The beginning of the year is an exciting time; one that offers us an opportunity to get to know our students. As we learn their interests, cultures, developing identities, and preferences we are simultaneously thinking about how we can create an equitable learning community that values and respects varied ideas, competencies, and contributions. A critical component of an inclusive classroom community is the development of norms.

Many of us remember the beginning of school as a time when teachers posted and explained their classroom rules. These rules were teacher-generated. Norms, on the other hand, are co-created by students and teachers, and describe “an agreement among members of a classroom or school about how they will treat one another.” (Borich, in Finley) These norms are agreed upon, tried out, and then discussed and revised as members interact with the norms and each other.

Norms should be responsive to our students’ current needs, identities, and beliefs. Norms specific to math class require a community that is prepared to work together, listen actively, and contribute ideas. There is a focus on respect for students’ thinking, acceptance of differences, and building on each child’s strengths. (More on the importance of equitable math learning communities here.)

Students enter our classrooms with varied past experiences, and differing beliefs and expectations. Some, especially those who have been historically marginalized, may not see themselves as having the potential to offer valuable ideas to their classmates. Their beliefs about math and math class can include “internalized negative stereotypes about their math abilities.” (Seda & Brown, p. 21.) Others, who have been historically privileged, may enter the classroom community with identities built on previous high status positions. Norms can counter such beliefs and send messages about what it means to be doers of mathematics and how to be resources for and learn from each other. Norms can foster equitable participation and support and promote autonomy, interdependence, and confidence. They can also disrupt both patterns of marginalization and privilege in the math classroom.

Here are some ideas for developing norms for your mathematics classroom, and for sustaining them throughout the year.

Build Norms from Students’ Ideas

Students enter our classrooms with preconceived notions of how math time will look and sound, so it’s important to begin by learning how they feel about math. Ask them to consider their math experiences, how they think of themselves as learners, and what it means to “do math.” You might ask them to imagine their ideal math class. Use their responses to get a feel for how students view themselves and each other as learners of mathematics. Their ideas may be sparse at first but it is important to develop and grow norms based on students’ existing identities and experiences. Here is one teacher’s reflection:

I asked my students to describe their ideal math class. To be able to work on class norms, I needed to know what their expectations and experiences were. It surprised me to find out how vulnerable they felt. It also astonished me that I was surprised by their vulnerability.

Once you’ve collected some data about how your students view math, hold a discussion informed by what you’ve learned, and begin a draft of your community norms. “Although you might initiate this discussion, you should draw on ideas from students since they are more likely to adhere to norms they generate themselves.” (Chval et. al., pp 48-49.) Pose questions such as:

  • What helps you learn math?
  • What can you do to help others learn math?
  • What makes you feel that your ideas are valuable?
  • How can you make others feel that their ideas are valuable?
  • What does it mean to be “smart” or “capable” in math?
  • What happens when we make mistakes in math?
  • What about doing math makes you feel joyful or happy?

Shows a first draft of one fourth grade classroom's norms

First draft of norms in a grade 4 classroom

Recording and Displaying the Norms

Many teachers write the norms on large poster paper so that they are easily visible and can be revised and referred to. Some teachers make copies of the current norms for students to have in their journals, create bookmarks for easy access, or place placards at small group tables and work areas. It is important to use kid friendly language that is concise and stated positively (e.g. “Listen with respect and interest” instead of “Don’t laugh or interrupt”). Keep your initial list of norms short and concise. Take time to discuss what a norm means, act it out, and/or talk about how it applies to individuals and to the entire class. Include pictures or photos that represent the norms to support emergent bilingual students. Norms can include commitments related to:

  • How we listen and respond to each other’s’ ideas
  • How we respect and are open to a variety of ideas
  • How we can advocate for ourselves
  • How mistakes are a part of learning
  • How we share ideas with words, tools, pictures
  • How we share and collaborate in partnerships or small groups
  • How we are expected to explain our thinking
  • How we encourage each other to speak and connect ideas

