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Understanding Students’ Experiences asListeners During Mathematical DiscussionAllison B. Hintz aa University of Washington , Bothell, WashingtonPublished online: 02 Sep 2011.

To cite this article: Allison B. Hintz (2011) Understanding Students’ Experiences as Listeners DuringMathematical Discussion, Canadian Journal of Science, Mathematics and Technology Education, 11:3,261-272, DOI: 10.1080/14926156.2011.595883

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CANADIAN JOURNAL OF SCIENCE, MATHEMATICSAND TECHNOLOGY EDUCATION, 11(3), 261–272, 2011Copyright C© OISEISSN: 1492-6156 print / 1942-4051 onlineDOI: 10.1080/14926156.2011.595883

Understanding Students’ Experiences as Listeners DuringMathematical Discussion

Allison B. HintzUniversity of Washington, Bothell, Washington

Abstract: This study examined students’ experiences participating in mathematical discussion witha focus on listening. Beginning with a broad look at the demands all students may experience,this manuscript narrows upon the case study of one fourth-grade student’s experience as a listener.Analyses of the data revealed (a) students experience a range of mathematical and interactionaldemands as listeners during mathematical discussions, (b) listening is an important form of partic-ipation, and (c) students may take on the role of listener in order to mitigate the risks of sharingan error.

Resume: Cette etude se penche sur les experiences des etudiants qui participent a des discussionsen mathematiques, en particulier pour ce qui a trait a l’ecoute. L’article presente d’abord en termesgeneraux les situations susceptibles d’affecter tous les eleves, et concentre ensuite son attention surune etude de cas portant sur les experiences d’un eleve de quatrieme annee comme « personnequi ecoute ». L’analyse des donnees revele que : (a) les etudiants sont confrontes a toute une seried’exigences mathematiques et interactionnelles en tant qu’interlocuteurs au cours des discussionsen classe de mathematiques, (b) l’ecoute est une forme importante de participation, et (c) les elevesassument parfois un role d’ecoute dans le but d’eviter le risque de commettre une erreur.

In the past few decades, mathematics reform efforts in the United States have called for spe-cific changes in the mathematics classroom, particularly the creation of collaborative, discursive,inquiry-oriented, and student-centered learning environments (National Council of Teachers ofMathematics [NCTM], 1989, 1991, 2000). The value of inquiry-oriented approaches to teachingand learning mathematics has shown many positive outcomes mathematically and socially, suchas an increase in student participation, engagement, and positive identities in mathematics (e.g.,Boaler, 1997); student experiences with mathematics that more closely reflect the nature of thediscipline (e.g., Lampert, 1990); an increase in students’ development of conceptual understand-ing of the mathematics they are learning (e.g., Hiebert, et al, 1997); more equitable learningenvironments (Khisty & Chval, 2002; Moschkovich, 2007; Zevenbergen, 2000); and studentstaking higher levels of mathematics (e.g., Boaler & Staples, 2008).

These promising learning outcomes come from the skillful and demanding work of teachersand students. Research in the field of mathematics education continues to identify features ofthis work that are demanding for teachers and support teachers as they work to implement the

Address correspondence to Allison Hintz, Education Program, University of Washington, Bothell, 18115 CampusWay NE, Bothell, WA 98011. E-mail: ahintz@uwb.edu

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ambitious goals of inquiry-oriented teaching (e.g., Chazan & Ball, 1999; Hufferd-Ackles, Fuson,& Sherin, 2004; Kazemi, 1998; Lampert, 1992; Mendez, Sherin, & Louis, 2007). The body ofresearch focused on teachers work implementing inquiry-oriented practices conveys an underlyingconcern for, and attention toward, children’s learning experiences. From this literature, we knowthat students are expected to engage in sensemaking and take more active roles in mathematicaldiscussions. We know that students are learning and participating in new, more demanding, waysthan ever before. We also know that good teaching takes knowledge of subject matter as well asknowledge of students’ experiences and who they are as learners and people in the world.

