Ensuring That Math Instruction Provides Opportunities for All

How diverse is your math class? What range of experience, motivation, interest, and ability do you see? For most of us who teach kids math, we witness a wide spectrum of skill, and our challenge is how to address needs and help students grow as mathematicians.

For the past eight years, I’ve taught fifth and sixth graders math in the same class at the same time. In each of my classes, I see students who are ready for algebra and students who are learning multi-digit multiplication. While most schools are not designed for multi-aged classes, I suspect that all math classes include a range of student abilities.

Over the years, I have paid attention to strategies and practices that help create a space for engagement, learning, and joy for all students in diverse-level classrooms. 

Build Community

When students are part of a community, they are more likely to invest in the things that make communities great. This means recognizing the skills of those around them, leaning on others for assistance, and celebrating success. Students must be a part of building community norms that allow for active participation, collaboration, and questioning. Teachers must model doing math, being curious about the ideas and solutions of others, and respecting community norms.

Teach Kids How to Engage in Mathematical Discourse

The first gear of engagement in math class is usually sharing solutions. However, when this is the only focus, kids tend to care only about what they think and whether or not they are correct. Helping kids talk about ideas and questions deepens understanding and elevates new voices. Discussing common misconceptions, innovative solutions, and visual representations gives everyone an entry into the conversation. 

Posing questions that are open-ended and require students to think is a good first step. Questions like Can you visualize/draw that? What makes you think that? Do you agree? What is a good estimate? create space for thinking and creativity and elevate good ideas and the class members who have them. 

Collaborate

Students receive support from one another that is different from the support they would get from adults. In order to have true collaboration, kids need protocols and practice. Helping students understand what roles to play, what questions to ask, and how to disagree without arguing allows them to work in small and diverse groups to solve challenging problems that are designed to elicit innovative solutions.

In my class, we solve thinking tasks (based on the work of Peter Liljedahl) in small groups. Each group has only one marker and one whiteboard and must collaborate to find and defend their answer. I also offer checklists that help students evaluate their own and classmates’ work. Simply taking the time to look at someone else’s work can start a conversation or impromptu tutoring session that can support learning.

Use Flexible Groups and Offer a Range of Problems

Most students find that some skills and standards pose a greater challenge than others. Kids who have difficulty finding a common denominator might find that they are confident when multiplying fractions. This means that for each skill or standard, kids will need a different level of instruction. Grouping decisions are best made in the moment, which means that teachers need to know their kids and be prepared with a variety of tasks and learning opportunities. 

Students need some agency, too, and should be able to opt into a more challenging group if they are or feel ready, or to join a review group if a skill feels tricky. During independent work time, teachers can offer differing levels of work—mild, medium, or spicy—for students to select. This offers problems at all levels of learning and and makes challenging work available to anyone. 

Be Competitive in Ways that Don’t Reward Fast Processing

Competition is a double-edged sword. Kids like it, and it’s kinda icky. When we value only processing speed, we see the same students always “winning.” By creating different opportunities to “win,” we can provide all students with success. I like contests like “the group with the funniest answer” or “the person with the best visual model” because they honor deep thinking about math and collaboration. Kids can also compete against themselves when they notice that they were more accurate today than they were yesterday. 

Highlight the Importance of Diversity of Voices

Traditional thinking will tell us that having students all performing at or around the same level makes for better learning. While it may simplify instruction, we know that the learning of all students is enriched by a range of perspectives and approaches. Classrooms must honor all voices as an integral part of the learning, and students need to know that each of their classmates has value and skills that are different from, and in some areas better than, their own. 

When I eavesdrop on conversations among students, I listen for ideas that are innovative and original, and I make sure to highlight these and the voices that shared them when we meet as a whole group. Kids notice, too, and begin to know where to go for help with what types of questions and to better appreciate the gifts of their classmates.

Knowing our kids, knowing our content, and building structures that support thinking and celebrate diversity is hard but essential and doable work. The time we spend building these systems will enable us to build joyful classrooms that honor all voices and support growth for all.