“The space has to be a sort of aquarium that mirrors the ideas, values, attitudes, and cultures of the people who live in it.” – Loris Malaguzzi, The Hundred Languages of Children.
The start of the school year is an exciting time for teachers, children, and families. I remember the joy of putting together an inviting, student-centered room. Early in my teaching career this meant shopping for folders, name tags, borders and cutouts, and countless hours designing bulletin boards and displays. Later, impacted by research I read about student-centered classrooms, I would make a few welcoming displays but leave wall and shelf space mostly empty, for students to design and fill with their ideas, thinking, interests and work.
The Investigations curriculum states that “creating supportive and productive learning environments involves deciding how to set up the classroom, how to make math tools readily available, and how to establish routines and expectations.” (TERC, p. 29) Aguirre et. al. challenge us to also be thinking about ways to distribute math authority among students, teachers, and text, and to encourage student-to-student interaction and broad-based participation (p. 47). And Godfrey reminds us that “No student should be asked to leave any part of who they are at the door. This includes race, languages, and ways of knowing, as well as the family and community knowledge and skills students bring with them.” (2021)
So, how do we create a classroom that says to students YOU are welcome here and this is OUR room and we will co-design it? How can the design of our room, the displays and seating arrangements, promote the distribution of math authority, equitable participation, and respect for different learners? How do we ensure that students see themselves in the classroom?
In Building Thinking Classrooms in Mathematics, Liljedahl summarizes research by Cobb, Wood, and Yackel (1991) that describes how “the normative structures that permeate classrooms in North America, and around the world, are so robust, and so entrenched, that they transcend the idea of classroom norms.” (p. 11) These institutional norms impact how we think classrooms should look and function. Even though we have new technology, desks, whiteboards, etc. we still see the “foundational structure of schools” (p. 12)—forward-facing, teacher-focused seating arrangements—in many classrooms. To be responsive to our students, we need to consider the ways the physical environment can disrupt norms that interfere with learning. As we make decisions about classroom setup, it’s important to encourage productive movement around the room and to support students in recognizing and calling on their individual and cultural strengths. When we design our classroom spaces with these considerations in mind, we support students’ agency and feelings of belonging.
In thinking specifically about a classroom setup that supports a math class focused on discourse and sense-making, there are some questions to consider:
In what ways does the physical space encourage individual, partner, and small group work? Collaboration with peers? Productive whole group discussions?
“It is important to consider that students in an Investigations classroom work individually, in partners, small groups and as a whole class.” (TERC, p. 29) Sometimes students are all working on the same thing; at other times, they are choosing which activity to work on, for how long, and in what order (i.e. Math Workshop). If we value an environment that encourages students to share and respond to mathematical ideas and to each other, to make responsible choices, and to work productively, we need to consider how the physical layout of the room fosters this kind of collaboration and participation.
A classroom that allows students to easily see and hear each other takes into account where desks, tables and chairs are placed. There should be spaces that allow students to work in pairs and small groups, as well as spaces where students can work independently or privately. Clusters of desks or tables allow the classroom space to be used for various purposes. They can serve as designated seating for students or as shared common space, for multiple uses. Some classrooms use “office spaces” when students are working alone or with a partner—open spaces around the room that students can choose from depending on their needs and preferences for a working environment. The use of clipboards, white boards, or non-permanent vertical spaces allow students to move and work in different ways.
Bringing the whole class together for discussions is an important part of creating a classroom community. We want to create a space that is conducive to conversation, where students can see each others’ faces (rather than the backs of heads). Some classrooms have a rug or open area where students can easily sit in a circle or horseshoe arrangement. Some teachers establish protocols for moving chairs so that students can see and hear each other; others facilitate discussions with students at desks or tables. Ultimately, “students should sit in such a way, so that everyone is focused on the discussion and can see each other and any work that is being shared.” (TERC, p. 30) Students should be able to “turn and talk” to a classmate, reach and use materials, and respond and connect to one another. This encourages student-to-student interactions, disrupting the teacher-student-teacher interaction patterns that can contribute to inequitable participation. It can also diminish students’ perceptions of the teacher as the sole authority in the classroom. The goal is to have a seating arrangement that decentralizes the teacher and invites students to speak and listen to each other respectfully and productively.
How does the physical arrangement of the classroom promote equal status, independence, and individual decision making (agency)? How does it help distribute math authority “among students, the teacher, and text”? (Aguirre, p. 47)
One thing to consider is where the teacher stands, sits, and displays tasks or student work. If the teacher is always the center of attention, this can contribute to the perception that they are the sole authority and the one responsible for carrying the work of classroom conversations. We can think about how to “de-front” the classroom by finding spaces where we can stand and sit with our students. If we are depending on teaching stations that incorporate technology, think about how to move among our students as we are sharing. A clicker can allow us to interact with the technology from different parts of the room and frees us from being in one place. Such moves are essential when challenging spaces of marginality since these are “practices that embrace student competencies, diminish status and value multiple mathematical contributions.” (Aguirre et. al. p. 43)
I always love it when someone comes into the classroom, and they have to search for me. My students love saying, “Oh, Ms. Wagner is over there on the floor with that group!” Or “She must be working at a table with another group.” When we gather for whole group discussions, I also am careful not to sit above my students but to take a place that lets them know we all are equal in this discussion.