While research has tended to focus on the demands that inquiry-oriented practices pose forteachers, there has been less emphasis on understanding students’ experiences and the demandsthat inquiry-oriented learning poses for them. However, there is a growing body of researchthat attends to students’ experiences, and this body of work provides much needed insights(e.g., Empson, Turner, Dominguez, & Maldonado, 2006; Moschkovich, 2007). Though previouswork tended to treat students as a homogeneous group, depicting their experiences as similar,the field began to attend to gender, race, ethnicity, class, and other socially defined identitiespresent in the classroom as well as the inequities in mathematics achievement and experiencesof marginalized students. Concerned with developing inquiry-oriented teaching and learning thatpromotes equitable participation for all students, researchers attend to understanding and sup-porting low-achieving students’ participation (Empson et al.); experiences of successful urbanhigh school students in multicultural and multilingual classrooms (Boaler & Staples, 2008);supporting bilingual students’ opportunities to contribute to, and learn from, mathematical dis-cussion (Moschkovich, 2007); success with detracking (Boaler 1997, 2005); and consequencesof detracking (Rubin & Silva, 2003). What is particularly important about this work is the wayin which it frames the study of students, avoiding essentializing characteristics of gender, race,ethnicity, and class, which places the source of underachievement within the individual studentor group, and instead looking at the social, political, and economic structures to uncover anddescribe the causes that underlie inequities in mathematics (Anyon, 2005).

This study contributes to existing literature by arguing that in order to give students accessto equitable participation, we need to better understand the various demands for participation.Supporting students’ equitable participation in mathematical discussion entails a focus on stu-dents’ experiences with, and perspectives of, mathematical discourse—specifically, identifying,describing, and understanding what we are asking them to do and hearing how they narrate theirexperiences with those demands. With an understanding of how students experience the demandsof mathematical discussion, teachers can better support the participation of all students.

A particularly understudied facet of student experience is the demands placed upon listeners.In mathematical discussion, listening is important. As Cazden (2001) wrote, “students have tolisten to and learn from each other as well as the teacher. That’s the only way for them to learnduring the time spent solving problems in a group” (p. 89). Wood (1999) placed high priorityon the student’s role as a listener and believed that it is listening that enables students to followthe mathematical thinking and reasoning being discussed. When a student listens in order tofollow the mathematical thinking and reasoning being discussed, she or he may be demonstratingwhat Rogoff, Paradise, Mej’ia Arauz, Correa-Chavez, and Angelillo (2003) referred to as “intentparticipation” (p. 176), which is participating through active listening with the possibility to moveto participation through talking.

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The limited body of research focused on listening during mathematical discussions bringsattention to the importance of this role. However, listening is a difficult dimension of discourseto study because there is little observable behavior. Listening is a part of students’ experiencesteachers do not typically have access to. Yet, knowing why students listen, what they listen for,and what they do with what they hear is important information in providing equitable access toparticipation, in recognizing and valuing different forms of participation, and in supporting allchildren during mathematical discourse. Therefore, this article focuses on the following researchquestion: What are the mathematical and interactional demands that students experience duringmathematical discourse? Specifically, what are the demands for a student in the role of listener?1

CONCEPTUAL FRAMEWORK

This study employed a sociocultural theory of learning as an analytic lens to understand students’experiences during mathematical discourse. A sociocultural perspective describes learning asit occurs through participation in cultural practices. Classroom discourse is a form of culturalpractice, with distinct patterns, roles, and expectations that children are socialized into as a partof the process of schooling.

Learning occurs as a child interacts with people, practices, and activities (Forman, 1993; Lave& Wenger, 1991; Rogoff, 1993, 1994). Therefore, in the social context of an inquiry-orientedmathematics classroom, learning occurs through mathematical discourse as students participate inshared experiences with other people such as their teacher and classmates. As students participatein shared experiences, their participation shapes, and is shaped by, the evolving mathematical andinteractional dimensions of their classroom. All students actively shape the classroom community,whether as an avid sharer or an active listener.

