In traditional math classrooms, teachers present lessons, students work through problems individually or in groups, or perhaps they’re asked questions or take a quiz to demonstrate understanding, and then teachers correct or affirm answers.
On the surface, it’s a concise, logical teaching model where the teacher “starts with an instructional objective and then designs a lesson with the goal of students demonstrating proficiency,” write educators Sam Rhodes and Christopher R. Gareis for ASCD’s In Service. But it’s an approach they say tends to “relegate equity to an afterthought, inadvertently positioning many students as passive observers of mathematics.” Over time, this passive positioning impacts students’ math identity—especially kids from diverse backgrounds who might already struggle to connect classroom learning to their own life experiences—building a “sense of disinterest, inadequacy, and disenfranchisement,” note Rhodes and Gareis.
A more equitable model of math instruction, they believe, begins with student identities firmly in mind during the lesson planning phase, with the teacher thinking first about students’ beliefs around math—for example, considering their comfort level with language, or how they view themselves academically and as mathematicians. “We cannot leave considerations of student identities to the end,” write Rhodes and Gareis, an assistant professor of elementary math education at Georgia Southern University and a professor of educational leadership at William and Mary, respectively. “Rather we need to consider what dispositional outcomes we intend for students,” and then intentionally design curriculum backward, keeping “the aims of equity and sense of self in mind” so that more kids begin to see themselves as competent mathematical thinkers.
Here are four things to keep in mind when designing student-centered math lessons.
Develop a Clear Mission Statement
Consider creating a mission statement that articulates the intentions of your school’s math curriculum and communicates “what teaching mathematics should look and feel like in the school,” write Rhodes and Gareis. This is a simple way to “codify the beliefs and identities that [teachers] aim to foster in students.”
The mission statement might highlight the importance of creating a community of learners “who are seen as doers of mathematics,” for example, and set a goal of giving every student the chance to “develop and communicate deeper understandings of mathematics through flexible thinking, reasoning, and problem-solving.”
Connect to Students’ Experience
Children are naturally drawn to explore the math around them. “From young ages, we quantify, recognize patterns, and question the equivalence of things, even before we have those words for it,” say Rhodes and Gareis. “As we grow, these informal learning opportunities are intrinsically tied to home and cultural experiences and identities.” Drawing on these experiences in the classroom can be a powerful way for teachers to “create mathematical understandings that are inherently connected to the lives of their students.”
While clearly not everything in the math curriculum can directly relate to students’ life experiences, it’s important to plan for lessons that include more connection points for kids in your classroom—similar to how a thoughtfully assembled classroom library would include a rich variety of options that reflect students’ diverse tastes, cultural backgrounds, reading levels, and specific interests.
In his seventh-grade math classroom, Kwame Sarfo-Mensah plans a unit where students investigate an issue of interest. It’s an effort to help students “make sense of the world in which we live,” he says, and in the process, connect them more deeply to mathematics. He starts the unit with a survey to gauge students’ areas of interest. One year, the responses led to a three-week project examining the intersection between law enforcement and communities of color in Boston.
Sarfo-Mensah helped students come up with a focus question and brainstorm the different math-related data points needed to investigate it—statistics, graphical representations, geometric diagrams, and functional relationships—and he made sure to align the work with the appropriate academic standards. He gave students three options for their final product, providing “multiple access points for diverse learners,” he writes.
Allow for Multiple Solving Pathways
In vibrant math classrooms, teachers often “show different ways to solve the same problem and encourage students to come up with their own creative ways to solve them,” writes Matthew Beyranevand, a K–12 math and science department coordinator for Massachusetts Public Schools. “The more strategies and approaches that students are exposed to, the deeper their conceptual understanding of the topic becomes.”
After students solve a problem using a single method, encourage them to brainstorm alternative solving pathways, then discuss the various options as a class. It’s a subtle shift that puts emphasis on developing critical thinking and encourages students to embrace asking questions and sharing strategies as a way to make sense of complex material. “Whereas a focus on [right or wrong] answers results in judgments of correctness, a focus on thinking builds and refines understandings from what students know and understand,” write Rhodes and Gareis.
Encourage Productive Struggle
Problem-solving is an integral component of math, and allowing students to struggle productively as they attempt to solve complex problems “sends the message that the teacher believes students are capable of doing and creating mathematics,” write Rhodes and Gareis.
High school math teacher Solenne Abaziou, in an effort to build up her students’ problem-solving skills and stamina, assigns weekly open-ended math tasks called problem solvers—problems like Dice in a Corner and Snowmen Buttons. “Students often struggle with persistence—they’re uncomfortable with the idea of trying a solution if they’re not confident that it will yield the desired results, which leads them to refuse to take risks,” Abaziou writes. “Helping students get past this fear will give them a big advantage in math and in many other areas of daily life.”
A good problem solver “has a low floor and high ceiling,” Abaziou notes. “The skills needed to tackle the problem should be minimal, to allow weaker students to engage with it, but it should have several levels of complexity, to challenge high-flying students.” As students engage with the problem, they should be “confused at the beginning, which encourages them to struggle until they get on a path that will likely lead them to the solution.” It’s only by working through that initial frustration that students begin to build “problem-solving resilience,” she writes.
All students are capable of doing math, Rhodes and Gareis insist. “We believe that diversity of thought enhances understandings of mathematics for all students, and we believe that allowing student voices and experiences to shine in mathematics classrooms is a crucial step towards rehumanizing the subject,” they conclude.