Establishing norms is critical to creating an environment where all students see themselves as knowers and doers of mathematics. Reflecting on the Illustrative Mathematics mission statement, Creating a world where learners know, use, and enjoy mathematics, how can we contribute to this mission as first year teachers implementing the IM curriculum in our classrooms?
By Anna Polsgrove, Marcela Aguila, and Brooke Braga
In thinking about how we wanted to develop these norms, we thought back to our work in our teacher preparation program at the University of California, Irvine, and our Illustrative Mathematics professional learning event. On the second day of the IM training, we engaged in an interactive activity designed to help us think about the culture we would like to foster in our own classrooms, and explicit norms that may support this work. This work was invaluable to our learning process.
Knowing how important it was for us to do the work of crafting norms and a vision of a positive, productive, collaborative classroom, we knew we wanted to involve our students to have a similar experience. We knew we wanted them to participate in the work of creating and owning norms, and that this work would be ongoing throughout the year. We didn’t want a top-down list to give students, something that would just be posted on the wall. We want this to be a living representation of who we are, how we interact, and how we exist as a community.
In planning for this work, we considered our own core values that would guide students. We want to create environments in which sense-making is valued—where all student voices are heard, where ideas are respected, where we persevere when problems are challenging, where we analyze and make sense of each others’ ideas, and where productive struggle, making mistakes, and revising our thinking is the norm.
But how to start with students? Middle school students care deeply about what their friends think, say, and do. As educators, we can use this to our advantage when we are developing norms with our students, rather than imposing a pre-established list of rules to which students have no personal connection. By co-creating classroom norms, we are giving students more responsibility, helping them become integral members of their own classroom mathematics community, and helping them have an understanding of what collaborative group work looks like.
We decided to begin with developing ways of working together, including how to consult one another with questions or opinions. We arranged students in table groups of 4 to 6, and asked them to hold small group discussions about what they thought successful group-work in mathematics looks like. Students suggested working together, listening to one another, and taking turns to share ideas.
We continued with the idea of thinking critically in math class. Having open and honest discussions with every student about this allows students to realize that mistakes are a crucial part of learning. To co-construct norms and practices in one classroom, students were shown a quote from Aristotle: “The more you know. . . the more you realize you don’t know.” They were given independent think time to reflect on the meaning. Students started to nod their heads in agreement. This started our conversations about sense-making and deepening reasoning.
Building from this experience, students were able to share what math means to them and why math discussions are valuable. One student shared, “There are multiple ways to do math!” Another student said, “You have to talk to understand what you are doing.” Comments like this drove a positive discussion about math and co-constructing norms for the class.
Students decided on six different norms:
- everyone has good mathematical ideas
- agree and disagree with mathematical ideas–not each other
- make sense of mathematics
- respect what our peers have to say
- give our peers ample think time
- listen before you speak
The norms were posted in the classroom for all of us to see. We planned to revisit the norms throughout the year, as we held one another accountable for creating the community we want.
We also realized that some students may not have had experience in such a collaborative environment. Having a conversation about what group work looks like might not be enough. Additionally, as a new community, we may not have a completely shared understanding of each norm. To unpack the norms further, we decided to use a video from a fourth grade math class to spark a conversation. Students were asked to watch the video and look for evidence of the norms that we created. They raised their hands as they noticed the students in the video following our co-constructed norms and we paused to talk about what students saw and heard. Immediately, a student raised his hand to point out how all of the fourth graders were participating in the discussion. Then, another classmate noticed that the environment was safe and judgement-free because two brave fourth-graders disagreed with the rest of the class regarding the math problem in discussion and their classmates listened respectfully.
Reflecting on what we observed in the video allowed us to develop specific moves to use during group work. The students saw how discussion framing such as “I agree with _____ because” or “I disagree with _____ because” can be productive and non-threatening. Giving students the opportunity to unpack the norms through real evidence allowed them to make a deeper meaning of what our classroom expectations could look like. More importantly, one of the biggest takeaways was how calm the classroom environment was in the video, and how respectfully and positively the group discussions developed. This experience proved to be very beneficial for students.
We consistently reminded one another of what these norms are and how we created this collaborative environment. The norms afforded a safe environment for all students involved, offering a sense of support to learners, especially when students discuss ideas that may generate disagreement. There were also instances when students realized the norms were not being followed, which lead to changing their actions, through their own agency.
The norms we constructed hold all of us accountable: accountable to be mathematicians, take risks, and not be afraid to discuss misconceptions. In order to learn math, the classroom has to have an environment where students and teachers are willing to be outside of their comfort zone. We believe co-constructed norms are an essential step in developing such a learning environment.
How will you develop the norms in your classroom this year? How can you ensure that there is a student ownership over the norms and a shared understanding of what they mean?