This study conceptualizes mathematical participation in a broad sense to include listening,watching intently, solving mentally, constructing written representations, and talking. Thoughparticipation is conceptualized broadly, this study is mainly focused on listening rather than otherforms of participation. I define equitable participation to mean that multiple forms of participationare valued in the classroom: students do not all have to participate in the same way, and variousforms of participation should be investigated to determine whether and how they might contributeto student learning.

This study focused on an analysis of students’ experiences during mathematical discussionthrough the discourse pattern of strategy reporting. During strategy reporting lessons, studentssolve a mathematical problem in many different ways and they share these multiple solutionswith one another. Strategy reporting is open ended; the conversation can go in many directionsdepending on what the teacher and students do and what they notice. During the discourse patternof strategy reporting, students experience mathematical demands and interactional demandsbecause there are expectations of what students must be able to do in order to engage in thediscourse. The multiple purposes of strategy reporting can include the following:

• Eliciting student ideas• Generating multiple strategies or mathematical approaches• Representing many students’ thinking

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• Making connections between mathematical ideas: comparing similarities and differencesacross strategies

• Building students’ repertoire of strategies and building flexibility over time

Strategy reporting is a predominant discourse pattern in elementary mathematics classrooms.Wood, Williams, and McNeal (2004) described a strategy-reporting classroom as a place wherechildren “present different strategies for problems and may be asked to provide more informationabout how they solved the problem by the teacher but rarely by other student listeners” (p. 224).The way in which the teacher and students in this study enacted mathematical discourse wasconsistent with Wood et al.’s description of strategy reporting. A primary goal of the discussionis to generate multiple strategies and make connections or comparisons between the strategies.In this discourse pattern, the teacher elicits students’ strategies and is typically at the center ofthe discussion. The talk most commonly flows from teacher to student and back to the teacher.In this study, strategy reporting is conceptualized as a discourse pattern, rather than a goal thatthe teacher sets for the students.

DATA AND METHODS

Data for this study came from a fourth-grade classroom at an elementary school in a large districtin the Pacific Northwest of the United States during the 2008–2009 academic year. Data werecollected at three different points throughout the school year (fall, winter, and spring). Duringthose weeks, data were collected for a minimum of 4 days. Data include 26 videotaped lessons,videotaped individual interviews with focal students, transcripts, and a collection of artifacts anddocuments. Focal students were selected to represent a range of learners typical in an elementaryclassroom, and the samples varied with respect to gender and race.

To capture the strategy-reporting lesson and the focal students’ experiences during the lesson,two video cameras were used. A stationary video camera was used to capture the teacher, thescreen, and the group of students seated on the carpet. A handheld video camera was used tocapture focal students.

Directly after the lesson and/or the days following the lesson, individual interviews with focalstudents occurred. During the interview, focal students were asked to describe general aspectsof their experiences with strategy reporting as well as specific occurrences during focal lessons.A variety of tools were used to help focal students narrate specific occurrences in the lessons.The tools included watching a particular segment of the videotaped lesson together, describing aspecific event that occurred, and/or using an artifact from the lesson such as the chart paper orthe student’s own math journal. The interviews tended to focus on a particular strategy that wasshared or a key mathematical idea that emerged in the discussion and asked the focal student tonarrate what she or he was thinking about as he or she listened to that portion of the discussion.

Several analytic passes were conducted over the videotaped interviews (with transcript) toidentify and describe the mathematical and interactional demands that students experience duringstrategy-reporting discourse. An open-coding technique (Strauss & Corbin, 1990) of highlighting,labeling, and categorizing was used to identify and describe the demands described by focalstudents during their interviews.

For this article, I focused on interviews with a particular focal student, Norah, who spokeat length about her experiences listening to others during strategy reporting. In the analysis of

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the videotaped interviews, all segments in which Norah described her experiences with, andreasons for, listening were selected. These segments were then coded into emerging categories ofstudents’ experiences with listening, such as how students listen, why students listen, and whatthey do with what they hear. Those categories were then coded with respect to experiences thatwere mathematical in nature and those that were social in nature.

