Webb Study

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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, Deanna

Freund, 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 ofstudents 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 promote

student learning, and increasing evidence exists about the kinds of interaction among

students that are necessary to achieve group works potential (ODonnell, 2006;

Webb & Palincsar, 1996). Less often studied is the role of the teacher in promoting

effective 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 how

their engagement with students during whole-class instruction relates to student

explaining during collaborative group work.

Empirical findings from group-work studies demonstrate the critical relationship

between explaining and achievement (see Fuchs et al., 1997; Howe et al., 2007; Howe

& Tolmie, 2003; King, 1992; Nattiv, 1994; Slavin, 1987; Veenman, Denessen, van

den Akker, & van der Rijt, 2005; Webb, 1991). Moreover, complex explanations

(e.g., giving reasons elaborated with further evidence) have been shown to be more

strongly related with learning than less complex explanations (providing simple

reasons: Chinn, ODonnell, & Jinks, 2000). Explaining to others can promote

*Corresponding author. Email: [email protected]

Cambridge Journal of Education

Vol. 39, No. 1, March 2009, 4970


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learning as the explainer has the opportunity to reorganize and clarify material, to

recognize misconceptions, to fill in gaps in her own understanding, to internalize and

acquire new strategies and knowledge, and to develop new perspectives and

understanding (Bargh & Schul, 1980; King, 1992; Peterson, Janicki, & Swing, 1981;

Rogoff, 1991; Saxe, Gearhart, Note, & Paduano, 1993; Valsiner, 1987). When

explaining their problem-solving processes, students think about the salient features

of the problem, which develops their problem-solving strategies as well as their

metacognitive awareness of what they do and do not understand (Cooper, 1999).

Given the relationship between explaining and student outcomes, what can

teachers do to promote student explaining in collaborative groups? Research has

found that providing instruction and practice in explanation-related behaviours has

beneficial effects on group discussion. Effective training programs include

instructing students in explaining their problem-solving strategies (instead of just

giving 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 (providing

reasons 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 combine

many 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 specific

high-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 listening

activities (Hythecker, Dansereau, & Rocklin, 1988; ODonnell, 1999; Yager,

Johnson, & Johnson, 1985), responding to specific prompts to explain why they

believe 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 and

supporting students as they engage together with the content.

Many cooperative learning researchers and theorists advise teachers to monitor

small group progress and to intervene when groups fail to progress or seem to be

functioning ineffectively, when no group member can answer the question, when

students exhibit problems communicating with each other, and when students

dominate 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 disagree

in unproductive ways and enable children to explore ideas more effectively. How

teachers should intervene with groups to facilitate productive small-group discussion is

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less clear. Cohen (1994) cautioned teachers to intervene minimally with small groups,

arguing that students will be more likely to initiate ideas and take responsibility for their

discussions if teachers provide little explicit content help. She recommended that

teachers carefully listen to group discussions to make hypotheses about the groups

difficulties before deciding on questions to ask or suggestions to make.

The results of some studies examining the relationship between teachers

interventions with small groups and the quality of group discussion support Cohens

(1994) caution against direct teacher supervision. Chiu (2004) found that higher

levels of teacher help (e.g., explaining a concept, or giving a solution tactic) reduced

groups subsequent time-on-task and depth of their discussions (whether students

provided new ideas and explanations) compared to lower levels of teacher help (e.g.,

drawing attention to an aspect of the problem through asking questions instead of

providing a solution strategy or telling groups how to proceed). Gillies (2004) and

Dekker and Elshout-Mohr (2004) also confirmed the detrimental effect of giving

groups direct help about the task content. In Gillies study, students in classrooms

with teachers who engaged in communication behaviours such as asking open andtentative questions to probe, clarify, and focus student thinking provided more

detailed explanations than did students in classrooms in which teachers provided

direct instruction and explicit content help. In Dekker and Elshout-Mohrs study,

students in classrooms in which teachers were instructed to provide only process help

to groups (e.g., encouraging students to explain and justify their work) engaged in

more extensive discussions and exhibited more equal participation among group

members than students in classrooms in which teachers were instructed to provide

only content help (e.g., hints about the mathematical content and strategies).

