What If We Each Saw Ourselves as Capable Doers and Learners of Mathematics?

Imagine walking into a classroom where every student, teacher, and leader confidently sees themselves as a capable doer and learner of mathematics.

• What would change?

• How would instruction shift?

• How would students engage differently?

For too long, the label "math person" has been reserved for a select few—those who excel at quick calculations, memorize formulas effortlessly, or see patterns others might miss. But what if we expanded that definition? What if we recognized that being mathematically capable isn’t about innate ability, but about how we engage with math—our curiosity, our persistence, and our willingness to explore and make sense of problems?

This shift in perception has the power to not only transform the classroom environment but also to have a profound impact on the achievement gap that persists in many educational systems.

The Power of Identity in Math

Students' perceptions of themselves as capable in mathematics shape how they engage with the subject. When students believe they “aren’t good at math,” they disengage, avoid risks, and see struggle as a sign of failure rather than learning. This belief often stems from a lack of representation, cultural disconnect, or experiences that reinforce feelings of inadequacy.

However, when students see themselves as capable doers and learners of mathematics—when they feel that math is a space for everyone, not just a select group—they begin to approach challenges with curiosity, resilience, and the belief that their thinking matters. This shift in identity is crucial in closing the achievement gap.

Impact on the Achievement Gap

The achievement gap often reflects disparities in math performance along lines of race, socioeconomic status, and language. Students from marginalized backgrounds often experience barriers that undermine their confidence and sense of belonging in math. However, when students are encouraged to see themselves as capable in mathematics, the learning environment becomes more inclusive, supportive, and empowering, which can lead to:

• Increased participation: Students who believe they belong in the math community are more likely to take risks, ask questions, and persist through challenges. This is key in bridging the gap where students from underrepresented groups often lack engagement or confidence in math.

• Equitable access to cognitive demand: By encouraging all students to see themselves as thinkers, we ensure that complex problems and higher-order thinking are accessible to everyone, not just the "advanced" learners.

• Improved problem-solving skills: When students are empowered to take ownership of their learning, they begin to tackle problems creatively and collaboratively, rather than relying solely on memorized procedures. This shift supports higher achievement by focusing on the development of deep mathematical understanding.

Shifting Instruction to Build Mathematical Identity

If we want every student to see themselves as a capable doer and learner of mathematics, we must design instruction that affirms this identity. Here’s what that looks like in practice:

1. Emphasizing Mathematical Thinking Over Speed

Too often, speed is equated with mathematical ability. But true mathematical thinking involves reasoning, questioning, and making connections. Instruction should slow down to allow students to explore different approaches, justify their thinking, and build deep understanding.

Instructional Impact:

• Shift from timed drills to open-ended problems that encourage discussion.

• Provide opportunities for students to explain their reasoning through multiple representations.

• Celebrate different ways of thinking rather than just correct answers.

This approach helps level the playing field, particularly for students who may struggle with procedural fluency but can demonstrate deep understanding when given the time and space to think critically.

2. Centering Student Voice and Agency

Mathematics should be an active process where students are not just passive receivers of information but active sense-makers. They should see their ideas valued and their strategies as meaningful contributions to the learning community.

Instructional Impact:

• Use classroom discussions to elevate student thinking (e.g., “What do you notice? What do you wonder?”).

• Create opportunities for students to pose and explore their own math questions.

• Normalize mistakes as part of the learning process.

When students see their voices and ideas matter, it builds their confidence and sense of belonging, especially for those who historically have been excluded from high-level math discourse. This boosts their achievement by encouraging ownership and engagement.

3. Connecting Math to Students’ Lives and Interests

Math should feel relevant. Students are more likely to see themselves as capable in mathematics when they see math as a tool for understanding and impacting their world.

Instructional Impact:

• Incorporate real-world contexts that matter to students.

• Highlight diverse mathematicians and their contributions to broaden the image of who does math.

• Encourage students to see math in their daily experiences, from budgeting to social justice data analysis.

By connecting math to students' lived experiences, we bridge the cultural gap that can often lead to disengagement. When math is relatable and empowering, it becomes a tool for success and expression.

4. Modeling a Growth Mindset Around Math

If educators want students to believe they are capable doers and learners of mathematics, they must first believe it themselves. Teachers can model the learning process by thinking aloud, sharing their own experiences with struggle, and emphasizing that mathematical ability grows with effort and practice.

Instructional Impact:

• Shift language from “I was never good at math” to “I’m learning new ways to think about math.”

• Praise effort, strategy, and persistence rather than just correctness.

• Engage in professional learning that deepens mathematical content knowledge and pedagogy.

By modeling a growth mindset, we foster an environment where all students, particularly those from historically underrepresented groups, feel they can improve and succeed.

A Future Where Everyone Sees Themselves as Mathematicians

What if we truly embraced this shift? Imagine classrooms where students confidently approach problems, where teachers feel empowered as mathematical thinkers, and where math becomes a space of joy, curiosity, and deep understanding.

This shift has the potential to close the achievement gap by ensuring that all students, regardless of background, see themselves as capable doers and learners of mathematics and are equipped with the tools to succeed.

So, let’s start now. How will you help someone see themselves as mathematically capable today?

Pam