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'Explain to your partner': teachers' instructional practices and students' dialoguein small groupsNoreen M. Webb a; Megan L. Franke a; Tondra De a; Angela G. Chan a; Deanna Freund a; Pat Shein a; DorisK. Melkonian aa University of California, Los Angeles, USA

Online Publication Date: 01 March 2009

To cite this Article Webb, Noreen M., Franke, Megan L., De, Tondra, Chan, Angela G., Freund, Deanna, Shein, Pat and Melkonian,Doris K.(2009)''Explain to your partner': teachers' instructional practices and students' dialogue in small groups',Cambridge Journal ofEducation,39:1,49 70To link to this Article: DOI: 10.1080/03057640802701986URL: http://dx.doi.org/10.1080/03057640802701986

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Explain to your partner: teachers instructional practices and students

dialogue in small groupsNoreen M. Webb*, Megan L. Franke, Tondra De, Angela G. Chan, DeannaFreund, Pat Shein and Doris K. Melkonian

University of California, Los Angeles, USA

(Received 12 June 2008; final version received 26 August 2008)

Collaborative group work has great potential to promote student learning, andincreasing evidence exists about the kinds of interaction among students that arenecessary to achieve this potential. Less often studied is the role of the teacher inpromoting effective group collaboration. This article investigates the extent towhich teachers instructional practices were related to small-group dialogue infour urban elementary mathematics classrooms in the US. Using videotaped andaudiotaped recordings of whole-class and small-group discussions, we examinedthe extent to which teachers pressed students to explain their thinking during theirinterventions with small groups and during whole-class discussions, and weexplored the relationship between teachers practices and the nature and extent of students explaining during collaborative group work. While teachers used avariety of instructional practices to structure and orchestrate students dialogue insmall groups, only probing students explanations to uncover details of theirthinking and problem-solving strategies exhibited a strong relationship withstudent explaining. Implications for future research, professional development,

and teacher education are discussed.Keywords: classrooms; grouping; cooperative group learning

Introduction

There is little doubt about the potential of collaborative group work to promotestudent learning, and increasing evidence exists about the kinds of interaction amongstudents that are necessary to achieve group works potential (ODonnell, 2006;Webb & Palincsar, 1996). Less often studied is the role of the teacher in promotingeffective group collaboration. This article investigates the extent to which teachers

instructional practices are related to the students dialogue when working in smallgroups. Specifically, we focus on teachers interventions with small groups and howtheir engagement with students during whole-class instruction relates to studentexplaining during collaborative group work.

Empirical findings from group-work studies demonstrate the critical relationshipbetween explaining and achievement (see Fuchs et al ., 1997; Howe et al ., 2007; Howe& Tolmie, 2003; King, 1992; Nattiv, 1994; Slavin, 1987; Veenman, Denessen, vanden Akker, & van der Rijt, 2005; Webb, 1991). Moreover, complex explanations(e.g., giving reasons elaborated with further evidence) have been shown to be morestrongly related with learning than less complex explanations (providing simplereasons: Chinn, ODonnell, & Jinks, 2000). Explaining to others can promote

*Corresponding author. Email: [email protected]

Cambridge Journal of EducationVol. 39, No. 1, March 2009, 4970

ISSN 0305-764X print/ISSN 1469-3577 online# 2009 University of Cambridge, Faculty of EducationDOI: 10.1080/03057640802701986http://www.informaworld.com

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learning as the explainer has the opportunity to reorganize and clarify material, torecognize misconceptions, to fill in gaps in her own understanding, to internalize andacquire new strategies and knowledge, and to develop new perspectives andunderstanding (Bargh & Schul, 1980; King, 1992; Peterson, Janicki, & Swing, 1981;Rogoff, 1991; Saxe, Gearhart, Note, & Paduano, 1993; Valsiner, 1987). Whenexplaining their problem-solving processes, students think about the salient featuresof the problem, which develops their problem-solving strategies as well as theirmetacognitive awareness of what they do and do not understand (Cooper, 1999).

Given the relationship between explaining and student outcomes, what canteachers do to promote student explaining in collaborative groups? Research hasfound that providing instruction and practice in explanation-related behaviours hasbeneficial effects on group discussion. Effective training programs includeinstructing students in explaining their problem-solving strategies (instead of justgiving the answer, Gillies, 2003, 2004; Swing & Peterson, 1982; Webb & Farivar,1994), giving conceptual rather than algorithmic explanations (Fuchs et al ., 1997), justifying their own ideas and their challenges of each others ideas, and negotiatingalternative ideas (exploratory talk, Mercer, 1996; Mercer, Dawes, Wegerif, & Sams,2004; Mercer, Wegerif, & Dawes, 1999; Rojas-Drummond & Mercer, 2003; Rojas-Drummond, Perez, Velez, Gomez , & Mendoza, 2003; Wegerif , Linares, Rojas-Drummond, Mercer, & Velez, 2005), and engaging in argumentation (providingreasons and evidence for and against positions, challenging others with counter-arguments, weighing reasons and evidence, Chinn, Anderson, & Waggoner, 2001;Reznitskaya, Anderson, & Kuo, 2007). A number of effective programs combinemany of these elements (see Baines, Blatchford, & Chowne, 2007; Baines,Blatchford, & Kutnick, 2008; Blatchford, Baines, Rubie-Davies, Bassett, &

Chowne, 2006).Teachers can also require group members to assume particular roles or engage in

specific practices during their group interaction, such as asking each other specifichigh-level questions about the material (Fantuzzo, Riggio, Connelly, & Dimeff,1989; King, 1999), asking questions to monitor each others comprehension(Mevarech & Kramarski, 1997), engaging in specific summarizing and listeningactivities (Hythecker, Dansereau, & Rocklin, 1988; ODonnell, 1999; Yager,Johnson, & Johnson, 1985), responding to specific prompts to explain why theybelieve their answers are correct or incorrect (Coleman, 1998; Palincsar, Anderson,& David, 1993), and generating questions and making predictions about text

(Palincsar & Brown, 1989). Yet, training teachers to teach their students how toengage in group work, while it can be done in ways that help students participate,does not address the role of the teacher in intervening in this group work andsupporting students as they engage together with the content.