Somewhat in contrast to the findings just described, Meloth and Deering (1999)

reported that high-content help (e.g., providing direct instruction about content) wasnot necessarily detrimental to productive group discussions.

An important qualification of these results may serve as a unifying thread

throughout these studies, helping to resolve the apparently inconsistent results.

Meloth and Deering found that high-content help facilitated productive group

discussion when the teacher listened to the groups ideas (for example, finding out

whether groups were focusing on irrelevant information) before providing specific

instruction. Chiu (2004) also suggested that what was effective about the indirect

help that teachers provided in his study was that teachers asked questions of students

to elicit their suggestions about how to proceed. Similarly, Gillies (2004) examples of

teachers who had received communications skills training showed teachersascertaining students ideas and strategies before offering suggestions or focusing

the groups attention on aspects of the task.

An intriguing possibility, then, is that what matters in terms of teacher

interventions with small groups is not whether teachers provide help that focuses on

the subject matter content of group work versus guidance about what collaborative

processes groups should carry out, or whether teachers should provide more-explicit

versus less-explicit content help. Rather, what may be important is whether teachers

try to ascertain student thinking and base their interaction with the group on what

they learn about students thinking on the task. The importance of teachers doing

this finds much support in wider literatures on effective teaching practices (see

Fennema et al., 1996; Franke, Carpenter, Levi, & Fennema, 2000; Franke, Kazemi,

& Battey, 2007; Lampert, 1990; Mercer, 2000).

Cambridge Journal of Education 51


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Kazemi and Stipek (2001) contrasted elementary school mathematics

classrooms in which teachers pressed students to explain and justify their

problem-solving strategies mathematically (they termed these practices high-

press) with classrooms in which teachers asked students to describe steps they

used to solve problems but did not ask students to link their strategies to

mathematical reasons or to explain why they chose particular procedures (low-

press). When working collaboratively, students in high-press classrooms used

mathematical arguments to explain why and how their solutions worked and to

arrive at mutual understanding, whereas students in low-press classrooms

summarized, but did not explain, their steps for solving a problem and did

not debate the mathematics involved in the problem. Webb et al. (in press) also

found similar results in that the extent to which teachers asked students to

elaborate on their explanations about how to solve mathematical problem

showed a strong relationship with the nature and extent of students explaining

to 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 in

that study did not ask students about their thinking but instead assumed most

of the responsibility for setting up the steps in the problem (typically with little

or no rationale given for the mathematics underlying the steps) and asked

students simply to provide the results of specific calculations that the teachers

themselves had posed.

Extending previous research, this study examines how teachers practices both

with small groups and with students in the larger classroom context may relate to

student 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, relates

to the accuracy and completeness of students explanations during collaborative

group work. It should be noted that the analyses reported here address associations

between teacher and student variables, not causal relationships; this issue is discussed

at 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 small

groups and the extent of student explaining in those groups?

(2) What are the correspondences between teacher-to-teacher differences in

their 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 large

urban school district in Southern California are the focus of this study.1 These

schools are large (more than 1100 students), serve predominantly Latino (with some

African-American) students, have a high percentage of students receiving free or

reduced lunch, have a substantial proportion of English language learners, and have

low standardized achievement test scores.

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Teacher professional development

The four teachers were part of a large-scale study focused on supporting teachers

efforts 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 ofstudents algebraic reasoning and, in particular, how that reasoning could support

students understanding of arithmetic. The professional development content, drawn

from Thinking mathematically: Integrating arithmetic and algebra in the elementary

school (Carpenter et al ., 2003), highlighted relational thinking, including:

(a) understanding the equal sign as an indicator of a relation; (b) using number

relations to simplify calculations; and, (c) generating, representing, and justifying

conjectures about the fundamental properties of numerical operations. Teachers

received guidance in how to engage their students in conversations in order to help

them explain their thinking and debate their reasoning and how to encourage

students to solve problems in their own ways. A primary focus was on teachers

eliciting student explanations and supporting students to describe the details of their

thinking (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 student

characteristics (e.g., achievement level, gender), group composition can be

considered random. Analysis of group composition showed a variety of groupings

in each class (e.g., some same-gender pairs, some mixed-gender pairs), with no

particular pattern predominating. The groups remained intact for the two occasions

of observations analyzed here; otherwise, group membership was fluid and teachers

changed group composition frequently.

