Tl;dr — Our classrooms are plagued with societal expectations which oppress certain students’ opportunities to learn and build an identity as a statistician/data scientist. Our students deserve more mindful approaches to group work and methods that create equitable spaces for everyone.
If you are interested, I’m holding a Birds of a Feather discussion surrounding this topic at JSM on Wednesday, August 10 at 12:30. If you can make it, I would love to talk about this with you! If you can’t make it and are interested in discussing these ideas or have experiences to share, I’d love to hear from you!
“The most significant narratives about oneself are often those that imply one’s memberships in, or exclusions from, various communities.”Sfard & Prusak (2005)
My Journey with Group Work
Like many of you, I’ve taught with “group work” for quite some time. During graduate school, I routinely used group work at least once a week for a full-class activity. Student groups were randomly selected, so no student was favored more by the selection process than any other. While watching students work, I noticed that some students would dominate the conversation while others appeared to sit silently by. To be completely honest, I would often label the students who dominated the conversation, as “good students,” and those who sat silently as “loafers.”
My group work continued to have a similar structure throughout graduate school. It wasn’t until my final year that I was forced to reconsider how I structured group work in my classroom. That year, two events occurred, (1) I took a graduate-level course that required group work, and (2) a mathematics education researcher presented results to our seminar displaying gendered interactions in a group setting.
For the previous five years, I had never experienced group work in any of my graduate courses. Advanced Mathematical Statistics, however, changed that. In that course, the instructor would regularly present our class with a set of problems and have students work in groups to tackle a specific problem and then share their solutions on the board. It was in these groups that I remembered what it feels like (to me) to be a woman in mathematics. In our course, there were two individuals who identified as women and six individuals who identified as men. Thus, for any selection of three students, I found myself working with a man. These were not always unfavorable experiences, but if I was in a group with a man who shared his ideas openly, I would provide him with unquestioned authority in how we should solve the problem at hand. In this particular scenario, I would rarely share my own ideas.
The mathematics education group at Montana State University has a biweekly seminar where researchers share the current projects they are working on. At one such seminar, Derek Williams, a mathematics educator, shared some preliminary results of his study on pre-service teachers’ mathematical thinking. In Derek’s study, they recorded the interactions of three heterogendered pairs of students while working on problems covering concepts of logarithms. Across all three pairs of students, the recordings showed that the ideas of the men were readily accepted, whereas the women only found their ideas accepted if they aligned with their partner’s thinking.
These experiences forced me to reconcile with who I had labeled a “good” student. I embarked on a mission to learn more about the dynamics of group interactions, only to find a wealth of research from mathematics education, specifically focused on inequitable group collaborations.
Student Identity & Discourse in the Classroom
A student’s disposition toward a discipline is a major factor in determining their success (NCTM, 2000, p. 131). In our classrooms, we hope to create confident and autonomous learners. Yet, becoming a confident learner hinges on students developing positive beliefs—identities—about themselves as learners and doers of statistics. From various theoretical perspectives (Gee, 2001; Holland, Lachicotte, Skinner & Cain, 1998; Lave & Wenger, 1991), researchers have posited that in mathematics classrooms, students learn more than mathematics. Rather, students learn who they are and what they can and cannot do “with respect to the norms, practices, and modes of interaction” (Bishop, 2012, p. 36). Students’ identities are “dynamically negotiated” and represent a synthesis of who they have learned to be through interactions with others (Bishop, 2012, p. 38).
Sfard and Prusak have used classroom discourse as a window into the formation and enactment of students’ identities. Every instance of discourse in a mathematics classroom affords students the opportunity to negotiate their identities and respective social positions (Davies & Harre, 2001; Gee, 2014; Sfard, 2001; Wetherell, 2001). Through these discursive actions, a student becomes recognized in a certain way and constructs narratives about themselves as learners.
Power & Authority in the Classroom
Although statistics education strongly advocates for active learning, research has shown that group collaborations fall prey to issues of status—the distribution of power among peers (Chohen, Lotan & Catanzarite, 1990; King, 1993). Fights over who gets to speak and whose words are recognized are indicative of power and status (Johnson, 2002). Students with higher status have greater intellectual authority, are positioned as credible sources of information, gain and maintain the conversational floor, and have their ideas attended to. Langer-Osuna and colleagues have documented how power and authority are negotiated among groups of students and are directly connected with how responsibilities for shared work are distributed (Engle et al., 2014; Langer-Osuna, 2016). Students as young as fifth grade have been seen to compete for intellectual and directive authority, which largely determine whose ideas are taken up and how effort is distributed among partners.
One of the first reports of this type of power is the story of Brianna and Kofi (Langer-Osuna, 2011). Brianna was a high school algebra student who took on an early leadership role in her group. However, less than halfway through the project, “group members increasingly positioned Brianna as bossy, claiming that Brianna was overstepping her authority” (p. 212). More specifically, two boys positioned themselves as a unified front against Brianna’s bossiness, repeatedly interrupting Brianna and berating her for “being bossy.” Simultaneously, these boys actively positioned Kofi—a student initially uninvolved in the group—as their desired leader by asserting his ideas deserved attention and seeking out help from Kofi.
