When I think of good math teaching, I think of teaching students to be mathematicians, rather than just to do math. Doing math is reminiscent of the majority of my math education: memorizing and applying rules and procedures without really understanding why. Being a mathematician, however, entails much more. It entails constantly thinking like a problem solver, using questioning, reasoning, and analytical skills to understand different mathematical scenarios. It means connecting math to real-world situations, and thereby gaining new understandings of the surrounding world. It involves collaborating with peers to figure out different strategies and solutions, and writing and reflecting about both individual and collective thinking.

Conceptual Understanding

Conceptual understanding plays an essential role in the development of students’ mathematical selves. Through noticing patterns – a seemingly simple yet intensely powerful and highly accessible entry point into problems – students discover for themselves why certain rules exist and how an underlying concept relates to other important concepts. This allows them to better understand the beautiful interconnectivity of mathematics that organizes the discipline. They also become situated as constructors of knowledge, which gives them agency over their education and enables them to learn new concepts easier, for they have a point of reference to frame their thinking. As such, students understand the context of math concepts not only within the real world, but also within the mathematical world.

Student-centered Teaching

A student-centered classroom gives students this sense of agency, for they become the ones leading the discussions, exchanging ideas, showing multiple representations, and supporting one another as they explain their thinking and persevere through problem-solving. 

Confidence in the Classroom

In order for students to co-construct this sort of classroom space and blossom as young mathematicians, they need to feel confident in the classroom. Math so often becomes a subject that makes students feel horrible about what they have come to believe is a lack of ability, and then their performance becomes a self-fulfilling prophecy of failure. As a teacher, I strive to reconstruct the idea of failure as a necessary and completely normal part of growth and ultimate success. I never want to shut down a student for giving the wrong answer in class or asking a question, but rather applaud them for being brave enough to put themselves out there. Students are encouraged to ask each other for help first, rather than immediately turn to me. Through this, students get to show their learning and further their understanding of a concept by actually teaching it to their peers. This challenges the idea that I am the only teacher in the room. Especially in heterogeneous classes in which there exist a variety of mathematical fluencies, students need to feel confident enough to engage in these mathematical behaviors. I do not want ability to hinder a student’s confidence, and I want them to feel supported by not only me, but also their classmates. With activities that provide multiple entry points and a classroom culture of respect, hopefully all students can feel encouraged to act as mathematicians.

Knowing my Students

Providing academic support goes hand in hand with providing emotional support. Developing relationships with my students and getting to know them helps me design math lessons that draw on their interests and strengths and shows them that their funds of knowledge have a place in mathematics. When they look at real-world scenarios as mathematicians, the scenarios are then more meaningful for them and connected to their lives. Through this, they can see how the habits they’ve developed as problem solvers – citing evidence to back up claims, clearly explaining their thinking using multiple representations, approaching situations with curiosity, collaborating with peers, and reflecting on their work –  become useful tools in almost all academic and non-academic experiences.