Math Proficiency for All

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 described why it is essential in math intervention initiatives and core instruction to grow students’ mathematical habits of thinking alongside their math content knowledge. Here in Part 2 and continuing in Part 3, we outline easy-to-implement strategies to cultivate empowering math habits in all students.

Part 2: The Habits of Mathematically Powerful People

Many educators, leaders, and parents are aware that people approach learning differently, but they do not realize that the effective ways of learning and problem-solving can be taught. Most teachers devote their time to teaching their content area, assuming that students know how to learn. (Boaler, 2024, p. 58)

Explicit Teaching About the Math Practices

Mathematical proficiency requires students to internalize the math practices or processes, known in many states as the Standards of Mathematical Practice. These math practices, as written and described in curriculum documents, can be difficult for students and even teachers to understand. Educators can support students in accessing and applying the cognitive habits described in the math practices by describing them in student-friendly language. The Habits of Mathematically Powerful People from the book Power Up Your Math Community: A 10-Month Practice-Based Professional Learning Guide (Burwell & Chapman, 2024) is an example of a student-friendly version of the math practices (see Figure 1).

Figure 1. Habits of Mathematically Powerful People

Table 1 provides a description and rationale for each habit. Teachers might use these ideas in planning mini-lessons, anchor charts, and learning activities to introduce the Habits of Mathematically Powerful People and cultivate the habits in all students.

Table 1. Description and Explanation of the Habits of Mathematically Powerful People

Habit	Description	How the Habit Supports Math Learning
I expect math to make sense.	Mathematically Powerful People expect math to make sense and know they can make sense of mathematical ideas. Cognitive dissonance is recognized as a natural part of the sense-making and learning process.	Expecting math to make sense is foundational to the other math habits. When we expect math to make sense and believe we can make sense of math, we are ready to take on challenging mathematics. Engaging in challenging math experiences will, in turn, grow our mathematical understandings, skills, and confidence, setting in motion an iterative cycle of self-directed math learning.
I love challenging math problems.	Mathematically Powerful People know that struggle is essential to learning. They also know that too much struggle can impede learning, so they develop a personal toolkit of strategies for turning unproductive struggle into productive struggle.	Embracing challenging math problems is central to what it means to be a math learner and mathematician. When we enthusiastically engage in struggle and persevere in making sense of and solving complex math problems, we live rich mathematical lives.
I learn from math mistakes.	Mathematically Powerful People know that mistakes are a key part of learning. They understand the importance of taking academic risks because they know learning is messy. They welcome others’ critiques of their mathematical thinking because they recognize the value of debate and refinement of mathematical conjectures.	Mistakes are essential to learning. Our brains use mistakes and missteps to create new neural pathways, allowing us to understand mathematical ideas more deeply.
I see myself as a mathematician.	Mathematically Powerful People see themselves and each other as mathematically capable, as people who engage in mathematical activity in and out of school because mathematics is useful, interesting, and fun.	A strong mathematical identity promotes and supports math learning. Our math identities are braided into our experiences as math learners.
I talk about math.	Mathematically Powerful People talk about their mathematical thinking to support their own and others’ reasoning and sense-making. They know mathematical discourse involves speaking and listening as well as non-linguistic forms of communication and that the exchange of mathematical ideas helps the class community co-construct mathematical knowledge and build mathematical proficiencies.	Talking about math is tightly connected to the other math habits. Our discourse with other math learners allows us to practice reasoning and sense-making and thus supports our math learning.
I represent math in different ways.	Mathematically Powerful People recognize that mathematicians represent their work in multiple ways. The ability to represent math ideas in multiple ways deepens understanding and reveals connections and underlying mathematical structures.	Creating and using representations is essential to deep mathematical understanding. Our brains make strong connections when content is represented in a variety of ways and when we take time to notice the similarities and differences between these representations.
I make math connections.	Mathematically Powerful People make connections between mathematical ideas and from math to real life. These connections strengthen understanding of school mathematics and also position them to think mathematically beyond concepts learned in school.	Math learning is supported when we see how newly discovered mathematical ideas connect to things we already know. Armed with a strong understanding of concepts and the knowledge that mathematics is everywhere, we become agents in our own learning, uncovering mathematical beauty and solving real-life mathematical problems.
I look for and use patterns.	Mathematically Powerful People notice and use patterns to make sense of mathematical ideas and the world around them. Math learners look for patterns in numbers, shapes, or ideas and use those patterns to generalize about the big ideas of mathematics. They are also aware of patterns in their lives, and they see the beauty of patterns in the natural world.	Noticing and using patterns is at the heart of mathematics. Patterns live outside the classroom in the world around us, but they also help us discover and learn about new mathematical ideas.

Teachers can introduce the Habits of Mathematically Powerful People to the whole class or in small-group lessons. They might focus on one habit each day for eight days or introduce a new habit each week or month using activities such as the following:

• Together with students, create a looks/sounds/feels-like chart for a specific math habit.
• Have students brainstorm strategies for a specific math habit on an anchor chart. The class can continue adding to the chart as students practice using the targeted habit.
• Post sentence frames to support discourse related to a specific math habit.
• During the closure of each day’s math lesson, have students reflect on their learning related to a math habit in a brief discussion, a journaling activity, or an exit card.

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? Prior to reading Part 3 of this blog series, we encourage you to consider one of the following ideas:

• Compare your state’s math practices or processes to the Habits of Mathematically Powerful People. How are they similar and different? How might using student-friendly language in describing these practices help students internalize them as learning habits?
• Think about your students. What is one math habit you might help your students to strengthen? How would that habit support their math learning?
• Think about a student who is not yet meeting grade-level proficiency standards in mathematics. What is one math habit that comes naturally to this student? How might you call this student’s and others’ attention to this mathematical strength? How might you tap into and build on this strength to support the student’s math learning?

References

Boaler, J. (2024). Math-ish: Finding creativity, diversity, and meaning in mathematics. HarperOne.

Burwell, H. & Chapman, S. (2024). Power up your math community: A 10-month practice-based professional learning guide. Corwin.