May 2025

What does a community of mathematical thinkers look like?

It starts when all students are doing the thinking. Students are talking to each other and discussing their ideas. Students are moving around the room, discussing their thoughts with other teams, and bringing information back to their own teams. Students are working with anyone, not just their friends, and they understand that all students in the classroom have ideas that are helpful when solving problems. Discussions flow naturally, with each member of the team contributing ideas that eventually lead to answers.

Building a Thinking Classroom

While this all sounds wonderful, as teachers, we know that getting students to work together and discuss ideas can be difficult. So, how do we build this community? Three years ago, I started incorporating many of the practices outlined in Building Thinking Classrooms in Mathematics (BTC), by Peter Lilijedahl. As suggested by the book, I started building my thinking classroom by assigning students to work in visibly random teams, on thinking tasks at whiteboards. Students immediately started discussing the problems. It was like a switch turned on in their brains, and they were able to solve problems in the lesson that they had deemed impossible while they were sitting. I do not know what it is, but there is something magical about standing at the whiteboard that motivates students to talk to each other. Happy with this result, I continued to incorporate more of the BTC practices.

Elevating Student Status to Encourage Collaboration

As the year continued, I noticed that some classes worked better at the whiteboards than others. About that same time, I went to a training session that talked about status. Social status in the classroom refers to an individual student’s perceived position within the social hierarchy of their class. Status is how students perceive each other. A student may have high status with one group of students and low status with another. Many factors contribute to how students assign status: popularity, athletic ability, academic performance, race, gender, and family background are all possibilities. 

After learning about status, I noticed that students with similar status tend to work well together while those with different status do not. This dynamic is not helpful to a classroom community of learners, so I was encouraged by the discovery that status is something that can change. I knew that if I could elevate the status of my students, there would be fewer gaps in status, and students would be more willing to work with each other.  

Fortunately, the practices of BTC help in elevating status. Working in different random teams often allows students to get to know each other and changes team dynamics. Using thinking tasks that are low-floor helps all students to engage in problem solving, which builds confidence. Vertical non-permanent surfaces allow students to look at other teams’ answers, which helps them perceive other students as experts. The teacher focuses on responding to students’ questions that show that they are thinking about the task. When a student asks a “stop thinking” type of question, (e.g. “Is this right?”, “Will this be on the test?”, or “When are we out of here?”) the teacher redirects the student back to the task and walks away. 

Motivating Students with Drastic Status Gaps

I found that these practices worked for most of my classes, but I had one class with students with very drastic gaps in status. It was very difficult to motivate the students in this class to work together, and the constant complaining was frustrating for everyone.

I was tempted to give in and start going over the problems in the lesson together as a class. I knew that switching to direct instruction was not what was best for my students. Instead, I tried to intentionally build the status of students to help them learn how to work together. 

Building status is not a quick fix. It takes time, but the results are worth the effort.

I started by looking for opportunities to highlight student work. I found that by recognizing students who normally did not volunteer, I was building their status. At the beginning of the class, I usually have students work on a quick warm-up. This is a great time to build status. As I walk around the room, I notice a student or two with interesting work, and then call on them to explain their answers when I go over the warm-up. 

I also use the time students are solving problems at the whiteboards to build status. If I know a certain team is on the right track, I will send others to ask them for help. Sometimes one member of a team will ask me a question. I will then ask the other members of the team to contribute an idea. If there is a student who is standing off to one side and not contributing, I will ask that student a question that I know they can answer to bring them into the team and build their status. Slowly, the gaps in status started to close, and students started working together without complaint. 

Students Elevating Their Own Status and the Status of Others

During that summer, at the BTC conference, I attended a session by Pam Seda and learned about her ICUCARE framework. 

• Include others as experts
• Be Critically conscious
• Understand how relationships improve learning 
• Use Culturally relevant resources
• Assess, activate, and build on prior knowledge
• Retain control
• Expect more

In her book, Choosing to See: A Framework for Equity in the Mathematics Classroom, Pam Seda gives both teacher- and student-facing action statements that correspond to each of the seven principles. This year, I decided to put up a poster of the student-facing statements in my classroom. I point out different statements regularly to my students, giving them concrete examples of how to elevate their status and the status of others. Next year, I plan on introducing these statements with my students at the beginning of the year. I want students to have a chance to really think about each statement and then take a survey to rank, on a scale of 1–5, how strongly they agree with each statement. I think the results will be interesting feedback for both me and my students. I am also interested in comparing results from the beginning of the year with results from the same survey at the end of the year. 

In closing, I think it is important to point out that every year, I have to work on building the status of my students. Each year brings new students or different combinations of students that will assign status differently than the year before. It is also important to note that I make sure to build the status of all students. Even the students whom I perceive to have high status already need to be recognized for their work. I have found that students who feel appreciated for their work are more likely to include and work with other students.