Many cooperative learning researchers and theorists advise teachers to monitorsmall group progress and to intervene when groups fail to progress or seem to befunctioning ineffectively, when no group member can answer the question, whenstudents exhibit problems communicating with each other, and when studentsdominate group work without allowing true dialogue (see Cohen, 1994; Ding, Li,Piccolo, & Kulm, 2007; Johnson & Johnson, 2008). Research by Tolmie et al . (2005)also suggests that teacher guidance may help counteract students tendencies to disagreein unproductive ways and enable children to explore ideas more effectively. Howteachers should intervene with groups to facilitate productive small-group discussion is

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Kazemi and Stipek (2001) contrasted elementary school mathematicsclassrooms in which teachers pressed students to explain and justify theirproblem-solving strategies mathematically (they termed these practices high-press) with classrooms in which teachers asked students to describe steps theyused to solve problems but did not ask students to link their strategies tomathematical reasons or to explain why they chose particular procedures (low-press). When working collaboratively, students in high-press classrooms usedmathematical arguments to explain why and how their solutions worked and toarrive at mutual understanding, whereas students in low-press classroomssummarized, but did not explain, their steps for solving a problem and didnot debate the mathematics involved in the problem. Webb et al . (in press) alsofound similar results in that the extent to which teachers asked students toelaborate on their explanations about how to solve mathematical problemshowed a strong relationship with the nature and extent of students explainingto each other during collaborative conversations. Webb, Nemer, and Ing (2006)

found that low-press teacher practices were a possible reason for the infrequentstudent explaining that occurred during cooperative group work. Teachers inthat study did not ask students about their thinking but instead assumed mostof the responsibility for setting up the steps in the problem (typically with littleor no rationale given for the mathematics underlying the steps) and askedstudents simply to provide the results of specific calculations that the teachersthemselves had posed.

Extending previous research, this study examines how teachers practices bothwith small groups and with students in the larger classroom context may relate tostudent explaining in collaborative groups. Specifically, we examine how the extent

to which teachers press students to explain their thinking during specificinterventions with small groups, as well as during whole-class discussions, relatesto the accuracy and completeness of students explanations during collaborativegroup work. It should be noted that the analyses reported here address associationsbetween teacher and student variables, not causal relationships; this issue is discussedat greater length in a later section of this paper.

The specific research questions addressed in this paper, then:

(1) What are the relationships between specific teacher interventions with smallgroups and the extent of student explaining in those groups?

(2) What are the correspondences between teacher-to-teacher differences intheir practices and classroom-to-classroom differences in student explainingduring collaborative group work?

Method

Sample

Four elementary-school classrooms (Grades 2 and 3) in three schools in a largeurban school district in Southern California are the focus of this study. 1 Theseschools are large (more than 1100 students), serve predominantly Latino (with someAfrican-American) students, have a high percentage of students receiving free orreduced lunch, have a substantial proportion of English language learners, and havelow standardized achievement test scores.

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Teacher professional development

The four teachers were part of a large-scale study focused on supporting teachersefforts to engage their students in algebraic thinking (see Carpenter, Franke, & Levi,2003; Jacobs, Franke, Carpenter, Levi, & Battey, 2007) and had participated in at

least one year of on-site professional development that explored the development of students algebraic reasoning and, in particular, how that reasoning could supportstudents understanding of arithmetic. The professional development content, drawnfrom Thinking mathematically: Integrating arithmetic and algebra in the elementaryschool (Carpenter et al ., 2003), highlighted relational thinking, including:(a) understanding the equal sign as an indicator of a relation; (b) using numberrelations to simplify calculations; and, (c) generating, representing, and justifyingconjectures about the fundamental properties of numerical operations. Teachersreceived guidance in how to engage their students in conversations in order to helpthem explain their thinking and debate their reasoning and how to encouragestudents to solve problems in their own ways. A primary focus was on teacherseliciting student explanations and supporting students to describe the details of theirthinking (Franke, Kazemi, & Battey, 2007).

Approximately 12 months after the conclusion of the professional development,we selected seven teachers for intensive observation who had shown a range of student achievement in the prior year. The four teachers analyzed here used small-group collaborative work as described below.

Observation procedures

In most cases, students worked in pairs, with the exception of a few larger groups

ranging in size from three to five. Teachers assigned students seated adjacently intopairs (or groups). Because students seating proximity was not based on studentcharacteristics (e.g., achievement level, gender), group composition can beconsidered random. Analysis of group composition showed a variety of groupingsin each class (e.g., some same-gender pairs, some mixed-gender pairs), with noparticular pattern predominating. The groups remained intact for the two occasionsof observations analyzed here; otherwise, group membership was fluid and teacherschanged group composition frequently.

