Book: Mathematical discourse that breaks barriers and creates space for marginalized learners
Cultural Narratives and Status Hierarchies
Tools for Identifying and Disrupting Inequity in Mathematics Classroom Interaction
Mathematical Discourse that Breaks Barriers and Creates Space for Marginalized Learners
Authors: Niral Shah and Sandra Crespo
ISBN: 9789463512121
Publisher: Brill
Print Publication Date: 14 Jun 2018
DOI: https://doi.org/10.1163/9789463512121_002
Pg 23
…the more students talk in rich ways, the more they learn (Lampert, 1990; O’Connor, 1998)
One lens is the sociological concept of status generalization, which refers to expectations of competence, based on status characteristics deemed valuable by society writ large (Cohen, 1994).
Building on the theoretical lens of status generalization, we also consider the broader discourses and cultural narratives that mediate the production of local status hierarchies. In
We use the dual lenses of status generalization and cultural narratives to analyze how status hierarchies can operate even in a classroom with very young children.
STATUS HIERARCHIES AND GENERALIZATIONS
In the field of sociology, the theory of status generalization has been used to research social inequities in various contexts (e.g., playground, jury room, and work groups) and grain sizes (see Webster & Foschi, 1988). The theory contends that status generalizations are made in relation to characteristics associated with social advantage and cultural preference.
Status generalization theory explains patterns of inequitable interaction by proposing that certain status characteristics create hierarchies of higher and lower expectations for individuals. This, in turn, affects how people participate and contribute, thereby reinforcing status hierarchies (Cohen, 1994; Webster & Foschi, 1988).
This research formed the basis of Complex Instruction (CI), a pedagogical approach designed to disrupt status hierarchies in classroom interactions (Cohen, 1994; Crespo & Featherstone, 2013; Jilk, 2016). In part, the success of CI lies in its recognition that classroom interactions occur in a larger social context, which influences how teachers perceive their students and how students perceive their classmates (Cohen & Lotan, 1997).
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CULTURAL NARRATIVES
Local negotiations over status in social spaces like classrooms should be understood in relation to broader cultural narratives that circulate in society. All human cultures construct storylines that facilitate people’s sense making about the world around them (McAdams, 2013). Regardless of their validity, these narratives come to constitute a society’s “common sense,” or what is taken to be “true” about people and the relations between them (cf. Foucault, 1972). Cultural narratives are not only ideological in character, they materialize in everyday social interaction as they are invoked in discourse.
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Importantly, cultural narratives structure, but do not determine, social interactions.
In education there exists a variety of cultural narratives. For example, there is the idea that some students are innately more “gifted” than other students— that there are “fast” kids and “slow” kids (cf. Horn, 2007).
Overall, cultural narratives exist about subject areas like mathematics, as well as about social identities (e.g., race, gender, and language proficiency). These narratives comprise the discursive context within which local teaching and learning interactions occur.
STATUS AND CULTURAL NARRATIVES IN MS. KELLY’S CLASSROOM
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…we argue that the criteria for being a “model” student were narrowly construed. That is, the ways a student could be defined as “model” were limited. Second, we argue that being “model” in Ms. Kelly’s classroom revolved around three themes that further exacerbated status hierarchies in the classroom: (1) control; (2) competitiveness; and (3) language proficiency.
Control
A dominant narrative in education is that “good” classrooms are ones where the teacher is in control of the lesson and student participation.
pg 28 The lesson follows the “flow” predetermined in the lesson plan, and students speak and act only in ways solicited and authorized by the teacher. Indeed, the “I do, we do, you do” structure of the lesson, also, may have contributed to the centralization of control with Ms. Kelly. Students listen and wait for the teacher’s instructions, and respond to teacher questions with single “yes” and “no” answers. “Model” participation is publicly praised (“They should still be in a pile, like Silvia and Beatriz and Carlos have them in a pile”). When students are sent to work independently, the teacher circulates while continually reminding students to line up the strips at the bottom of their papers to ensure correct ordering of the strips.
…we did find that many different students in the class were afforded opportunities to participate in the whole-class discussion. This suggests that the teacher was interested in engaging students in classroom discourse, rather than only lecturing at them. However, we also found that these opportunities were nearly always limited IRE-style sequences. Students were placed in the role of “filling in the blanks” of the teacher’s predetermined lesson script.
…In other words, student participation existed, but was heavily regulated by the teacher.
pg 29 In teacher-centered classrooms, teachers have considerable influence over how participation opportunities are distributed with respect to socially constructed identities, such as gender.
On two occasions during the lesson the teacher initiated a class-wide affirmation where students—if they had the correct answer—were directed to pat themselves on their backs and say, “Good job self.” Altogether, these discourse moves signal that right answers are valuable, and that students can accrue intellectual status in the eyes of their classmates and the teacher by being right. In effect, students needed to be right in order to be a “model” student.
Alternatively, wrong answers are met with imposing looks or leading questions from the teacher. Rather than opportunities for discussion and sense making, the implication is that wrong answers are hiccups to the lesson flow and must be uprooted.
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Ms. Kelly’s reactions to right and wrong answers reflect a dominant narrative in mathematics education that claims mathematics learning is centrally about the pursuit of right answers. While this view of mistakes and misconceptions is common in mathematics education, it conflicts with research on how people learn (Bransford, Brown, & Cocking, 2000; Smith, diSessa, & Roschelle, 1993), as well as a growing counter-narrative in mathematics education that values Dweck’s (2006) notion of growth mindset (see Boaler, 2013).