FINDINGS

Mathematical and Interactional Demands

During the common mathematical discourse pattern of strategy reporting, all students experiencemathematical and interactional demands. There are certain things that students have to knowand do mathematically because there is subject matter knowledge that students must make useof and work with. There are certain things students have to be able to do socially because theyare learning mathematics in a classroom with other children as they engage in the discourse. Imake a distinction between mathematical and interactional demands because I think it is useful toanalyze them separately, even though they occur simultaneously. This distinction, I would argue,allows us to better understand and appreciate the dual mathematical and interactional nature ofstudents’ experiences in more detail.

In a broader study (Hintz, 2010), I analyzed the various demands that students faced duringmathematical discussions. Some were mathematical in nature, such as having a mathematicalstrategy and explaining your mathematical thinking. Some were social, such as sharing andlistening. In this article, I will focus on the demands that students experienced while listening,including both mathematical and social.

Listening

The two primary roles available for students to take on and enact during strategy reporting aresharer and listener. When a student is the sharer, or speaker, she typically uses words, gestures,and/or written numbers to communicate her answer as well as the steps she took to solve andpossibly why she solved it in that way. Because only one student speaks at a time during strategy-reporting lessons, at any given moment most students are taking on the role of listener. When astudent is a listener, he or she is expected to listen to and learn from his classmates and teacher.The concern of this article is how listeners experience the mathematical talk that occurs.

As the listener, a student experiences a host of interactional demands because he or she islearning mathematics in a classroom with other people. A student may have to set his or her ownthinking aside, listen to a classmate’s thinking, listen to the teacher revoice a classmate’s thinking,compare his or her own strategy to the strategy being shared, try on others’ thinking, listen tothe teacher revoice his or her own thinking, make sense of and learn a strategy highlighted bythe teacher, listen to and follow teacher’s requests, agree or disagree, and celebrate a classmate’sthinking.

As focal students narrated their listening experiences, they articulated different dimensions ofa listener’s experience. For example, students must know how to listen (e.g., face the speakerand lay your own strategy aside temporarily in order to listen to, understand, and think within

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the strategy being shared) as well as why listening is important during mathematical discourse(e.g., listening is important because you learn from other people’s ideas). Though students werein agreement that one important reason why you listen is to learn from other people’s ideas, eachof the focal students offered differing reasons, such as listening in order to:

• Grow a repertoire of strategies over time.• Confirm that your answer is correct.• Learn faster or easier ways.• Mitigate the risk of sharing something incorrect.• Not get in trouble.

To delve into a few of the reasons students described in their interviews, this article presentsa case study of one particular student’s experience as a listener. I have chosen to highlight thefocal student Norah because her story provides unique insights into the experiences of a listener.Her perspective as a student who listens in order to grow a repertoire of strategies yet alsolistens in order to mitigate the risks of sharing something incorrect illustrates the simultaneous,multidimensional demands that students navigate as they enact the role of listener. Her story alsohelps us think about what counts as participation as students engage in mathematical discourse.

Norah: A Student Who Listens

During strategy reporting in her fourth-grade classroom, Norah sits on the carpet with her legscrossed, head down, and a steady focus on her math journal. She looks up from her journal tostudy the screen while her teacher and classmates discuss ideas. She holds a look of concentrationas she listens. She rarely shares her thinking, yet she seems acutely aware and engaged in thediscussion happening around her.

Observing children listening during mathematical discussion is interesting. Yet one can onlyknow so much about students’ listening experiences by watching. As I layered Norah’s narrationsof her experiences during mathematical discussions upon my observations, I gained a fascinatingwindow into the world of a student who listens for two very different reasons.

Through the case study of Norah, we gain insights into one student’s experience as a listenerduring mathematical discussion. She illuminates critical reasons why listening is demanding andimportant work for a student. The two elements of listening that she describes, for the sake oflearning and to mitigate risks of sharing, further shed light upon the dual mathematical and socialnature of the demands students’ experience.