Each class was videotaped and audiotaped on two occasions within a one-weekperiod. We recorded all teacher-student interaction during whole-class instruction,

and recorded a sample of groups, selected at random, from each classroom. Thenumber of students recorded in each class ranged from 11 to 15 out of the 20students enrolled in each class. Comparison of the recorded students with the non-recorded students revealed no significant differences in gender, ethnicity, orperformance on the achievement tests administered in this study.

Observers recorded classroom activity as teachers taught problems of their choicerelated to the topics of equality and relational thinking. Teachers posed such problemsas (a) 50 + 505 25+ % + 50, and (b) 11 + 25 5+ 8 (true or false?). Consistent with theiraccustomed practice, teachers incorporated group-work time into the class duringwhich students worked together to solve and discuss problems assigned by the teacher.Teachers introduced a problem, asked groups to work together to solve the problemand share their thinking, and then brought the whole class together for selected studentsto share their answers and strategies with the whole class, usually at the board.

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We made comprehensive transcripts of each class session consisting of verbatimrecords of teacher and student talk, annotated to include the details of their non-verbal participation. These transcripts included whole-class discussion as well asgroup-work discussion for recorded students. We also collected student writtenwork, took field notes during class sessions, and administered student-achievementmeasures.

Measures of student achievement

We used two measures of student achievement in this study. The written assessmentwas designed to measure relational thinking. Some items were designed to assessstudents understanding of the equal sign, and whether students held a relationalview of the equal sign (Jacobs et al ., 2007). For example, to answer the problem3+ 45 % + 5, students needed to know that the numbers to the left of the equal signsummed to the same result as the numbers to the right of the equal sign, rather than

treating the equal sign as an operation such as the answer comes next. Other itemswere designed to assess students abilities to identify and use number relations tosimplify calculations. For example, in 889 + 118 2 118 5 % , students could simplify thisproblem by recognizing that 118 2 118 5 0.

We also individually interviewed the students from each class who were audio orvideotaped on the observation days. We asked students what number they would putin the box to make certain number sentences true, for example, 13 + 185 % + 19, andasked them to describe their problem-solving strategies. For this paper, we analyzedthe accuracy of their answers. Internal consistency alpha coefficients for the writtenassessment and interview were .88 and .74, respectively.

Coding of student and teacher participation

Using transcripts of all classroom talk we coded teacher and student participationduring whole-class and group-work discussions. To analyze whole-class discussions,we separated the interaction into segments, each of which consisted of one boundedinteraction between the teacher and a particular student. A segment consisted of aminimum of two conversational turns each for the teacher and the student. Whenanalyzing group interaction, we coded each group conversation on a problem as asingle unit. The group conversation started when the group began discussing theassigned problem and ended when the teacher called the class together again.

We coded teacher practices across the entire lesson (all whole-class segments andall group conversations). The four teacher practices coded were: (a) probes studentsexplanations to uncover details or further thinking about their problem-solvingstrategies (asks specific questions about details in a students explanation); (b)engages with students around their work on the problem (either an answer or aninitial explanation) but does not probe the details of student thinking about theirproblem-solving strategies (typically, repeats or revoices the students work withoutasking further questions); (c) interacts with the group only around norms forbehaviour (typically, directing students to talk to, or share with, each other); and (d)makes other brief comment or suggestion (e.g., acknowledges work on a problem,repeats the problem assigned, makes a brief suggestion, or makes a commentconcerning classroom management).

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We coded student participation along two dimensions. First was the highest levelof student participation on a problem: (a) gives correct and complete explanation;(b) gives ambiguous, incomplete, or incorrect explanation; (c) gives answer only; and(d) gives neither an answer nor an explanation (see Table 1). An explanation wasconsidered complete if the coder could unambiguously discern how the studentsolved the problem. This included evidence from both verbal and non-verbalcommunication (such as gesturing to different parts of the number sentence). Acorrect and complete explanation was any explanation that described in detail astrategy that would consistently work for the problem, and involved anunambiguous and appropriate solution to the problem. Any explanation notconsidered complete was coded as incomplete, which included both incomplete andambiguous explanations. An incorrect explanation was an explanation that wasmathematically inconsistent with the problem posed.

The second student participation dimension reflected the extent of the groupexplaining during or after a teachers intervention compared to the group explainingprior to the teachers intervention, and was coded only for groups that had not givena correct/complete explanation prior to the teachers intervention. The three codeswere: (a) the group gives more explanation than before the teachers intervention,and the explanation is correct and complete; (b) the group gives more explanationthan before the teachers intervention, but it is not correct and complete; and (c) thegroup gives no further explanation.

Seven members of the research team coded student and teacher participation. Wedeveloped and set standards for the application of the coding through an iterativeprocess that occurred over many regular weekly meetings. Each research-team

Table 1. Examples of student explanations.

Explanation category Example

Correct and complete Problem: 10 + 102 105 5+Five? Its cause look. We could do this, oh no. Hold up. Cause

ten plus ten equals twenty, huh? And then it says minus tenequals five plus blank. So it gotta be equal ten, so five plusfive equals ten. And thats how I got it. Get it?

Ambiguous or incomplete Problem: 8 + 25 7+ 3 (True or false?)

[True] because theres a two and a three and a seven and aneight. Theyre like an order. [While the answer is correct, thisexplanation does not make it clear (a) whether the student isconsidering the difference in quantity between 2 and 3 and between 7 and 8, (b) what the student means by order, and (c) how the student is using order to justify that the numbersentence is true.]

Incorrect Problem: 4 + 95 56 32 2 (True or false?)I thought it was false because four plus nine is thirteen, and five

times three is fifteen. Those two do not match.