Each class was videotaped and audiotaped on two occasions within a one-week

period. 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 20

students enrolled in each class. Comparison of the recorded students with the non-

recorded students revealed no significant differences in gender, ethnicity, or

performance on the achievement tests administered in this study.

Observers recorded classroom activity as teachers taught problems of their choice

related to the topics of equality and relational thinking. Teachers posed such problems

as (a) 50+50525+%+50, and (b) 11+255+8 (true or false?). Consistent with their

accustomed practice, teachers incorporated group-work time into the class during

which students worked together to solve and discuss problems assigned by the teacher.

Teachers introduced a problem, asked groups to work together to solve the problem

and share their thinking, and then brought the whole class together for selected students

to 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 verbatim

records of teacher and student talk, annotated to include the details of their non-

verbal participation. These transcripts included whole-class discussion as well as

group-work discussion for recorded students. We also collected student written

work, took field notes during class sessions, and administered student-achievement

measures.

Measures of student achievement

We used two measures of student achievement in this study. The written assessment

was designed to measure relational thinking. Some items were designed to assess

students understanding of the equal sign, and whether students held a relational

view of the equal sign (Jacobs et al., 2007). For example, to answer the problem

3+45%+5, students needed to know that the numbers to the left of the equal sign

summed 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 to

simplify calculations. For example, in 889+11821185%, students could simplify this

problem by recognizing that 118211850.

We also individually interviewed the students from each class who were audio or

videotaped on the observation days. We asked students what number they would put

in the box to make certain number sentences true, for example, 13+185%+19, and

asked them to describe their problem-solving strategies. For this paper, we analyzed

the accuracy of their answers. Internal consistency alpha coefficients for the written

assessment and interview were .88 and .74, respectively.

Coding of student and teacher participation

Using transcripts of all classroom talk we coded teacher and student participation

during whole-class and group-work discussions. To analyze whole-class discussions,

we separated the interaction into segments, each of which consisted of one bounded

interaction between the teacher and a particular student. A segment consisted of a

minimum of two conversational turns each for the teacher and the student. When

analyzing group interaction, we coded each group conversation on a problem as a

single unit. The group conversation started when the group began discussing the

assigned problem and ended when the teacher called the class together again.

We coded teacher practices across the entire lesson (all whole-class segments and

all group conversations). The four teacher practices coded were: (a) probes students

explanations to uncover details or further thinking about their problem-solving

strategies (asks specific questions about details in a students explanation); (b)

engages with students around their work on the problem (either an answer or an

initial explanation) but does not probe the details of student thinking about their

problem-solving strategies (typically, repeats or revoices the students work without

asking further questions); (c) interacts with the group only around norms for

behaviour (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 comment

concerning classroom management).

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We coded student participation along two dimensions. First was the highest level

of 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 was

considered complete if the coder could unambiguously discern how the student

solved the problem. This included evidence from both verbal and non-verbal

communication (such as gesturing to different parts of the number sentence). A

correct and complete explanation was any explanation that described in detail a

strategy that would consistently work for the problem, and involved an

unambiguous and appropriate solution to the problem. Any explanation not

considered complete was coded as incomplete, which included both incomplete and

ambiguous explanations. An incorrect explanation was an explanation that was

mathematically inconsistent with the problem posed.

The second student participation dimension reflected the extent of the group

explaining during or after a teachers intervention compared to the group explaining

prior to the teachers intervention, and was coded only for groups that had not givena correct/complete explanation prior to the teachers intervention. The three codes

were: (a) the group gives more explanation than before the teachers intervention,

and the explanation is correct and complete; (b) the group gives more explanation

than before the teachers intervention, but it is not correct and complete; and (c) the

group gives no further explanation.