Listening to Grow a Repertoire of Strategies Over Time

Throughout Norah’s narrations of her listening experiences, she described herself as a listenerwho made sense of speakers’ ideas and tried them on herself. She was interested in how otherpeople think and she believed that listening to her classmates’ ideas helped her become smarter.When Norah’s classmates shared their mathematical ideas, she told me, “I really listen to them tosee what they are saying.” She was interested in her classmates’ ideas because “they might have adifferent idea that makes sense and that might be a different way of thinking.” For instance, whenshe heard a classmate explain a mathematical strategy that was different than hers, she told me she

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thought “about what they are saying and how I could use that strategy.” She tried her classmate’sstrategies “basically every time” she tried a problem. When she did not readily understand theideas, she persisted and eventually reached clarity (e.g., “I was trying to think in my head whatshe was saying because I didn’t really get it at first—I was thinking it through in my head andnow I’m getting it”). As Norah tried on new strategies, she was trying to expand her repertoire ofstrategies. Over time her repertoire may expand because of how the discourse pattern of strategyreporting allows her to see multiple strategies. Growing a repertoire of strategies is a goal ofstrategy reporting and happens over time (not within one session).

What is important to notice about a student who listens to grow a repertoire of strategies overtime is what that student has to do with her own thinking. In order to listen to, make sense of,and really understand someone else’s strategy, a student must set her own thinking aside. Norahexplained this facet of listening by describing how her ideas “kind of just [went] away and Istarted thinking about it their way and then if this [wasn’t] working I get my way back.”

Also important to notice, and recognize, is that listening is a form of active participation inmathematical discussions. When a student, like Norah, sets her own thinking aside in order to thinkwithin her classmates’ ideas and incorporates others’ ideas into her own repertoire of strategies,she is navigating sophisticated terrain. Her active participation through listening is at the heartof, and fulfills, a main mathematical goal of strategy reporting (building students’ repertoire ofstrategies). Her participation through active listening challenges the idea that participation ishappening only when a child is sharing.

Though active listening in order to grow a repertoire of strategies is one reason why a studentlike Norah may not be sharing, listening for the sake of learning mathematics may not be the onlyreason a student is not talking. Norah’s story also illustrates the fact that listening, or not sharing,is a way for a student to mitigate the risks of sharing a mathematical mistake publicly.

Listening to Mitigate the Risks of Sharing

Making mistakes is an unavoidable part of learning mathematics. During strategy reporting,mistakes commonly arise and are an important learning opportunity for the sharer as well aslisteners. However, it can often be challenging for a student to share a mistake and work throughhis or her mistake in public, in front of his or her teacher and classmates.

When Norah narrated her experiences as a sharer, she described what was happening for herwhen she chose to share and when she chose not to share. During strategy reporting, she raisedher hand to share “every time [she] knew something” and she liked when the teacher called onher to share her strategy when she had enough time to solve a problem and she felt she had theright answer. For example, she explained, “When my classmate shared out the doubling strategyI started raising my hand more because I thought that way of solving was working for me, so Istarted raising my hand.” However, she chose not to volunteer to share her mathematical strategywhen the problem was challenging for her to solve (e.g., “When I was multiplying in my head Ididn’t really raise my hand all that much because with big numbers like this it can be hard forme to multiply in my head”), when she had not finished solving a problem by the time strategysharing began, and/or when she did not think she had the right answer. She explained that sharingher mathematical strategy, “unless it is really easy like a fact,” makes her “nervous” because“there are people listening.”

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During one particular interview, Norah and I rewatched the videotape of an episode during alesson when she shared a mistake and I listened to her talk about that experience. After solvingthe problem 14 × 5 mentally, she had offered up her answer saying, “I think it is 120.” As she saidher answer she was grimacing with a look of uncertainty and concern. She turned to her neighborand gestured her hand back and forth in a flip-flop motion showing that she was unsure abouther answer. Later in the discussion, as a different answer was decided to be correct, Norah raisedher hand and said with a shy smile and shrugging downward, “I counted wrong.” The teacherresponded, “You counted wrong. And that’s OK, we do that all the time don’t we? That’s part ofour life,” and moved on with the discussion.