Answer but no explanation Problem: 375 5 + (3* 10)Let me see. 345?


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member was involved in the development of the codes and had primaryresponsibility for coding particular problems and particular groups of studentsfrom each classroom. We resolved questions about coding through discussion, andthese questions often led to further refinement of the teacher and student codes.After we refined the codes, research-team members systematically reviewed theirown and others coding to ensure that the codes reflected the final coding scheme andto uncover inconsistencies in coding. All inconsistencies were brought to the entireteam and were resolved through discussion and consensus.

Results

In the following sections, we provide results about teachers instructions for studentbehaviour during group work (to produce a picture of these classrooms climates forstudent participation), the relationship between student participation and achieve-ment, teacher interventions with small groups and the links between those

interventions and student participation during group work, teacher practices inthe whole class, and classroom differences in students explanations and studentachievement.

Teachers instructions about student collaboration

All of the teachers in this study gave frequent reminders to students about how tocollaborate during group work. First, in the majority (70%) of the 40 problemsassigned for group work across the four classrooms observed here, teachers gavepreliminary reminders to the whole class about student participation in their groups.The most common reminders were for students to share with their neighbour andtalk with your table partners. Some teacher instructions were more specific, such asthe need to share why you think so or why you dont think so, What kind of thinkingwent on? How did you solve it? and Instead of just saying true or false, tell [yourpartners] why you think its true or why you think its false. Second, during about half (54%) of the teacher interventions with small groups, the teacher gave specificreminders for students to work together, to talk about the problem with each other, todiscuss with their group how they were solving the problem, and to explain to eachother. These results show that teachers frequently communicated expectations forstudents to share their work and, often, for students to explain their thinking behindtheir answers or to describe the procedures they used to solve the problem.

Consistent with the expectations communicated about student behaviour duringgroup work, groups showed a high incidence of explaining. Of the 208 group workconversations observed across the four classrooms, groups gave explanations in 129(62%) of them. Thus, these classrooms had climates that seemed to be conducive toexplaining during collaborative group work.

Relationship between student participation during group work and student achievement

We next examined the relationship between student participation during group workand their achievement to confirm that the previously established relationshipbetween explaining and achievement held up in these classrooms. Consistent withprevious research, Table 2 shows that explaining was significantly correlated withachievement. 2 In particular, giving correct and complete explanations was positively

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related to achievement scores. That is, the greater the percentage of groupconversations during which students gave a correct and complete explanation, thehigher were their achievement scores. Other kinds of student participation (givingambiguous, incomplete, or incorrect explanations; giving only answers; givingneither answers nor explanations) were not related or were negatively related toachievement. The remaining sections, then, pay particular attention to therelationship between teacher practices and students giving correct and completeexplanations.

Nature of teacher interventions with small groupsAcross the 208 group-work conversations, teachers intervened in 81 of them (39%). 3

Of the 81 conversations with a teacher intervention, in 27% of them, groups hadalready produced a correct/complete explanation at the time the teacher intervened;in 16%, groups had engaged in some explaining but it was not correct or complete;and in 57%, groups had not produced any explanation. Of the 127 episodes of collaborative work without any teacher intervention, in 38%, groups produced acorrect/complete explanation; in 19%, groups produced some explanation but it wasnot correct or complete; and in 43%, groups did not produce any explanation. Thedifference in explanation patterns for group episodes with a teacher intervention and

those without a teacher intervention was not statistically significant ( x2

(2;N 5 208) 5 3.74, p5 .15), which suggests that teachers did not target groups forintervention based on students explaining behaviour.

When they engaged with groups, teachers used a variety of practices, as shown inTable 3. In about half of the interventions (53%), teachers interacted with groupsaround explanations or other work (e.g., answers) on the mathematics problems. Inmany of these interventions, teachers probed students explanations to uncoveradditional details about their problem-solving strategies or further thinkingunderlying their strategies. In about half of the teacher interventions (47%), teachersinteracted with groups only around norms for behaviour or management issues. Thedistributions of teacher practices were similar for groups that had already provideda correct/complete explanation when the teacher intervened (22 interventions)and groups that had not given a correct/complete explanation (59 interventions;

Table 2. Correlations between student participation during group work and achievementscores.

Highest level of student participation on aproblem a

Written assessmentscore b

Individual interviewscore b

Gives explanation .46*** .27Correct and complete .61*** .46***Ambiguous, incomplete or incorrect 2 .18 2 .30*

Gives no explanation 2 .46*** 2 .27*Answer only .08 .20No answer or explanation 2 .41** 2 .35*

Notes: (a) Percent of group conversations in which a student displayed this behaviour. (b)Percent of problems correct. *p , .05 **p , .01 ***p , .001.


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x2 (3; N 5 81) 5 2.70, p5 .44). Importantly, teachers were just as likely to probe

students explanations in groups that had already given correct/complete explana-tions as in groups that had not.

Teacher interventions and subsequent student explanations

Table 4 shows, for each teacher practice with small groups, the explanations thatwere given after the teachers arrival, specifically whether groups gave moreexplanation while interacting with the teacher or afterwards than they had before the

teacher intervened, and whether their group conversation led to a complete/correctexplanation. These results focus on the 59 instances of teacher interventions withgroups that had not already given a correct/complete explanation by the start of theteacher intervention. 4

As shown in Table 4, when teachers probed students explanations, groups nearlyalways gave additional explanation and many of them produced a correct/completeexplanation of how to solve the problem by the end of the groups discussion of thatproblem. The other teacher practices, in contrast, were less likely to be associatedwith additional explaining or to produce correct/complete explanations. Thedifferences in effectiveness of teacher practices for group behaviour were statisticallysignificant (Fishers exact test, p5 .001). 5

Although probing students explanations was more likely than other teacherpractices to be associated with groups producing correct/complete explanations, not

Table 3. Teacher practices with small groups.