Seven members of the research team coded student and teacher participation. We

developed and set standards for the application of the coding through an iterative

process that occurred over many regular weekly meetings. Each research-team

Table 1. Examples of student explanations.

Explanation category Example

Correct and complete Problem: 10+1021055+

Five? Its cause look. We could do this, oh no. Hold up. Cause

ten plus ten equals twenty, huh? And then it says minus ten

equals five plus blank. So it gotta be equal ten, so five plus

five equals ten. And thats how I got it. Get it?

Ambiguous or incomplete Problem: 8+257+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, this

explanation does not make it clear (a) whether the student is

considering 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 number

sentence is true.]

Incorrect Problem: 4+9556322 (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: 3755 + (3* 10)Let me see. 345?



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member was involved in the development of the codes and had primary

responsibility for coding particular problems and particular groups of students

from each classroom. We resolved questions about coding through discussion, and

these questions often led to further refinement of the teacher and student codes.

After we refined the codes, research-team members systematically reviewed their

own and others coding to ensure that the codes reflected the final coding scheme andto uncover inconsistencies in coding. All inconsistencies were brought to the entire

team and were resolved through discussion and consensus.

Results

In the following sections, we provide results about teachers instructions for student

behaviour during group work (to produce a picture of these classrooms climates for

student 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 student

achievement.

Teachers instructions about student collaboration

All of the teachers in this study gave frequent reminders to students about how to

collaborate during group work. First, in the majority (70%) of the 40 problems

assigned for group work across the four classrooms observed here, teachers gave

preliminary reminders to the whole class about student participation in their groups.

The most common reminders were for students to share with their neighbour and

talk with your table partners. Some teacher instructions were more specific, such as

the need to share why you think so or why you dont think so, What kind of thinking

went on? How did you solve it? and Instead of just saying true or false, tell [your

partners] 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 specific

reminders for students to work together, to talk about the problem with each other, to

discuss with their group how they were solving the problem, and to explain to each

other. These results show that teachers frequently communicated expectations for

students to share their work and, often, for students to explain their thinking behind

their 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 work

conversations observed across the four classrooms, groups gave explanations in 129

(62%) of them. Thus, these classrooms had climates that seemed to be conducive to

explaining during collaborative group work.

Relationship between student participation during group work and student achievement

We next examined the relationship between student participation during group work

and their achievement to confirm that the previously established relationship

between explaining and achievement held up in these classrooms. Consistent with

previous research, Table 2 shows that explaining was significantly correlated with

achievement.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, the

higher were their achievement scores. Other kinds of student participation (giving

ambiguous, incomplete, or incorrect explanations; giving only answers; giving

neither answers nor explanations) were not related or were negatively related to

achievement. The remaining sections, then, pay particular attention to the

relationship between teacher practices and students giving correct and complete

explanations.

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 had

already 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 a

correct/complete explanation; in 19%, groups produced some explanation but it was

not correct or complete; and in 43%, groups did not produce any explanation. The

difference in explanation patterns for group episodes with a teacher intervention and

those without a teacher intervention was not statistically significant (x2

(2;N5208)53.74, p5.15), which suggests that teachers did not target groups for

intervention based on students explaining behaviour.

When they engaged with groups, teachers used a variety of practices, as shown in

Table 3. In about half of the interventions (53%), teachers interacted with groups

around explanations or other work (e.g., answers) on the mathematics problems. In

many of these interventions, teachers probed students explanations to uncover

additional details about their problem-solving strategies or further thinking

underlying their strategies. In about half of the teacher interventions (47%), teachers

interacted with groups only around norms for behaviour or management issues. The

distributions of teacher practices were similar for groups that had already provided

a 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 achievement

scores.

