**Believing Our Students Can Do Mathematics: Identity, Agency, and Authority**

**September 2020**

Do I really believe that each and every student can do mathematics?

Do I believe each and every student can engage in rigorous mathematics and problem solving?

Do I believe that each and every student can contribute to classroom discourse about rich mathematical concepts?

I have been asking myself these questions as I reflect on when I taught high school to collectively over 2,000 students. Did I really believe each and every one of my students could do mathematics? Did my students leave my class seeing themselves as doers and thinkers of mathematics? Was I intentional in creating a classroom environment that supported their development of a positive mathematical identity and a strong sense of agency to engage in mathematics as well as positioned them to share mathematical authority? Did I support my students in seeing themselves as significant contributors to the collective knowledge and understandings of the class? I would like to think that I did. But it is one thing for me to say it in words and quite another to examine my actions as a teacher of mathematics to see if I *really *believed in my students.

What we as teachers believe about our students, as manifested in not only our words but our actions, matters. It affects what we teach and how we teach. It influences the tasks and problems we select, how we engage students in mathematical discourse, which students we include in purposeful questioning, the level of rigor we choose for our students, and the strength of the mathematical goals we use to guide instruction. It contributes to whether we focus primarily on procedures or build on conceptual understanding. It determines if we strive to support mathematical connections to deepen mathematical understanding or focus only on memorization and learning in isolation. And it affects how effective we are in adjusting instruction to support each and every student in our classroom.

Does this sound familiar? It probably does because it reflects the Effective Mathematics Teaching Practices described in
*Principles to Actions: Ensuring Mathematical Success for All*
(NCTM 2014). I ask, though, that we think about these practices in terms of what we truly believe about our students and whether we believe they can do mathematics. Our beliefs about our students directly connect to these practices and how we do or do not engage in them effectively. In the recent
Catalyzing Change series (2018, 2020a, 2020b) the third of the four recommendations highlights the importance of implementing equitable mathematics instruction and states, “Teachers and their instructional practices have strong influences, often far greater than one realizes, on children as they learn mathematics” (NCTM 2020, p. 45). Thus, students’ identity, agency, and authority in the mathematics classroom are affected either negatively or positively by our actions as teachers.

What can or should we do? Zollman, Smith, and Reisdorf in
*Motivation and Disposition: Pathways to Learning Mathematics, 73rd Yearbook *
(2011) note that as a first step, students need to identify themselves as a “mathematics student,” which is influenced by whether they are successful in the mathematics classroom and feel valued, whether the classroom environment supports mathematical understanding and achievement and empowers students in feeling competent in mathematics. They offer four teacher actions that support students’ identity development: (1) fostering self-determination, (2) cultivating self-regulation, (3) capitalizing on social goals, and (4) establishing an engaging classroom (pp. 47–48). Actions range from giving students choices and opportunities to reflect to establishing a positive mathematical community to using authentic problems and making mathematical connections.

For many students who have been marginalized in mathematics education, it is essential that we as teachers are not only aware of our critical role in teaching and learning mathematics but also the inequities that often contribute to negative identities. We should both acknowledge these issues and focus our actions to ensure implementation of equitable teaching practices. For too long, many students from nondominant ethnic, racial, cultural, and language backgrounds, students with varying disabilities, and students from economically challenged areas have not been valued and supported in many mathematics learning environments. Tan and colleagues, in
*Humanizing Disability in Mathematics Education: Forging New Paths*
(2019), recommend that our teaching philosophy embody a “flexible, humanizing mathematics” approach (p. 48). Further, Victoria Hand in *Mathematics for Equity: A Framework for Successful Practice *(2014) states, “Learners must feel invited to participate in classroom mathematics communities, and . . . classroom norms must be flexible enough for students to take up their space around mathematics learning in a variety of ways” (p. 106).

In our current COVID-19 situation with virtual classrooms, hybrid variations, and face-to-face social distancing, we are certainly challenged to create this type of environment in our mathematics classrooms. But in my virtual encounters with mathematics educators across the United States and Canada, I am seeing such commitment, creativity, and dedication among mathematics teachers to ensure that each and every student is highly engaged in mathematics; that all students have the opportunity to share their insights and understandings; and that they are supported to persist, persevere, and productively struggle. Teachers do believe that it is about the students and that their students can do mathematics! It is more than words and extends to important, intentional actions.

This is a difficult time for mathematics teachers because they are being called on to do so much more than ever before. This is a time to support one another in teaching mathematics because teachers are also facing so many challenges. Many are teaching virtually and face to face at the same time. And in that scenario, teachers are working to implement strategies to allow students to see themselves as doers and thinkers of mathematics, build confidence and see themselves as capable of working through misunderstandings and understandings, and make valuable contributions to classroom discussions in mathematics. Mathematics teachers are participating in professional development to learn new technologies, collaborating with colleagues and families to support their students in learning mathematics, and going above and beyond expectations to ensure all students are supported. It has been quite the journey in teaching this year. We must believe each and every student can do mathematics, and we must follow that belief with actions that support that belief, even in these trying circumstances. I thank you for your commitment, and NCTM supports you!

Trena Wilkerson

NCTM President

@TrenaWilkerson

### References

Hand, Victoria. 2014. “‘Taking Up Our Space’: Becoming Competent Learners in Mathematics Classrooms.” In *Mathematics for Equity: A Framework for Successful Practice,* edited by Na'ilah Nasir, Carlos Cabana, Barbara Shreve, Estelle Woodbury, and Nicole Louie, pp. 91–106. Reston, VA: National Council of Teachers of Mathematics.

National Council of Teachers of Mathematics (NCTM). 2018. *Catalyzing Change in High School Mathematics: Initiating Critical Conversations*. Reston, VA: NCTM.

National Council of Teachers of Mathematics (NCTM). 2020a. *Catalyzing Change in Early Childhood and Elementary Mathematics: Initiating Critical Conversations*. Reston, VA: NCTM.

National Council of Teachers of Mathematics (NCTM). 2020b. *Catalyzing Change in Middle School Mathematics: Initiating Critical Conversations*. Reston, VA: NCTM.

National Council of Teachers of Mathematics (NCTM). 2014. Principles to Action*s: Ensuring Mathematical Success for All*. Reston, VA: NCTM.

Tan, Paulo, Alexis Padilla, Erica N. Mason, and James Sheldon. 2019. *Humanizing Disability in Mathematics Education: Forging New Paths*. Reston, VA: National Council of Teachers of Mathematics.

Zollman, Alan, M. Cecil Smith, and Patricia Reisdorf. 2011.“Identity Development: Critical Component for Learning in Mathematics.” In *Motivation and Disposition: Pathways to Learning Mathematics*, 73rd Yearbook of the National Council of Teachers of Mathematics (NCTM), edited by Daniel J. Brahier, pp. 43–54. Reston, VA: NCTM.