Teacher practice All teacherinterventions

(81 group

conversations)

Groups gave correct/complete explanationprior to the teachers intervention

Yes (22 groupconversations) No (59 groupconversations)

Teacher probed studentsexplanations to uncoverdetails or further thinkingabout their problem-solvingstrategies

26a 23 27

Teacher engaged with studentsaround their work on theproblem but did not probe

the details of student thinkingabout their problem-solvingstrategies

27 32 25

Teacher interacted with thegroup only around norms forbehaviour

33 41 31

Teacher made other brief comment or suggestion

14 5 17

Note: (a) Percent of group conversations in which the teacher exhibited this practice.

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all instances of teacher probing showed the same results. The following examplescontrast more-effective and less-effective instances of teacher probing. In the firstexample, the teacher responds to a students ambiguous explanation by asking asequence of questions specific to what the student said. The questions direct thestudent to say more about particular aspects of her strategy. The teacher asksquestions about the students strategy until the student has described an explicitconnection between the two sides of the number sentence: 7 + 1 and the 10 2 2. Duringthis interchange, the student engages in additional explaining (lines 3, 5, 11, 13) beyondthe initial explanation (line 1) and arrives at a correct/complete explanation (line 13).

Problem: 7 + 15 102 %

1. Student 1: Eight take away two is ten. Ten take away eight so you have to

regroup. Ten take away eight is two. So you take the one to thezero and it would be zero but it would be a two. And this one isbecause seven plus one is eight. Ten take away two is eight.

Table 4. Teacher interventions with student explaining during group work a .

Group explaining during or after teachers intervention

Group gave more explanation than

before the teachers intervention

Group did not give

more explanationthan before theteachers intervention

Teacher practice b Additionalexplanation wascorrect/complete

Additionalexplanation was not

correct/complete

Teacher probed studentsexplanations to uncoverdetails or further thinkingabout their problem-solving

strategies

63c 31 6

Teacher engaged with studentsaround their work on theproblem but did not probethe details of studentthinking about theirproblem-solving strategies

20 20 60

Teacher interacted with thegroup only around normsfor behaviour

33 11 56

Teacher made other brief comment or suggestion

0 20 80

Notes: (a) Includes only teacher interventions in which groups did not give a correct/completeexplanation by the time the teacher intervened (59 interventions). (b) Number of groupconversations in each teacher practice category are 16, 15, 18, 10, respectively. (c) Percent of interventions in which teacher used this practice and in which group exhibited this category of explaining.


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2. Teacher: What were you doing here?3. Student 1: Regrouping. Eight take away two4. Teacher: No, this is eight plus two.5. Student 1: Eight plus two is ten. You have to regroup. Ten take away eight

is two. And cross this out so it would be zero so the answerwould be two.

6. Teacher: What made you write eight plus two?7. Student 1: Huh?8. Teacher: Where did you get the two from?9. Student 1: Its cause10. Teacher: Were you doing this one here?11. Student 1: I did this one first and then I did this one.12. Teacher: Where did you get the eight and the two from?13. Student 1: Eight is cause seven plus one is eight and ten take away two it

would be eight.14. Teacher: OK.

In the second example, the teacher responds to a students ambiguousexplanation (line 1) with a follow-up question (line 2) that seeks clarification of what the student said. The teacher makes a claim in the follow-up question thatextends what the student said and then asks the student if that is what he wasthinking. The student responds by adding clarification to the teachers claim (line 3).In doing so, the student exhibits further thinking, but this interchange does not yielda correct/complete explanation, nor does this student or group ever produce acorrect/complete explanation for this problem.

Problem: a 5 b+ b. True or false?

1. Student 2: I think not true because an A needs to have a partner and a B too.

2. Teacher: So you think that it has to be two As and two Bs?3. Student 2: And the B should be on the A side and the A should be on the Bside.

These examples highlight how probing student thinking can play out differentlyfor students. In both instances students had not yet verbalized a correct/completeexplanation before interacting with the teacher and the interactions elicited morestudent explaining. However, in the first example, the teacher used details of thestudents strategy given in the students initial explanation to drive her probingquestions. Her specific questions allowed the student to clarify the specifics of theinitial explanation and provide a correct/complete explanation. While the second

example also showed teacher probing, the teacher interjected her own interpretationof student thinking into her probing questions, and seemed satisfied with studentsengaging in additional explaining, even if the explanations were not correct orcomplete.

When teachers engaged with students around their work on the problem but didnot probe the details of student thinking about their problem-solving strategies(Table 4), groups often gave no additional explanation. Teacher behaviour oftenconsisted of repeating or revoicing something the students had said, althoughteachers sometimes evaluated students answers or strategies or, when groups werehaving difficulty, led them through the steps in the solution. Sometimes, teachersrevoicing of students explanations left the mistaken impression that the groupswork was correct. In the following example, the teacher asked groups to fill in thebox to make the number sentence true, but the group misinterpreted the problem.

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The teacher repeated the students answer (line 4) and implied that their answer wascorrect. The group did not talk about the problem after line 5.

Problem: 1000 + A 5 1000 + 50. A 5 %

1. Student 3: I think its A because the other A dont have no partner.2. Student 4: I think its A because A equals A is A because it didnt have a

partner at first.3. Student 3: I think A isnt, the A dont have no partner. So we should choose

the other4. Teacher: You think A equals A? OK.5. Student 4: You had it.

