Lesson Study, Cycle 3: Literature Synthesis

How can we empower all students to see the value in their own thinking and take initiative in the collective learning of their class by sharing their ideas fearlessly and voluntarily?

I am a Humanities teacher. In high school, I did well in math classes but never loved it, and in college I took my required credits before moving on to classes in the realms of literature, history, philosophy, and religious studies. However, for this third lesson study cycle, I asked to be in an interdisciplinary group and found myself working closely with two math teachers to design a lesson for a 9th grade geometry class. This experience has driven home the importance of understanding students’ experiences outside of my own classroom, and the insight that can come from seeing how equitable teaching practices are used to help students access a wide range of content. In particular, this lesson study cycle pushed me to look more closely at students’ status in my classroom. Many students walk into their math class each fall with a strong sense of whether or not they are a “math person.” These preconceptions play into students’ relationships to each other as well as to the content within the math classroom.

In an effort to break down these hierarchies within the math classroom, my lesson study team and I focused our research on ways that we might help students share their ideas more fearlessly and voluntarily. To that end, we also began to use the language of helping students “see themselves as mathematicians”—an idea that can translate into any classroom as students begin to see themselves as historians and poets and social critics and chemists and more. In particular, this research brought out three themes for our teaching practices:

1. Identifying and utilizing both formal and informal roles in the classroom
2. Helping students practice their empathy-building skills
3. Positioning ourselves (as teachers) as community members who disrupt patterns of academic status in the classroom and actively seek to uphold more equitable structures

Identifying and Utilizing Both Formal and Informal Roles in the Classroom

One of the most tangible takeaways from this research was the importance of group roles—both formal and informal—within the classroom. As Boaler (2006) writes, well-utilized group roles are part of a “complex interconnected system that operate[s] in each classroom, a system in which everyone [has] something important to do.” One way to begin creating such a system is to build students’ understanding of the diverse roles we all take on when working collaboratively. This involves broadening our understanding of “group roles” to include not only “task roles,” but also “social-emotional roles” and “negative group roles” (Dugas, 2017). As students’ fluency with these roles increases, they gain the language to describe not only how they and their peers mostly often choose to participate, but also how those choices affect the group they are working with and how they might leverage their choices to build a stronger community (Dugas, 2017).

Part of what makes Dugas’ (2017) expansion of groups roles effective is that it includes actions that are often informal roles students—and all collaborators—step into. In this act of naming, teachers can formalize roles that, while often unnamed and informal, can have a deep effect on the culture and learning environment of a classroom. One particularly salient example is that of the “quiet” student. While students may not be explicitly assigned the job of being a “quiet group member,” this role is one that is often given to them and reinforced by peer and teacher actions and reactions (Fink, 2019).^[1] As Fink shows, students who have been informally assigned as “quiet” can be seen by peers as a “non-contributing silent beneficiary of learning” or as “fragile, sensitive, and less knowledgeable.” Teachers, however, can begin to disrupt these patterns by identifying and naming them. Similarly, Solorzano & Delgado (2001) not only identify behaviors that often define “problem” students, but also put these behaviors into context by acknowledging their relationship to “transformative resistance.” Transformative resistance is a critical behavior social justice-minded teachers seek to instill in their students, and understanding the relationship between this and other student behaviors and attitudes can help teachers effectively push students forward instead of simply writing them off as unwilling to learn or change. These relationships can be seen in the graph below:

In the same way that Fink’s (2019) work offers teachers tools for identifying and uplifting quiet participation, Solorzano & Delgado (2001) offer teachers a framework for understanding defiant behaviours in students, all of which is relevant to the quote from Boaler (2006) that I referenced earlier. These behaviors and outcomes do not exist in a vacuum—they create a “complex system” that is continually co-created and upheld by the community of learners. To use a term coined by Boaler (2006), teachers can utilize “relational equity” as a way to fight the negative and prescriptive co-constructions.

Helping Students Practice Their Empathy-Building Skills

One critical aspect of “relational equity” that carries through a significant amount of our research for this lesson study is the facilitation of empathy-building work.While Boaler (2006) doesn’t use the term “empathy” in “How a Detracked Mathematics Approach Promoted Respect, Responsibility, and High Achievement,” she references students’ appreciation for diverse “insights, methods, and perspectives that different students offered in the collective solving of problems.” This appreciation for others’ perspectives builds student empathy that is rooted not in pity but in respect for each other as contributing members of a learning community. Similarly, Fink’s (2019) work highlights a lack of perspective-taking on the part of “quiet” students’ peers, and Dugas’ (2017) work is rooted in social-emotional learning, which explicitly prioritizes the skill of “understanding and empathizing with others.”