Highest level of student participation on a

problemaWritten assessment

scorebIndividual interview

scoreb

Gives explanation .46*** .27

Correct and complete .61*** .46***

Ambiguous, incomplete or incorrect 2.18 2.30*

Gives no explanation 2.46*** 2.27*

Answer only .08 .20

No 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; N581)52.70, 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 that

were given after the teachers arrival, specifically whether groups gave more

explanation 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 with

groups that had not already given a correct/complete explanation by the start of the

teacher intervention.4

As shown in Table 4, when teachers probed students explanations, groups nearly

always gave additional explanation and many of them produced a correct/complete

explanation of how to solve the problem by the end of the groups discussion of that

problem. The other teacher practices, in contrast, were less likely to be associated

with additional explaining or to produce correct/complete explanations. The

differences in effectiveness of teacher practices for group behaviour were statistically

significant (Fishers exact test, p5.001).5

Although probing students explanations was more likely than other teacher

practices to be associated with groups producing correct/complete explanations, not

Table 3. Teacher practices with small groups.

Teacher practice All teacher

interventions

(81 group

conversations)

Groups gave correct/complete explanation

prior to the teachers intervention

Yes (22 groupconversations) No (59 groupconversations)

Teacher probed students

explanations to uncover

details or further thinking

about their problem-solving

strategies

26a 23 27

Teacher engaged with students

around their work on the

problem but did not probe

the details of student thinkingabout their problem-solving

strategies

27 32 25

Teacher interacted with the

group only around norms for

behaviour

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 examples

contrast more-effective and less-effective instances of teacher probing. In the first

example, the teacher responds to a students ambiguous explanation by asking a

sequence of questions specific to what the student said. The questions direct the

student to say more about particular aspects of her strategy. The teacher asks

questions about the students strategy until the student has described an explicit

connection between the two sides of the number sentence: 7+1 and the 1022. During

this interchange, the student engages in additional explaining (lines 3, 5, 11, 13) beyond

the initial explanation (line 1) and arrives at a correct/complete explanation (line 13).

Problem: 7+15102%

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 worka.

Group explaining during or after teachers intervention

Group gave more explanation than

before the teachers intervention

Group did not give

more explanationthan before the

teachers intervention

Teacher practiceb Additional

explanation was

correct/complete

Additional

explanation was not

correct/complete

Teacher probed students

explanations to uncover

details or further thinking

about their problem-solving

strategies

63c 31 6

Teacher engaged with students

around their work on the

problem but did not probe

the details of student

thinking about their

problem-solving strategies

20 20 60

Teacher interacted with the

group only around norms

for 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/complete

explanation by the time the teacher intervened (59 interventions). (b) Number of group

conversations 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 ambiguous

explanation (line 1) with a follow-up question (line 2) that seeks clarification ofwhat the student said. The teacher makes a claim in the follow-up question that

extends what the student said and then asks the student if that is what he was

thinking. 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 yield

a correct/complete explanation, nor does this student or group ever produce a

correct/complete explanation for this problem.

Problem: a5b+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 B

side.

These examples highlight how probing student thinking can play out differently

for students. In both instances students had not yet verbalized a correct/complete

explanation before interacting with the teacher and the interactions elicited more

student explaining. However, in the first example, the teacher used details of the

students strategy given in the students initial explanation to drive her probing

questions. Her specific questions allowed the student to clarify the specifics of the

initial 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 students

engaging in additional explaining, even if the explanations were not correct or

complete.

When teachers engaged with students around their work on the problem but did

not probe the details of student thinking about their problem-solving strategies

(Table 4), groups often gave no additional explanation. Teacher behaviour often

consisted of repeating or revoicing something the students had said, although

teachers sometimes evaluated students answers or strategies or, when groups were

having difficulty, led them through the steps in the solution. Sometimes, teachers

revoicing of students explanations left the mistaken impression that the groups

work was correct. In the following example, the teacher asked groups to fill in the

box 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 was

correct. The group did not talk about the problem after line 5.

Problem: 1000+A51000+50. A5%

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 apartner at first.

3. Student 3: I think A isnt, the A dont have no partner. So we should choosethe other

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

In some group conversations, the teacher intervened only to remind students to

talk 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 the

following example, the students had given the correct answer (lines 1, 2) but did not

give 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 did

provide explanations (lines 10, 11).

Problem: 8+257+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, did

not provide additional explanation. In the following example, as in the example

above, the group had provided an answer but no explanation (line 2) before the

teacher intervened to remind students about the norms for behaviour (line 4).

Despite their acknowledging the teachers statement (line 5), they did not do more

than repeat the answer (line 8). Neither student gave any explanation.