 Norms from a grade 4 multilingual classroom

In this 4th grade, half of the class is comprised of multilingual students whose first language is Spanish. The class began by describing the things they do in math class. The teacher would build on these statements over time.
Norms from a grade 2 classroom

Norms from a grade 2 classroom

Using Shared Experiences to Reflect on and Expand the Norms

If your students have not had an opportunity to work with a partner or participate in a whole-class discussion, it could be challenging to write norms about those situations. During the first few days of school, your students will work with others, explore materials, and take part in discussions. Take advantage of those experiences to discuss what is working well for them as individuals and for the class. Spend a few minutes after a new activity to share how the experience felt. For example, after engaging her second graders in Quick Images, a teacher asked the class about the short Classroom Routine.

Some students were quite excited by this Classroom Routine. Others voiced anxiety about knowing the picture would disappear before they knew the answer. Others shared that it made them nervous to see lots of hands waving before they were done thinking. We talked about how they’ll always get to see the image three times and revise their thinking. I also shared that we’ll be doing this activity a lot this year, so they’ll get lots of practice with it. Finally, we talked about ways to share our thinking and excitement without making our classmates anxious. We added “give people time to think” and “use a quiet thumb” to our Norms poster.

Maintaining and Sustaining Norms

Class norms are “living documents” which deserve attention all year long. Look for examples of student behaviors that can be highlighted as the community makes sense of and expands on the norms. Ask students to share specific examples of how the norms are supporting their learning, and take time to celebrate those successes. Pause when there is evidence that a new norm is needed or an old norm needs revisiting. Some teachers use a new color on their poster, to show revisions. Others ask students to write examples of how they are interacting with the norms on stick-on notes, and then add those to the poster to offer an interactive ongoing connection. Questions to pose over time might include:

  • Is there a norm you don’t yet understand?
  • Is there a norm that you are still working on?
  • Is there a norm that our class is really good at? One that we need to work on?
  • Which is your favorite norm and why?
  • Is there a norm that you made use of today? How?

In addition to reflecting as a class, and as individual learners, it is also important to reflect on your norms, as a teacher. Are you seeing the impact of norms in your classroom? In what ways? Are you seeing more equitable participation? Are students broadening their sense of what mathematics is and who can do it? Have you seen shifts in students’ perceptions of math status in the classroom? Students who display more confidence and agency in their math learning? What if you are not seeing such impacts?

I found it useful to be transparent with students about what I was noticing and the decisions I was making. For example, when I changed talk partners, I talked with students about wanting to give them more opportunity to learn with and from others, one of our math norms.

Conclusion

As we begin the school year, our goal is creating an equitable mathematics learning community that promotes equal status interactions. An important aspect of this is co-creating, practicing, and establishing clear, actionable norms that help foster mathematical learning and equitable participation. Our norms send messages about what mathematics is and what it means to be mathematically “capable.” They can promote both autonomy and interdependence, and support teachers as they work with students to “disrupt or eliminate, rather than perpetuate, negative images of what it means to learn mathematics, and beliefs about who can learn mathematics.” (Aguirre, et al, p. 10.)

Note: Investigations 3 builds explicit opportunities for developing math norms into the curriculum. The next blog will provide and discuss examples at each grade level.

References

Aguirre, J., Mayfield-Ingram, K., & Martin, D. B. (2013). The impact of identity in K-8 mathematics. National Council of Teachers of Mathematics.

Chval, K. Smith, E., Trigos-Carillo, L. & Pinnow, Rachel. (2021). Teaching Math to Multilingual Students Grades K-8: Positioning English Learners for Success. Corwin.

Finley, T. (2014). The Science Behind Classroom Norming. https://www.edutopia.org/blog/establishing-classroom-norms-todd-finley

Seda, P. & Brown, K. (2021.) Choosing to See: A Framework for Equity in the Math Classroom. Dave Burgess Consulting, Inc.

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Tag(s): classroom community | classroom culture | Equity | norms |