Positioning Elementary Students as Experts in Math Class

What happens when teachers purposefully look for ways to share authority and expertise with the children in their math classrooms?

A few months back, a fourth-grade teacher came to me with a conundrum. “I know some of the students in my class are struggling with fractions,” she shared, “but I can’t figure out how to give them the extra support they need.” She asked if I, the math specialist, would observe her class and then help her brainstorm solutions. Of course I would!

The following morning, the teacher delivered an excellent lesson on comparing fractions. When she wrapped up her instruction, she wrote this on the board:

1. Complete workbook pages.

2. Check work with a teacher.

In this class, students were encouraged to collaborate and had been actively taught to do so, so as they got started, immediately a buzz of energy filled the room. When students completed their workbook pages, they found their teacher, who looked over each student’s work, either checking off the page or asking questions to encourage more thinking. However, by the end of the class, I too recognized the teacher’s dilemma: She was spending most of her time reviewing the work of the students who understood the material, not supporting the students who didn’t.

During our debrief after the lesson, we considered how we might free her up to work one-on-one or in small groups with more students. Could her students take on a more shared responsibility for the collective learning of the class?

According to the authors of The Impact of Identity in K–12 Mathematics, the answer is a resounding “Yes!” In fact, when teachers take purposeful steps to position students as sources of expertise and distribute mathematical authority among all members of the classroom community, they strengthen both student learning and positive identity development.

Positioning Students as Experts

One of the easiest ways to position students as experts is to encourage them to take on roles traditionally designated for the teacher. In my own classroom, I do this by having students check their answers with each other, not with me. Specifically, when my students are done with their work, instead of “Check with a teacher,” I write on the board, “Check with a classmate.”

When students check their answers with each other, most of the time they confirm their correct answers and they move on. Because students are less reliant on me and more reliant on each other, I am freed up to work with more focus and intention with students who really need my support. In addition, when students find their answers are different, they are motivated to work together to figure out how or why they got different responses. Through these conversations, students come to both recognize and rely on the expertise of their classmates for feedback and understanding. Conversations among students increase, knowledge becomes more mobile, and the collective mathematical learning of the whole class improves.

Distributing Mathematical Authority

When I first suggested that the fourth-grade teacher have her students check with each other, the teacher was worried: What if students just copied off each other? How would the teacher know that the students were doing the work if she didn’t check each page?

While these are reasonable fears, we decided that an important part of developing a shared culture is helping the students recognize their own agency and independence as math learners. So instead of increasing teacher oversight, we decided the best way to encourage students to take ownership of their learning was to further release control and to relinquish the primary tool we as teachers use to maintain our mathematical authority: the answer key.

When we give students the answers, we reframe the narrative that what matters is not the answer itself, but the thinking, process, or understanding that the answer is indicative of. When we share the answer key with students, we send them the message that this work is for them, not us.

The next day, the teacher printed a copy of the answers to the students’ workbook pages and hung it on the whiteboard, ensuring that the answers were accessible to all. She wrote this on the board:

1. Finish workbook pages.

2. Check thinking with a classmate.

3. Confirm answers with the answer key.

When she read the directions out loud and told her students the answers were on the board, most of her students looked at her like she was crazy. One student raised his hand and asked, “But couldn’t we just copy?”

She shrugged and responded, “Yes, you could just copy. But that’s kind of a waste of your time. You have this time to check your understanding. You have a tool—the answer key—to help you do just that. And your classmates and I are here to answer any questions if you’re not sure.”

Once again, students took out their workbooks and got to work, and the teacher began to circulate and check in with students who needed support. As the first students completed their assignments, instead of seeking out the teacher, they scanned the room, looking for another student who was also done. This was exactly what we had been hoping for: students looking to each other as sources of expertise and mathematical authority.

But what happened next was even more exciting: We had anticipated that if two students had different responses, they would immediately go to the answer key to see who was right. However, when the first pair of students found one answer that didn’t match, instead of going to the answer key, they returned to their desks to try to figure out where one of them went wrong. Soon, more and more students were sharing their thinking and discussing their answers with each other, while the answer key remained largely untouched.

Contrary to our fears that students would copy off the answer key or each other, the answer key was serving as a visible reminder of the culture of the classroom, one in which students are collectively responsible for their own and their classmates’ learning and intellectual growth.

Over the next few weeks, the teacher reported further progress toward a more shared classroom culture. She continued to encourage students to check their answers with each other. She experimented with having one answer key for the class and printing the answer key on the back of individual worksheets. She found that some students were able to move more confidently through their work by confirming their thinking as they went, while others ignored the answer key until they were done. But all students benefited from being part of a classroom in which the success of each individual was a collective responsibility, shared among the group.

Implementing a shared culture of teaching and learning

We can all take small steps toward fostering a more shared culture of teaching and learning in our classrooms: First, we can guide students to check their work with their classmates, thereby positioning students as viable sources of mathematical expertise for their classmates. Second, we can make sure that all students have access to the answer key, which distributes mathematical authority more equitably among both students and teachers. Finally, we can encourage students to recognize the collective success and achievement of the class as an integral part of their own individual achievement and growth. When we take these actions, we help all students see themselves as both competent and confident mathematical thinkers and doers.