In some group conversations, the teacher intervened only to remind students totalk to each other, to share, or to explain (interaction around norms for behaviour).Some of these groups went on to give a correct/complete explanation. In thefollowing example, the students had given the correct answer (lines 1, 2) but did notgive an explanation until the teacher reminded students to talk to each other (line 3).The students responded that they had been talking about it (lines 48), but they didprovide explanations (lines 10, 11).

Problem: 8 + 25 7+ 3. True or false?

1. Student 5: Its true. Oh, I didnt see the three before.2. Student 6: Eight, nine, ten. True.3. Teacher: Talk to your neighbour about it.4. Student 6: I told her.5. Student 5: We did it.6. Student 6: I said it was true.7. Student 5: I know.8. Student 6: Its true.9. Student 5: Because10. Student 6: Because that equals ten and that equals ten.11. Student 5: Yeah. Eight plus two equals ten. Seven plus three equals three

I mean, ten.

Most groups receiving a norm-related statement from the teacher, however, didnot provide additional explanation. In the following example, as in the exampleabove, the group had provided an answer but no explanation (line 2) before theteacher intervened to remind students about the norms for behaviour (line 4).Despite their acknowledging the teachers statement (line 5), they did not do morethan repeat the answer (line 8). Neither student gave any explanation.

Problem: 10 + 105 10+ 10. True or false?

1. Student 7: I think its what do you think?2. Student 8: What do you think? Youre the person who writes.3. Student 7: I think its false. I mean true.4. Teacher: You guys need to do a better job today with communicating.5. Student 8: Yes.6. Teacher: Thank you.7. Student 7: You think its true or false?8. Student 8: True.

Comparison of the groups that gave more explanation after the teachersreminder about norms for behaviour and groups that gave no further explanationdid not provide any clues about the reasons for differences in groups behaviour. The


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two sets of group episodes were similar in terms of the nature of studentparticipation prior to the teachers intervention (e.g., the accuracy of their answers,the nature of any explanations they gave), their group work behaviour on previousproblems, and the wording of teachers reminders about the norms for behaviour. Toaccount for the effectiveness of these teacher reminders about group workbehaviour, it may be necessary to consider other factors such as general norms forbehaviour in a particular classroom, the nature of the problem, and the particularstudents who were working together (and their previous history of collaboration).

Finally, as shown in Table 4, when teachers made brief comments or suggestions,groups seldom gave more explanation after the teachers intervention. Teachersbrief comments or suggestions included acknowledging or evaluating student work(very creative, it looks good), repeating the problem assigned (Can you find yourown numbers to fill in instead of letters?), suggesting a strategy (Can we use the boxstrategy?), or commenting on behaviour (quiet down, let him borrow yourpencil). Typically, groups did little work after these teacher interjections.

Differences between classrooms in teacher practices

We next turned to investigating teacher practices at the classroom level to examinehow teacher practices in general both during whole-class instruction and whenintervening with small groups may have played a role in students explaining insmall groups. Table 5 shows the percentage of whole-class problems and teacherinterventions with small groups in which teachers probed student thinking and thepercentage in which they did not (teacher interaction around norms and classroom

Table 5. Teacher practices in whole-class and small-group comments.

Teacher practice Teacher a

1 2 3 4

Teacher probed students explanations to uncover details orfurther thinking about their problem-solving strategies

Whole-class instruction 23 b 25 92 71Small-group interventions 36 c 25 77 50

Teacher engaged with students around their work on theproblem but did not probe the details of student thinkingabout their problem-solving strategies

Whole-class instruction 77 75 8 29Small-group instruction 64 75 23 50

Note: (a) Number of problems with teacherstudent engagement in whole-class instruction foreach teacher are 30, 8, 12, 7, respectively. Number of small-group interviews for each teacherare 14, 8, 13, 8, respectively. (b) Percent of teacher engagements with students in whole-classinstruction in which the teacher exhibited this practice. (c) Percent of teacher interventionswith small groups in which the teacher exhibited this practice (includes only teacher

interventions around the math content; excludes teacher interventions around only norms forbehaviour or classroom management because those teacher practices did not occur duringwhole-class instruction.

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management issues are excluded from this table because they did not occurduring engagements with students in the whole-class context). Not only didteachers differ from one another in terms of their practices (differences betweenteachers in the whole class in the proportion of segments in which they probedstudents explanations to uncover details or further thinking about their problem-solving strategies, Fishers exact test, p, .001; differences between teachers insmall groups in the proportion of conversations in which they probed studentsexplanations to uncover details or further thinking about their problem-solvingstrategies, Fishers exact test, p5 .001), but their practices in the whole-classsetting were strikingly similar to their practices when engaging with small groups.Teacher 3 showed a strong tendency to probe students explanations, whether inthe whole class or in small groups. Teacher 4 probed student thinking asubstantial proportion of the time. Teachers 1 and 2, in contrast, most oftenengaged with students around their mathematics work without probing studentthinking beyond about the details of their strategies, both in the whole class andwith small groups.