In a subsequent study, Langer-Osuna (2016) witnessed Jerome, a young African American identifying boy, struggle to have his ideas valued intellectually and have the opportunity to lead his group. Jerome’s partner, Ana, a Latina-identifying student, however, was able to garner unrivaled intellectual and directive authority—having nearly all her ideas taken up and constantly issuing directives to Jerome. Unlike previous studies, Langer-Osuna pays particular attention to the role of the teacher in how the interactions between Jerome and Ana unfolded. During class, the teacher reprimanded Jerome for being “off task” ten times, whereas Anna was applauded for being a “good student” twice. This authoritative positioning of Ana with social power over Jerome was further manifested by the teacher’s reluctance to critique Ana’s ideas, implicitly “suggesting to Jerome that Ana had the intellectual authority in the pair” (p. 122).
These studies might suggest that inequitable group interactions should be easy to see. Yet, there are many ways in which group collaborations can be inequitable without students berating one another or telling each other what to do (Theobold & Williams, 2022). For example, Lakoff (1973) suggests there is one syntactic rule in English a woman will use in conversations more than a man — tag-question formation. A “tag-question” lies between an outright statement and a yes or no question, being “less assertive than the former, but more confident than the latter” (p. 54). We know that women tend to exhibit less confidence in mathematics (Fennema & Sherman, 1978; Ellis et al., 2016; Steele & Ambady, 2006), so it seems reasonable to assume that a woman may rarely make statements about her thinking when engaging in classroom discourse.
Classrooms as a Microcosm of Society
Gholson and Martin (2020) suggest oppression admits a number of manifestations, some more visible than others. Classrooms are not apolitical. Rather, they are microcosms of the historical and political contexts of society. Historically, White, male students have been positioned with power both in society and in the mathematics classroom (Webb & Kenderski, 1985; Wilkinson, Lindow & Chiang, 1985). For decades we have read about the dwindling numbers of women and people of color in mathematics. Yet, these conversations have only recently begun to acknowledge how political contexts seep into the classroom. A discursive lens has allowed us to see how these subservient positions manifest in classrooms, where women and people of color do not have access to the conversational floor, are not able to decide what is correct, and are not seen to contribute meritorious ideas.
Tools for Facilitating Equitable Collaborations
Through reading research in education about group dynamics and reflecting on my own classroom, I have developed a set of four tools that I have found to aid in creating equitable group collaborations.
- Recognize your authority in interactions with students.
The language we use is directly related to the identities our students build in the classroom. I have long felt that reflexivity is the next superpower. If we want our students to build positive identities around statistics, we need to create a welcoming environment for every student. Think to yourself—do I respond differently to questions/comments posed by students of different identities (e.g., race, ethnicity, gender, etc.)? When a student asks a “dumb” question, what tone do I use? Do I use the same tone for everyone? Some of these questions may be difficult to answer on your own. This is a great place to bring a colleague into your classroom! Yes, that might sound scary, but wouldn’t you like to know how you could build a stronger classroom community?
I have also grown to appreciate the authority I have when responding to student ideas in the classroom. When we applaud a student’s thinking, we build their intellectual authority. We can use this power “for good” when we see inequitable group collaborations unfolding in our classroom. Assigning competence is a public statement by a teacher which specifically recognizes the intellectual contribution a student made to the group task (Cohen & Lotan, 1995).
- Create group-worthy tasks!
A group-worthy task (Lotan, 2003) is a task that is specifically designed to require multiple perspectives. Specifically, these tasks are (1) open-ended and complex, (2) have multiple opportunities to demonstrate intellectual competence, (3) have discipline-based intellectually important content, (4) require positive interdependence and individual accountability, and (5) include clear criteria for evaluation of the group’s product.
- Use cooperative learning to structure participation.
Cooperative learning is where each student in a group takes on a specific role. Each role has specific tasks associated with it, which are necessary for the group to reach a final product. In my classroom, I have students rotate through a set of four roles once a week for four weeks. I believe circulating these roles prevents students from getting trapped in subservient positions solely taking notes or being the proofreader. Moreover, these roles make all the labor associated with effective collaborations visible.
Manages team progress through the task
– Leads discussion
– Makes sure everyone understands the task
– Checks in with group members
– Keeps the group moving forward
|Recorder / Reporter|
Manages in-class report
– Responsible for organizing and recording answers to the assignment during discussions
– Compiles a summary of the solutions discussed
– Sends summary to report editor
Manages out-of-class report
– Asks professor team questions
– Reviews draft summary provided by reporter
– Solicits feedback from the team
– Shares summary with the team
– Submits final assignment
Manages team participation
– Encourages participation
– Enforces norms
– Brings conversation back if it deviates
– Substitutes for absent roles
- Setting classroom discourse norms.
I started setting classroom norms two years ago and I won’t ever go back. I borrowed elements of my classroom norms from what we used when teaching Safe Zone workshops at Montana State University, elements from complex instruction, and some from my own experiences. I state these expectations at the beginning of every class and I revisit them throughout the quarter. More importantly, I specifically have the Team Captain of each group enforce the norms required for our classroom.
My classroom norms are:
- Zero tolerance policy for racism, sexism, homophobia, transphobia, ageism, and ableism
- Do not make generalizations – Use “I” statements
- Respect one another
- Intent and impact both matter
- Take space and make space
- Embrace discomfort
- Make decisions by consensus
- Helping your peers means explaining your thinking, not giving the answers, or doing the work for others.
- Any statement you make must be backed with justification.
These tools are not an exhaustive list of the possibilities, nor will they “fix” all of the power dynamic issues you might come across. Rather, they are great steppingstones to get started with the hard work of creating equitable group spaces for every student.
Contributing author Allison Theobold is an Assistant Professor in the Statistics Department at Cal Poly.
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