Problem: 10+10510+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 teachers

reminder about norms for behaviour and groups that gave no further explanation

did 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 student

participation prior to the teachers intervention (e.g., the accuracy of their answers,

the nature of any explanations they gave), their group work behaviour on previous

problems, and the wording of teachers reminders about the norms for behaviour. To

account for the effectiveness of these teacher reminders about group work

behaviour, it may be necessary to consider other factors such as general norms for

behaviour in a particular classroom, the nature of the problem, and the particular

students 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. Teachers

brief comments or suggestions included acknowledging or evaluating student work

(very creative, it looks good), repeating the problem assigned (Can you find your

own numbers to fill in instead of letters?), suggesting a strategy (Can we use the box

strategy?), or commenting on behaviour (quiet down, let him borrow your

pencil). 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 examine

how teacher practices in general both during whole-class instruction and when

intervening with small groups may have played a role in students explaining in

small groups. Table 5 shows the percentage of whole-class problems and teacher

interventions with small groups in which teachers probed student thinking and the

percentage in which they did not (teacher interaction around norms and classroom

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

Teacher practice Teachera

1 2 3 4

Teacher probed students explanations to uncover details or

further thinking about their problem-solving strategies

Whole-class instruction 23b 25 92 71

Small-group interventions 36c 25 77 50

Teacher engaged with students around their work on theproblem but did not probe the details of student thinking

about their problem-solving strategies

Whole-class instruction 77 75 8 29

Small-group instruction 64 75 23 50

Note: (a) Number of problems with teacherstudent engagement in whole-class instruction for

each teacher are 30, 8, 12, 7, respectively. Number of small-group interviews for each teacher

are 14, 8, 13, 8, respectively. (b) Percent of teacher engagements with students in whole-class

instruction in which the teacher exhibited this practice. (c) Percent of teacher interventions

with 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 during

whole-class instruction.

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management issues are excluded from this table because they did not occur

during engagements with students in the whole-class context). Not only did

teachers differ from one another in terms of their practices (differences between

teachers in the whole class in the proportion of segments in which they probed

students explanations to uncover details or further thinking about their problem-

solving strategies, Fishers exact test, p,.001; differences between teachers in

small groups in the proportion of conversations in which they probed students

explanations to uncover details or further thinking about their problem-solving

strategies, Fishers exact test, p5.001), but their practices in the whole-class

setting were strikingly similar to their practices when engaging with small groups.

Teacher 3 showed a strong tendency to probe students explanations, whether in

the whole class or in small groups. Teacher 4 probed student thinking a

substantial proportion of the time. Teachers 1 and 2, in contrast, most often

engaged with students around their mathematics work without probing student

thinking beyond about the details of their strategies, both in the whole class and

with small groups.

Classroom differences in student explanations and student achievement

Teacher differences in their practices when engaging with students were reflected

in corresponding classroom differences in student explanations during group work

and in student achievement. Table 6 gives the distribution of student explanations

and achievement across classrooms. Significant differences appeared between

classrooms on all variables (level of student explaining during group work,

p,.001; written assessment, F(3, 74)55.28, 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 small

groups did so, with the percentage in Classroom 1 being quite low. Differences

between classrooms in student achievement showed the same pattern, with

achievement in Classrooms 3 and 4 being highest and achievement in Classrooms

1 and 2 being lowest.

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

Classroom

1 2 3 4

Student explaining in small groups

Group gave correct/complete explanation 16a 33 72 56

Group did not give correct/complete explanation 84 67 28 44

Student achievement

Written assessment score 17b 30 47 45

Individual interview score 13b 24 37 44

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

of problems correct.



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distinguishing teachers was the extent to which they probed student thinking both

when interacting with students during whole-class instruction, and when intervening

with small groups. Not only did some teachers probe student thinking much more

frequently than did other teachers, the tendency of teachers to probe (or not probe)

student thinking was remarkably consistent between their interactions with students

during whole-class interactions and when intervening with small groups. In the

classrooms in which teachers often probed student thinking, groups showed the

highest incidence of giving correct/complete explanations. In the classrooms in which

teachers 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 small

groups) and the nature and extent of explaining in small groups, especially whe-

ther groups gave correct/complete explanations. How might we interpret these

relationships?