But empathy-building in social justice pedagogy must extend beyond students’ most immediate relationships and into their worldview. Or, to put these two types of empathy-building in conversation with each other, their peer-to-peer empathy must be used as a foundation for building a more empathetic understanding of the world. The centrality of this is reinforced by Leonard, et al. (2010) in their discussion of the “nuances and complexities” of social justice mathematics—particularly in the case of a math class in the Midwest studying the differences in resource allocation between neighborhoods in South Central LA. In this lesson, students analyzed data and found that while community centers and movie theaters were underrepresented in this area (they found none of either), liquor stores were overrepresented. Although the lesson “attended to cultural relevance, social justice, and rigorous mathematics,” it also reinforced stereotypical views of people in South Central LA for some students who attributed this allocation of resources to the desires of the population rather than to systemic issues (Leonard, et al., 2010).

This lesson is a prime example of the ways in which empathy building within a class can be disconnected from students’ empathy-building and social critiques in a broader context. Leonard, et al. (2010) offer a couple of tactics for addressing this in similar projects, such as using a context closer to home (in this case, using examples from the students’ own Midwestern city), or providing examples of students in areas like South Central LA who worked to get rid of liquor stores. These tactics present two different ways of generalizing students’ empathy. The first simply asks students to work within a more personal context. Sometimes, this alone will help students see beyond stereotypes by offering them the opportunity to bring their own experiences to the work. It is also important, however, for students to build empathy for those outside their own communities. This can be done by providing empowering examples like the one mentioned above. In this case, students are given role models within communities they may have otherwise seen as full of people who just “want to… drink!” (Leonard, et al., 2010). Both of these tactics can be generalized for use in any project where teachers are seeking to extend students’ empathy building to community members beyond the classroom.

Positioning Ourselves (as Teachers) as Community Members Who Disrupt Patterns of Academic Status in the Classroom and Actively Seek to Uphold More Equitable Structures

That final note—that these tactics are meant to be adapted by teachers for use in their own classrooms—highlights something that has served as a sort of undercurrent for this lesson study cycle and this entire year: that being a teacher involves recognizing the unique opportunity to effect change and shape a classroom culture and community. Leonard, et al.’s (2010) work helps us teachers see where we might push students’ empathy. Boaler’s (2006) work helps us see how we might cultivate a sense of collective responsibility and respect in our classrooms. Dugas’ (2017) work helps us see how linguistic tools can help students take charge of their classroom community. And while Fink’s (2019) work offers a warning of how teachers might reinforce students’ status in the classroom, she also offers a hopeful view of teachers’ efficacy in the classroom, reminding us that “while teachers alone cannot fix these historical injustices, they can disrupt patterns of marginalization by supporting more equitable interactions among students.”

It’s here that I am struck by the effect lesson study has had on my view of my own teaching practice. Undergoing a months-long process of research, revision, and collaboration to design a single lesson is no small task, and engaging in such a process requires a foundational understanding that our small actions, as teachers, can have a large effect on our students and the classroom community. Within that idea, however, there rests another, perhaps even more foundational thought—that we, as teachers, have the power and responsibility to effect change in our students’ lives. Having students take collective responsibility for our community does not mean that we, as teachers, simply put our hands up and let things play out. We must actively cultivate a community of respect, care, and growth. We must lead by showing students what it can mean, as I said at the beginning of this paper, to be “community members who disrupt patterns of academic status in the classroom and actively seek to uphold more equitable structures.”

Lesson study has given me a lens through which to understand my efficacy as a teacher, and for that I’m grateful. I hope to continue to step into this responsibility in my classroom, and, as Gutiérrez (2016) reminds us, with colleagues. I hope to find ways to employ creative insubordination and push back on dehumanizing language and frameworks (Gutiérrez, 2016).  I hope to help those around me—in and out of my classroom—continue to discover new ways to love and care for each other. And I hope to empower my students to help create a world that reflects that same love and care more deeply each day.

Reference List

Boaler, J. (2006). How a Detracked Mathematics Approach Promoted Respect, Responsibility, and High Achievement. Theory Into Practice, 45(1), 40–46. https://doi.org/10.1207/s15430421tip4501_6

Dugas, D. (2017). Group Dynamics and Individual Roles: A Differentiated Approach to Social-Emotional Learning. Clearing House, 90(2), 41–47. https://doi.org/10.1080/00098655.2016.1256156 

Fink, H. (2019). Co-Constructing “Quiet” through Peer Interactions: Understanding “Quiet” Participation in a Small-Group Math Task. In North American Chapter of the International Group for the Psychology of Mathematics Education. North American Chapter of the International Group for the Psychology of Mathematics Education. https://eric.ed.gov/?id=ED606904 

Gutiérrez, R. (2016). Strategies for Creative Insubordination in Mathematics Teaching. Teaching for Excellence and Equity in Mathematics, 7(1), 52–60.

Leonard, J., Brooks, W., Barnes-Johnson, J., Berry III, R. Q. (2010). The Nuances and Complexities of Teaching Mathematics for Cultural Relevance and Social Justice. Journal of Teacher Education, 61(3), 261–270. https://doi.org/10.1177/0022487109359927 

Solorzano, D. G., & Delgado Bernal, D. (2001). Examining Transformational Resistance Through a Critical Race and LatCrit Theory Framework: Chicana and Chicano Students in an Urban Context. Urban Education, 36(3), 308–342.