As Norah narrated her experience during this episode, she shared,

Since I did 14 × 5 = 120, I messed up because I added differently than I should have. I did 4 × 5 is20 and then I put the one from the 10 right on as 100. I should have thought more about it instead ofgoing right to it. It is kind of embarrassing.

What she felt was embarrassing was “getting it wrong,” and she added, “But if you make amistake then you can keep practicing that problem and it will become a fact that you know. Nexttime I would still start with 4 × 5 = 20 but then I would do a different step.” This commentreveals that she sees the potential for learning from your mistakes and continued practice. Yet thesocial consequences of making a mistake publicly weighed heavy on her mind and shaped howshe chose to take on the roles of sharer and listener.

An important part of why Norah did not like to share when her solution had a mistake wasbecause of how she may have been asked to engage in talk about the mistake with her teacher infront of the other students. It is common during strategy reporting for a teacher to ask questionsabout a student’s strategy when there is a mistake in an effort to uncover a misconception andwork through an error. In talking about this experience, Norah said, “Sometimes I don’t like tomake mistakes because it’s kind of embarrassing when you thought you got it right and then yougot it wrong and then you have to keep working out loud.” Norah’s narration highlighted twosignificant challenges of sharing a solution that is incorrect. First, she describes the demands ofpublicly realizing that the solution you are sharing contains an error. Second, she brings attentionto the demands of engaging in talk about the error on the spot in front of other people.

From Norah’s own words, and the words of her teacher, who said that Norah was a “reluctantsharer,” it appears that the teacher saw Norah, and Norah saw herself, as someone who tried tofit into the classroom in the role of listener in part to mitigate the risks of sharing a mistake.Norah remembered when she started to feel embarrassed about getting an answer wrong duringmath talk with her classmates. She described, “When I was in third grade I was thinking about ananswer I thought was right and then I got the answer wrong and I thought that was embarrassing.”She is unsure whether she will always feel embarrassed by making a mistake. “I don’t know if itgoes away.”

Staples (2008) studied how mistakes or errors are perceived during whole-group inquiry-oriented lessons. She illustrated the delicate work of a teacher as she reshaped students’ negativeperceptions about giving incorrect responses in her classroom. The teacher in Staples’ studyworked to frame mistakes as a necessary, acceptable, productive part of their classroom discus-sions and called them “desirable contributions” or learning opportunities (p. 52). Staples’ findingsbring attention to the importance of cultivating strategy-reporting discourse that frames mistakesas desirable contributions and supports students through discussion about errors. If mistakes are

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not framed in a productive way and/or students do not feel socially supported in public discussionabout their errors, some students may take on the role of listener in order to be quiet and avoidthe risks of sharing. Being quiet during discussion, which looks like listening, in order to avoidrisk is not a desirable form of participation.

Norah’s descriptions of her role as sharer and listener raise questions regarding the developmentof her mathematical identity. Black (2004) found that “Patterns of unequal participation in whole-class discussions may lead to the construction of different types of pupil identities within theclassroom” (p. 34), and students who consistently interact in the classroom develop an identityof full participation, whereas students who have less interaction can become marginalized fromclassroom learning. Applying Black’s findings to Norah’s case, a host of questions arise, suchas: Does Norah listen primarily to hear other people’s ideas or to mitigate the risk of sharingher ideas? What aspects of her academic and social history, the structure of the discourse, andthe classroom context shape how Norah participates as a sharer and listener? How is the role oflistener valued, or not valued, by teachers and students in mathematical discussions?