One interpretation is that teacher probing is an effective intervention strategy forpromoting explaining in small groups, especially for giving correct/complete

explanations. Teachers questions may help students clarify ambiguous explanations,

make explicit steps in their problem-solving procedures, justify their problem-solving

strategies, and correct their misconceptions or incorrect strategies. Another

interpretation is that frequent teacher probing of student thinking communicates

the expectation that students should engage in extended explaining, especially

continuing until they are able to give correct/complete explanations. This

expectation then becomes a feature of the classroom climate that influences student

participation. 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 for

students to publicly display their thinking underlying how they solved mathematical

problems.

We must be cautious, however, about interpreting the direction of effects

between teacher practice and student participation. While one interpretation of the

positive association between teacher probing and group explaining is that teacher

probing helped groups to explain further and give correct/complete explanations, it

is also possible that (a) these groups would have given correct/complete explanations

even 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 or

observations) that they would be able or likely to provide more complete or correct

explanations (previous group behaviour influenced the teachers practice); (c) high-

level student explaining (possibly due to higher student mathematical ability) elicited

teacher probing (when students revealed details about their strategies and thinking,

teachers had more information on which to base probing questions); or (d) teacher

practices and student participation influenced each other in reciprocal fashion

(teacher probing promoted student explaining, and student explaining enabled

teacher probing).

Similar caveats apply to the relationship observed here between teacher-to-

teacher differences in teacher practices and classroom-to-classroom differences in

group 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 teachers

practices (perhaps as a result of classroom experiences in previous years; or as a

result of greater mathematical understanding to start with). To test these alternative

interpretations, it would be important to observe small-group processes at the

beginning of the school year before teacher practices have a chance to influence

student behaviour and before norms are developed, and, optimally, examine changes

in both teacher practices and student behaviour over time.

A further qualification of the findings concerns the task and subject matter. The

mathematical group-work tasks used here (often open-ended questions about

mathematics conjectures) were conducive to student explaining and teacher probing

of student thinking. Whether the details of teacher practices and student

participation 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, more

significant than asking students to give explanations was teachers probing of theparticulars in student thinking; and more significant than whether students gave

explanations was the accuracy and completeness of students explanations.

Our approach and findings have important methodological implications for future

research 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 us

understand the details of practice that matter for student learning. It is imperative not

only to analyze the dialogue among students, but also to examine student participation

in 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 us

understand the ways in which teachers can support students understanding through

dialogue that supports students in explaining their thinking.

The findings also have important implications for teaching and professional

development of teachers in connection with small-group work. Teachers questions

shape what happens for students. More than simply asking students to explain their

thinking, it is important that teachers focus on what students say in relation to

critical ideas (here, in mathematics) and help students make the details of their

thinking 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. These

principles can and should be embedded in professional development for teachers to

help them develop their intervention practices with small groups. The findings of this

study provide good exemplars to include in such professional development.

Acknowledgements

This work was supported in part by the Spencer Foundation; the National Science

Foundation (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 number

ESI-0119732 from the National Science Foundation.

66 N.M. Webb et al.


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

article.

Notes

1. Analyses of teacher practices and student participation in three of these classrooms were

reported in Webb et al. (in press). The current study is larger and more comprehensive than

the 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) coding

of teacher practices and student activity, and analyzes links between teacher practices and

student activity during the same group episodes.

2. For some classes prior achievement scores (standardized test scores from the previous

spring) were not available. Consequently, we could not compute partial correlations to

control for prior achievement.

3. All recorded students except one (n550) experienced a teacher intervention.

4. All recorded students except one (n550) 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, and

educational 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 on

understanding 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, with

a 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 include

exploring ways to support English Learner students in mathematics learning.

Doris K. Melkonian is a doctoral student in the Department of Education, Graduate

School of Education & Information Studies, University of California, Los Angeles. Her

interests include collaborative learning, and gender related issues in mathematics and science

education.



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