you are validating your students’ abilities and communicating to them and those around them that they are capable mathematicians. In turn, students will generally be more open to you as you nudge them forward in their learning. And if you’re lucky you will start to notice a very specific type of smile after you name your students’ strengths. Although they are sometimes small and almost shy-looking smiles, you won’t want to miss them. These are the smiles of proud mathematicians. (Picha, 2022, p. 79)
Mathematical proficiency requires students to internalize the math practices or processes, known in many states as the Standards of Mathematical Practice. In Part 2 of this blog series, we shared the Habits of Mathematically Powerful People, a student-friendly version of the math practices from our book Power Up Your Math Community: A 10-Month Practice-Based Professional Learning Guide (Burwell & Chapman, 2024) (see Figure 1). We offered simple ideas for explicitly teaching students about each of these habits in intervention settings as well as in core instruction.
Figure 1. Habits of Mathematically Powerful People
Reprinted with permission from Burwell and Chapman, 2025, p. 19
Once students understand the math habits, we can help them internalize these important learning habits through strategic coaching. Lambert (2024) describes strategic coaching as one-on-one conferencing with a student that provides just-right, just-in-time scaffolding of their learning. Strategic coaching for the math habits is a form of “cognitive apprenticeship” (Safir & Dugan, p. 113) designed to help students learn how to be self-directed math learners. It is a partnership process that mentors students as they practice and strengthen the habits of mathematical thinking.
Three-Minute Coaching Conversations
Strategic coaching for the math practices needn’t be time-consuming. Teachers can interact with students as they engage in mathematics using a simple coaching protocol:
- Ask a question to elicit a student’s reflection related to their use of a math habit.
- Name a student’s strength related to the habit and state why that strength is important.
- Ask a question to solidify or extend the student’s learning related to the habit.
These brief conversations communicate to students that we see them as mathematical thinkers and expect them to take an active role in their math learning. They help students own and internalize the Habits of Mathematically Powerful People (see Table 1).
Table 1. Examples of Coaching Conversations in Support of the Math Practices
| I expect math to make sense. | Ask a question to elicit reflection. | Does this mathematical idea make sense? Why or why not? |
| Name a strength. | You’re noticing when a mathematical idea doesn’t make sense, which helps you to take charge of your learning. | |
| Ask a question to extend learning. | What are some things you can do when a mathematical idea doesn’t make sense to you? | |
| I enjoy challenging math problems. | Ask a question to elicit reflection. | What is challenging about this problem? How are you persevering through this challenge? |
| Name a strength. | You’re paying attention to your feelings as you work through a challenging problem, which helps you learn how to persevere. | |
| Ask a question to extend learning. | What are you learning about perseverance? | |
| I learn from math mistakes. | Ask a question to elicit reflection. | What did you learn from this mistake? |
| Name a strength. | You’re thinking about mistakes as a natural part of learning, which will help you learn better and faster. | |
| Ask a question to extend learning. | What advice would you give another student about making mistakes in math? | |
| I see myself as a mathematician. | Ask a question to elicit reflection. | What math habits are you using as you do this learning work? |
| Name a strength. | You’re noticing your math habits growing stronger and realizing these habits help you do important mathematical work. | |
| Ask a question to extend learning. | What is one math habit that you’re especially proud of? What is one math habit that you’re working to strengthen? | |
| I talk about math. | Ask a question to elicit reflection. | How is talking about these mathematical ideas helping you to learn? |
| Name a strength. | You’re sharing your math thinking, which can help you understand and remember important math ideas. | |
| Ask a question to extend learning. | When might it be especially important to discuss your math thinking with someone else? | |
| I represent math in different ways. | Ask a question to elicit reflection. | Tell me about the math representations you’ve used. How are these representations helping you as a math learner? |
| Name a strength. | You represent your math thinking in multiple ways, which helps you understand math ideas and share your math thinking. | |
| Ask a question to extend learning. | What are your go-to math representations? Which types of representations are you pushing yourself to use more? | |
| I make math connections. | Ask a question to elicit reflection. | What connections are you seeing from this problem to other mathematical ideas? How are these connections helping you? |
| Name a strength. | You’re connecting this new math idea to other math you already know. This helps you move new learning into your long-term memory. | |
| Ask a question to extend learning. | What are some ways you can share your math connections with others? | |
| I look for and use patterns. | Ask a question to elicit reflection. | What patterns are you finding in this math work? Why are these patterns important? |
| Name a strength. | You’re looking for and using mathematical patterns. This can help you to use the math you know to understand new mathematical ideas. | |
| Ask a question to extend learning. | How is the habit of looking for and using patterns important to you as a mathematician? |
Teaching Up for Future Mathematical Success
In her book Culturally Responsive Teaching and the Brain, Zaretta Hammond (2015) differentiates between independent and dependent learners. Independent learners, she says, have strategies for tackling and persevering with challenging learning. They draw on prior knowledge to build new understandings and skills. Dependent learners, on the other hand, don’t yet have the internal resources needed to take initiative in their learning. Hammond says:
We have to help dependent students develop new cognitive skills and habits of mind that will actually increase their brainpower. Students with increased brainpower can accelerate their own learning, meaning they know how to learn new content and improve their weak skills on their own. (p. 15)
If we’re committed to helping each of our students develop the mathematical proficiency they need for success in school and life, we must give all students access to rigorous math learning aligned to their grade-level curriculum by teaching up to this mathematics content. We must also build our students’ capacity for self-directed math learning by growing their mathematical practices. Habits of mathematical thinking lead to mathematical agency and equip our students for future success as math learners.
Try It Out
How do these ideas relate to your context? How do they affirm and/or challenge your current beliefs about teaching and learning mathematics? We encourage you to consider one of the following ideas:
- Think about the math habit that you worked to strengthen in your class after reading Part 2 of this blog series. Preplan a couple of strategic coaching questions related to this habit that you might ask students as they work on mathematics tasks. Try them out. What happened? What are you learning about your students and the math habits? What will you try next?
- Think about the student you identified after reading Part 2 of this blog series. Preplan a couple of strategic coaching questions related to this student’s mathematical strengths and try them out. What happened? What are you learning about this student? What is this student learning about themself? Why is this important?
- What are some ways you can help your students become more independent and self-directed in their math learning as you continue to teach mathematics concepts and skills?
References
Burwell, H. & Chapman, S. (2024). Power up your math community: A 10-month practice-based professional learning guide. Corwin.
Hammond, Z. (2014). Culturally responsive teaching and the brain: Promoting authentic engagement and rigor among culturally and linguistically diverse students. Corwin.
Lambert, R. (2024). Rethinking disability and mathematics: A UDL math classroom guide for grades k-8. Corwin.
Pica, G. (2022). Conferring in the math classroom: A practical guidebook to using 5-minute conferences to grow confident mathematicians, k-5. Stenhouse.
Safir, S., & Dugan, J. (2021). Street data: The next-generation model for equity, pedagogy, and school transformation. Corwin.