Another aspect to consider is how students will access math materials. As the curriculum states, “All students benefit from being able to use materials to model and solve problems and explain their thinking. If materials are used only when someone is having difficulty, students can get the mistaken idea that using materials is a less sophisticated and less valued way of solving a problem or modeling a solution. Therefore, they should see how different people, including the teacher, use a variety of materials to solve the same problem.” (TERC, p. 31)
The more available materials are, the more likely students are to use them, so it’s important to think about where they will be stored and accessed, for example on students’ desks or on a classroom table or shelf, where students can retrieve them as needed. Students benefit from a visible organization, clear information about particular materials that are needed that day, and clear expectations about use and storage. All of this supports them in becoming responsible for selecting, using, and caring for the tools that will best support their thinking.
Most years, I organize my math materials, in labeled boxes, in a central place. But one year, after introducing the many math tools available (e.g. cubes, tiles, graph paper, dice), one student responded, “We are in fifth grade; we don’t need those things anymore!” Many students chimed in. I was struck by their perceptions about the use of tools. After that exchange, I realized I was probably not going to see anyone getting up to get tools! So the next day, I put baskets on every table, each with a variety of math tools. I told the class, “Today you have tools right at your table. Your group can decide when and how to use any of the tools in your basket. We will take a walk around to other tables in a bit to see how people used the tools.” As students worked, I noticed many curiously looking in their baskets and pulling out tools to consider in their work.
What messages are present about what it means to be a doer of mathematics?
As soon as students step into a classroom, they look for ways to connect to their new environment. The space sends messages to students and others regarding what we value in behavior and learning (Savage, 1999; Weinstein, 1992). We can think about how the environment helps us manage student interaction and behaviors, but also as an extra “teacher,” one that encourages and motivates students to learn about themselves and others (Strong-Wilson, pp. 40-47). We can draw from our students’ cultures, communities, and interests to fill the classroom with interesting and useful materials and resources that both support their math identities and the work of ambitious mathematics. Students should see on the walls documentation of their learning experiences including their questions, wonderings, conjectures and claims.
"The curriculum is not only what takes place in the classroom. What shows up on the walls is part of the curriculum. What *doesn't* show up on the walls is part of the curriculum." @MilnerHRich #edantiracism2021
— Educators for Antiracism (@EdAntiRacism) July 31, 2021
We can take a tour of our classrooms and take note of the displays, books, posters, pictures, student work and materials that are available. What do you notice about what is visible and what is missing? Some questions to consider:
- Whose work gets displayed (and whose does not)?
- Is there a variety of student work? Finished and in progress? Correct and in process?
- Can students choose what work they want to display?
- Are a variety of cultures and contributors to the mathematics community represented?
- How do displays mirror the cultural capital that your students bring to the class? How do they offer windows into the cultural knowledge of others?
- In what ways is the community in which your students live evident in the classroom environment?
Author and educator Mike Hopkins “urges teachers to forget about the way things have always been done and to visit museums, libraries, other schools, and colleagues’ classrooms to identify different ways of organizing learning space.” (Hopkins, in Shalaway)
We can foster an environment that is inclusive and responsive by beginning to examine the way our room is set up and observing and reflecting on how it is used by the class. Classroom routines and norms that inspire students to behave in equitable, powerful ways are connected to and impacted by the physical space. The design of our classroom environment sends messages about authority, identity and equitable engagement. As Lynne Godfrey reminds us, “Classrooms are microcosms of a larger society in which racism, power and privilege converge to empower some students and disenfranchise others.” (2021) As we reflect on and then reconceptualize how our classroom space is contributing to equitable participation and positive identities, we can move one step closer to our goal of more equitable learning communities.
Aguirre, J., Mayfield-Ingram, K., & Martin, D. B. (2013). The Impact of Identity in K-8 Mathematics. National Council of Teachers of Mathematics.
Cobb, Wood, & Yackel (1991). Analogies from the philosophy and sociology of science for understanding classroom life. Science Education, 75.
Godfrey, Lynne. (2021). Establishing an Equitable Learning Community in the Investigations Classroom. Retrieved from: https://investigations.terc.edu/establishing-an-equitable-learning-community-in-the-investigations-classroom/
Liljedahl, Peter. (2021). Building Thinking Classrooms in Mathematics. Corwin Press, Inc.
Malaguzzi, L. (1996). The Hundred Languages of Children: The Reggio Emilia Approach to Early Childhood Education. New Jersey: Ablex Publishing Corporation.
Savage, T. V. (1999). Teaching self-control through management and discipline. Boston: Allyn and Bacon.
Shalaway, Linda. Classroom Organization: The Physical Environment. Retrieved from: https://www.scholastic.com/teachers/articles/teaching-content/classroom-organization-physical-environment/
Strong-Wilson, T. & Ellis, J. (2009). Children and Place: Reggio Emilia’s Environment As Third Teacher. Theory Into Practice, pp. 40-47.
TERC. (2017). Implementing Investigations in Grade X. Investigations in Number, Data, and Space®, (3rd ed.). Savvas Learning Company.
Weinstein, C. S. (1992). Designing the instructional environment: Focus on seating. Series on Highly Effective Practices—Classroom Environment 5 Bloomington, IN: Proceedings of Selected Research and Development Presentations at the Convention of the Association for Educational Communications and Technology. (ERIC Document Reproduction Service No. ED 348 039) .
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