Across her narrations, Norah revealed many facets of a student’s experience as a listener duringstrategy reporting. She described instances when she was more confident in her classmates’strategies than her own (e.g., she often started new problems by trying her classmate’s strategies).She also identified other students as smart and worth emulating (e.g., “We have pretty smart kidsin our class and I try to use their strategy if it is easier or harder than mine”). She described feelingvulnerable sharing her ideas publicly (e.g., “Maybe I don’t like really sharing my thoughts thatmuch”). She also described instances when she took command of her own learning (e.g., “If Itry to use my strategy and I can’t really figure it out I try to move on to a different strategy thatI’ve heard”). Finally, she narrated how she found sharing her mistakes to be embarrassing (e.g.,“I don’t like to share when I get the wrong answer and then I’m glad she didn’t call on me”) andmay mitigate the risk of sharing by listening.

DISCUSSION

Participating in mathematical discussions is demanding work for all students. Supporting stu-dents’ equitable access to participation in mathematical discussions means focusing on students’experiences with, and perspectives about, mathematical discourse—specifically, identifying, de-scribing, and understanding what we are asking them to do and hearing how they experience thosedemands. Through the case study of Norah we learned that (a) students in the role of listener maynavigate a host of demands, and their active participation through listening is an important formof participation in mathematical discussion; and (b) students may take on the role of listener inorder to mitigate the risks of reporting an incorrect idea or answer.

Through Norah’s case we also learned that it is important to recognize and value the work oflisteners during mathematical discussion. Norah is an example of a student who listens carefully,setting her own thinking aside, in order to understand and try on her classmates’ strategies. Herwork during mathematical discussion is demanding, and it is at the heart of the discourse patternof strategy reporting. Furthermore, her story pushes us to recognize her participation throughactive listening as a valuable and important type of participation and challenges the idea thatparticipation happens only when a child is sharing.

Because existing research has focused so much on talk, we know little about how to helpstudents learn to listen better. The broader study illuminates particular pedagogical practices that

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may support students as listeners; specifically, supporting students in knowing how to listen andwhat to do with what they hear as well as framing mistakes as desirable contributions and beingclear in what will happen when mistakes occur. Research on complex instruction (Cohen, 1998;Cohen & Lotan, 1995) also suggests some strategies that encourage students to listen to oneanother, including a strategy in which the teacher highlights important academic contributionsfrom low-status students, contributions that had previously been ignored. Over time, students canlearn to value and listen to one another’s ideas more frequently (Boaler & Staples, 2008).

This study also illuminates the need for further research. It is important to provide finer analysesof the demands of listening in order to distinguish listening demands that are mathematical innature from those that are social, or interactional, in nature. Another avenue for further researchis an exploration of how the simultaneous mathematical and interactional demands of listeningpose a challenge to students (like Norah) as they must deal with both types of demands and makechoices about whether to listen for the sake of learning or for the sake of avoiding social risksand weigh the risks of sharing against the opportunity to learn. Finally, there is a lack of researchon how teachers can better support productive listening from students.

When we notice the ways in which students participate through listening, we expand the rangeof what counts as participation. Including the ways in which students participate through listen-ing, instead of just talking, and defining what counts as participation more broadly has criticalconnections to equity issues. If we only value students who participate by talking, we are over-looking other important forms of participation that may be part of the “repertoires of practice” thatstudents from nondominant communities bring to classrooms (Gutierrez & Rogoff, 2003, p. 22).Gutierrez and Rogoff reported that some students may watch intently but talk less and still learn,which is similar to how Norah participates in mathematical discourse. The research presented herehighlighted the importance of knowing more about how students are experiencing the classroomand revealed to us some positive and some negative aspects of listening. Lastly, a deeper under-standing of the demands that students experience as they participate in mathematical discoursewill enable teachers to better support students’ access to equitable participation and orchestratediscussions that are both mathematically productive and socially supportive for all students.

ACKNOWLEDGMENTS

The author communicates her sincere gratitude to Elham Kazemi for her dedicated help inthis research study; the teachers and students who opened up their classrooms and shared theirimportant thoughts and ideas; and Indigo Esmonde and Judit Moschkovich, who generouslyprovided careful and helpful reviews.

NOTE

1. The findings presented in this article are part of a broader study (Hintz, 2010).

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