Classroom differences in student explanations and student achievement

Teacher differences in their practices when engaging with students were reflectedin corresponding classroom differences in student explanations during group workand in student achievement. Table 6 gives the distribution of student explanationsand achievement across classrooms. Significant differences appeared betweenclassrooms on all variables (level of student explaining during group work, p, .001; written assessment, F (3, 74) 5 5.28, p, .01; individual interview, F (3, 74) 5

2.82, p, .05). In Classrooms 3 and 4, the majority of small groups producedcorrect/complete explanations; in Classrooms 1 and 2, only a minority of smallgroups did so, with the percentage in Classroom 1 being quite low. Differencesbetween classrooms in student achievement showed the same pattern, withachievement in Classrooms 3 and 4 being highest and achievement in Classrooms1 and 2 being lowest.

Table 6. Student explaining during group work and achievement across classrooms.

Classroom1 2 3 4

Student explaining in small groups

Group gave correct/complete explanation 16 a 33 72 56Group did not give correct/complete explanation 84 67 28 44

Student achievement

Written assessment score 17 b 30 47 45Individual interview score 13 b 24 37 44

Note: (a) Percent of group conservations in which group exhibited this behaviour; (b) Percentof problems correct.


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Discussion

This study examined the relationship between teacher practices and studentexplaining when they worked in collaborative small groups. We examined teacherpractices in two ways: (1) the relationship between specific teacher interventions with

small groups and the extent of student explaining in those groups; and (2)correspondences between teacher-to-teacher differences in their practices andclassroom-to-classroom differences in student explaining during collaborative groupwork. We discuss the results for each of these in turn.

When intervening with small groups, the teacher practice that had the strongestrelationship with student explaining was probing students explanations to uncoverdetails or further thinking about their problem-solving strategies. More than anyother teacher practice, probing students explanations when intervening with smallgroups corresponded to students giving more details about their problem-solvingstrategies, especially their producing correct/complete explanations of how to solvethe problem. Other ways of engaging with groups engaging around theirmathematics work (e.g., acknowledging an answer or explanation) without probingthe details of student thinking, referring to norms for behaviour, making other brief comments or suggestions were rarely linked to groups providing additionalexplanations or giving correct/complete explanations.

Not all instances of probing students explanations seemed to function in thesame way, however. Probing of students explanations was most likely to beassociated with additional student explaining (especially correct/complete explana-tions) when teachers used details of students strategies given in initial explanationsto drive the probing questions, when teachers persisted in asking questions to pushstudents to clarify ambiguous aspects of their explanations, and when teachers did

not interject their own thinking (or their own assumptions about what students werethinking) into their probing questions.

The kind of teacher probing of students thinking just described stronglyresembles the practices of teachers in the high-press classrooms that Kazemi andStipek (2001) found to correspond with a high level of student explaining. It alsoresembles the teacher practices that Hogan, Nastasi, and Pressley (2000) found toencourage a high level of scientific reasoning during group discussions: teachersasked students to describe their initial thinking, asked students to elaborate onspecific points they made in their initial explanation, and asked students to clarifylanguage they used and to expand and extend their explanations.

The finding in this study that issuing reminders or giving directives concerningnorms for behaviour was not often followed by additional explaining by groups isfairly consistent with Meloth and Deerings (1999) finding that non-specific teachermonitoring statements did not change the nature of group discussions, although it isinconsistent with Dekker and Elshout- Mohrs (2004) observations that remindersabout behaviour seemed to stimulate groups to share ideas. Further research isneeded to determine whether such norm-related reminders function differentlydepending on the general classroom norms for behaviour, the particular compositionof the group (as well as the groups history), the specific task or problem that a groupis working on (and challenges that the group may be facing in completing the task),and the nature of the groups communication prior to the teachers reminder.

In this study, teacher-to-teacher differences in their practices also correspondedto classroom-to-classroom differences in student explaining. The key variable

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distinguishing teachers was the extent to which they probed student thinking bothwhen interacting with students during whole-class instruction, and when interveningwith small groups. Not only did some teachers probe student thinking much morefrequently than did other teachers, the tendency of teachers to probe (or not probe)student thinking was remarkably consistent between their interactions with studentsduring whole-class interactions and when intervening with small groups. In theclassrooms in which teachers often probed student thinking, groups showed thehighest incidence of giving correct/complete explanations. In the classrooms in whichteachers did not often probe student thinking, groups showed lower incidences of giving correct/complete explanations.

This paper, then, uncovered positive associations between teacher probing of student thinking (during whole-class instruction and when interacting with smallgroups) and the nature and extent of explaining in small groups, especially whe-ther groups gave correct/complete explanations. How might we interpret theserelationships?

One interpretation is that teacher probing is an effective intervention strategy forpromoting explaining in small groups, especially for giving correct/completeexplanations. Teachers questions may help students clarify ambiguous explanations,make explicit steps in their problem-solving procedures, justify their problem-solvingstrategies, and correct their misconceptions or incorrect strategies. Anotherinterpretation is that frequent teacher probing of student thinking communicatesthe expectation that students should engage in extended explaining, especiallycontinuing until they are able to give correct/complete explanations. Thisexpectation then becomes a feature of the classroom climate that influences studentparticipation. Wood, Cobb, and Yackel (1991) observed this process in action. By

asking students to explain their methods for solving problems and refraining fromevaluating students answers, teachers helped create expectations and obligations forstudents to publicly display their thinking underlying how they solved mathematicalproblems.

We must be cautious, however, about interpreting the direction of effectsbetween teacher practice and student participation. While one interpretation of thepositive association between teacher probing and group explaining is that teacherprobing helped groups to explain further and give correct/complete explanations, itis also possible that (a) these groups would have given correct/complete explanationseven in the absence of the teachers probing questions (the teachers practice was

unrelated to group behaviour); (b) teachers chose certain groups for apply probingbehaviour with the expectation (perhaps based on previous experience orobservations) that they would be able or likely to provide more complete or correctexplanations (previous group behaviour influenced the teachers practice); (c) high-level student explaining (possibly due to higher student mathematical ability) elicitedteacher probing (when students revealed details about their strategies and thinking,teachers had more information on which to base probing questions); or (d) teacherpractices and student participation influenced each other in reciprocal fashion(teacher probing promoted student explaining, and student explaining enabledteacher probing).