As a beginning teacher Ms. Kelly had less autonomy to pursue a more open-ended type of lesson. In fact, the school itself signaled control through the choice of scripted curricula and the requirement that both students and teachers wear uniforms. Understanding what is happening locally in the classroom must also be situated within this context.
Competitiveness
In addition to control, Ms. Kelly’s classroom was also organized around a culture of competitiveness. The kindergarteners in Ms. Kelly’s classroom were seated at round tables in groups of five or six. Though this set up suggests that the classroom may have been a collaborative space for learning, this particular lesson had been structured in ways that promoted competitive and individualistic classroom interactions.
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… She asked the class: “Who can tell me which strip is the shortest?” Students quickly raised their hands and competed for the teacher’s attention to be picked to answer her question. Clearly, the teacher could not pick all of the students.
…the chosen student, Joaquin, repeatedly does not produce the desired answers, and seems unsure as to how to correctly answer the teacher’s questions. He appears to change his answer each time the teacher repeats it back and questions it. While this is happening, Joaquin’s classmates keep their hands raised and compete with one another to be the teacher’s next pick. It is noteworthy that when one student is speaking, other students are permitted to have their hands raised, as if hoping that their classmates answer incorrectly so that they can have a turn answering the teacher’s question. Ms. Kelly does not ask students to lower their hands and listen to Joaquin.
Pg 32 The atmosphere of competitiveness in Ms. Kelly’s classroom reflects a more general narrative in education about schools being places where students compete for limited resources. Rather than collaborators, students are positioned as rivals for their teacher’s attention and approval. This narrative of “learning as competition” overlaps with another narrative pervasive in mathematics education: that speed is central to mathematical success. That is, it is commonly thought that mathematics learners should not only get the right answer, but they should get the right answer as quickly as possible (cf. Schoenfeld, 1988). The emphasis on speed fosters a classroom culture of competitiveness, where students attempt to accrue status by being publicly recognized as having the right answer before their classmates.
Parks (2009) has referred to this particular genre of teacher-student interactions as a “game show,” where students are expected to answer quickly and correctly. In this classroom, getting called on by the teacher before one’s classmates becomes desirable and high-status because only a few students get the opportunity to experience this public recognition of competence.
Language Proficiency
All of the students had proficiency in Spanish, but the teacher did not use their home language. To make vocabulary less of a barrier, the teacher could have used Spanish words like “pequeño” (small) and “grande” (large). Scholars have argued that too much emphasis is placed on vocabulary—as opposed to mathematical sense making and engagement in mathematical practices— in the mathematics education of emerging bilingual students (see Moschkovich, 2013). Leveraging this linguistic resource might have mitigated both the linguistic challenges of the lesson and status hierarchies around language proficiency.
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In the transcript presented earlier involving Joaquin, Ms. Kelly made a point of clarifying whether Joaquin understood what the word “shortest” means. This seems to be a very reasonable teacher move because all of Ms. Kelly’s students were learning English as an additional language. However, using the lens of status generalizations in this particular exchange, we can also see that Joaquin’s mathematical competence and English proficiency were both called into question.
DISCUSSION AND IMPLICATIONS
Much of the literature on status hierarchies in mathematics classrooms has focused on small cooperative groups. In part, this is due to the relatively substantial body of work on Complex Instruction, which emphasizes group work (e.g., Featherstone et al., 2011; Nasir, Cabana, Shreve, Woodbury, & Louie, 2014).
In Ms. Kelly’s classroom the “model” student is compliant, attentive, answers correctly, and follows rules. “Non-model” students provide wrong answers and do not follow directions. Because these categories are binary and oppositional, they serve to sort students and foster a learning environment that is more competitive than collaborative.
Disrupting: Control
One strategy Ms. Kelly could consider is to use a version of the EQUIP approach employed here to study the amount; distribution, and length of participation in her classroom (see Shah et al., 2016).
[The EQUIP Program is a three-part intervention method for working with antisocial or behavior disordered adolescents. The EQUIP program combines the use of peer-helping group methods with cognitive development and skills training intended to motivate and teach youth to think and act responsibly]
Implementing talk moves that foster student discourse (e.g., turn-and-talks, “say more”, and “who can repeat?”) might also help (see Chapin et al., 2009).
Another suggestion to disrupt the narrative of control—while considering contextual constraints—is to identify and plan for opportunities/spaces for mathematical disagreement.
Disrupting: Competitiveness
pg 35… implement new norms for soliciting student participation. Rather than students participating individually, Ms. Kelly might ask students to come up with consensus answers in their groups.This would serve to slow down the rapid pattern of IRE sequences, and also would address Ms. Kelly’s concern that her students “think before shouting out answers.”
A relevant strategy from Complex Instruction (CI) is to consider how tasks can be constructed as “group-worthy” (Lotan, 2003). The physical materials (e.g., manipulatives) used to support lessons can serve as tools for promoting collaborative learning.
CONCLUSION
Inequities in the form of status hierarchies can have substantial impact on students’ opportunities to learn. For that reason, it is important that teachers be constantly vigilant for issues of status in their classrooms. However, deconstructing such inequities is a complex endeavor because they operate at multiple levels…Equitable teaching poses a considerable challenge that should not be underestimated.