Similar caveats apply to the relationship observed here between teacher-to-teacher differences in teacher practices and classroom-to-classroom differences ingroup behaviour. For example, students in some classrooms may be more capable of


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giving explanations than students in other classrooms, independent of their teacherspractices (perhaps as a result of classroom experiences in previous years; or as aresult of greater mathematical understanding to start with). To test these alternativeinterpretations, it would be important to observe small-group processes at thebeginning of the school year before teacher practices have a chance to influencestudent behaviour and before norms are developed, and, optimally, examine changesin both teacher practices and student behaviour over time.

A further qualification of the findings concerns the task and subject matter. Themathematical group-work tasks used here (often open-ended questions aboutmathematics conjectures) were conducive to student explaining and teacher probingof student thinking. Whether the details of teacher practices and studentparticipation found to be important in this study will emerge with other kinds of group-work tasks and in other content domains remains to be investigated.

The results of this study show the importance of paying attention to the details of teacher practices and student participation during group work. In this study, moresignificant than asking students to give explanations was teachers probing of theparticulars in student thinking; and more significant than whether students gaveexplanations was the accuracy and completeness of students explanations.

Our approach and findings have important methodological implications for futureresearch on teachers instructional practices and students learning in small groups.Close attention to what students say and do in relation to what a teacher says helps usunderstand the details of practice that matter for student learning. It is imperative notonly to analyze the dialogue among students, but also to examine student participationin relation to teacher participation and the context of the classroom. This type of analysis is difficult as one cannot strip what teachers say from the context in which it

happens or from how students engage with each other and with the teacher. Yet, thistype of analysis, in conjunction with a variety of student outcomes, can help usunderstand the ways in which teachers can support students understanding throughdialogue that supports students in explaining their thinking.

The findings also have important implications for teaching and professionaldevelopment of teachers in connection with small-group work. Teachers questionsshape what happens for students. More than simply asking students to explain theirthinking, it is important that teachers focus on what students say in relation tocritical ideas (here, in mathematics) and help students make the details of theirthinking explicit. There is a great deal of knowledge and skill embedded in these

practices, including making sense of what students are saying, drawing out thesubject-matter ideas, and supporting students in detailing that thinking. Theseprinciples can and should be embedded in professional development for teachers tohelp them develop their intervention practices with small groups. The findings of thisstudy provide good exemplars to include in such professional development.

Acknowledgements

This work was supported in part by the Spencer Foundation; the National ScienceFoundation (MDR-8550236, MDR-8955346); the Academic Senate on Research, Los

Angeles Division, University of California; and the Diversity in Mathematics EducationCenter for Learning and Teaching (DIME). Funding to DIME was provided by grant numberESI-0119732 from the National Science Foundation.

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We would like to thank Marsha Ing for her helpful comments on an earlier version of thisarticle.

Notes

1. Analyses of teacher practices and student participation in three of these classrooms werereported in Webb et al . (in press). The current study is larger and more comprehensive thanthe previous one: it uses a larger sample of classrooms, considers all instances of collaborative group work in all classrooms, uses more in-depth (and finer grained) codingof teacher practices and student activity, and analyzes links between teacher practices andstudent activity during the same group episodes.

2. For some classes prior achievement scores (standardized test scores from the previousspring) were not available. Consequently, we could not compute partial correlations tocontrol for prior achievement.

3. All recorded students except one ( n5 50) experienced a teacher intervention.4. All recorded students except one ( n5 50) were members of groups that had not already

given a correct/complete explanation by the start of the teacher intervention.5. For contingency tables with small expected cell counts, we used a Fishers exact test (Fisher,

1935).6. Unless otherwise indicated, all significance levels are the results of Fishers exact tests of

contingency tables.

Notes on contributors

Noreen M. Webb is a Professor in the Department of Education, Graduate School of Education & Information Studies, University of California, Los Angeles. Her research spans

domains in learning and instruction, especially the study of teaching and learning processesand performance of individuals and groups in mathematics and science classrooms, andeducational and psychological measurement.

Megan L. Franke is a Professor in the Department of Education, Graduate School of Education & Information Studies, University of California, Los Angeles. Her work focuses onunderstanding and supporting teacher learning through professional development,particularly within elementary mathematics.

Tondra De is a doctoral student in the Department of Education, Graduate School of Education & Information Studies, University of California, Los Angeles.

Angela G. Chan is a doctoral student in the Department of Education, Graduate School of Education & Information Studies, University of California, Los Angeles. Her researchinterests include issues of equity in the development of elementary mathematics teachers, witha particular focus on classroom practice and teacher identity.

Deanna Freund is a doctoral student in the Department of Education, Graduate School of Education & Information Studies, University of California, Los Angeles.

Pat Shein is a doctoral student in the Department of Education, Graduate School of Education & Information Studies, University of California, Los Angeles. Her interests includeexploring ways to support English Learner students in mathematics learning.

Doris K. Melkonian is a doctoral student in the Department of Education, GraduateSchool of Education & Information Studies, University of California, Los Angeles. Herinterests include collaborative learning, and gender related issues in mathematics and scienceeducation.


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