Effects of Workgroup Structure and Size on Student Productivity during Collaborative Work on Complex Tasks

Effects of Workgroup Structure and Size on Student Productivity during Collaborative Workon Complex TasksAuthor(s): Lynn S. Fuchs, Douglas Fuchs, Sarah Kazdan, Kathy Karns, Mary Beth Calhoon,Carol L. Hamlett and Sally HewlettSource: The Elementary School Journal, Vol. 100, No. 3 (Jan., 2000), pp. 183-212Published by: The University of Chicago PressStable URL: http://www.jstor.org/stable/1002151 .

Accessed: 13/07/2014 11:06

Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp

.JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range ofcontent in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new formsof scholarship. For more information about JSTOR, please contact [email protected].

.

The University of Chicago Press is collaborating with JSTOR to digitize, preserve and extend access to TheElementary School Journal.

http://www.jstor.org

This content downloaded from 130.217.227.3 on Sun, 13 Jul 2014 11:06:38 AMAll use subject to JSTOR Terms and Conditions

http://www.jstor.org/action/showPublisher?publisherCode=ucpress

http://www.jstor.org/stable/1002151?origin=JSTOR-pdf

http://www.jstor.org/page/info/about/policies/terms.jsp


Effects of Workgroup Structure and Size on Student Productivity during Collaborative Work on Complex Tasks

Lynn S. Fuchs Douglas Fuchs Sarah Kazdan

Kathy Karns

Mary Beth Calhoon Carol L. Hamlett

Sally Hewlett Peabody College of Vanderbilt University

The Elementary School Journal Volume 100, Number 3 C 2000 by The University of Chicago. All rights reserved. 0013-5984/2000/10003-0001$02.00

Abstract

The purpose of this study was to examine the effects of workgroup size and structure during collaborative work on complex tasks. We randomly assigned 36 third- and fourth-grade classrooms to 2 workgroup sizes (pairs vs. small groups) and to 3 background structures (individual vs. collaborative vs. collaborative with structured role, goal, resource, and reward interdependence). After 4 weekly classroom performance assessments (PAs) in these conditions, 1 workgroup from each classroom, which incorporated the lowest- and highest-achieving student (as well as 2 middle achievers in small groups), was videotaped outside the classroom. Analyses of variance conducted on videotaped data indicated that, regardless of students' achievement status, pairs earned higher scores than small groups on participation, helpfulness, cooperation, quality of talk, and PA work. Al- though dyads produced greater collaboration for low-achieving students, small groups generated more cognitive conflict among other students. Productivity did not differ as a function of background structure. We discuss implications for optimizing grouping arrangements and prepar- ing students to work productively during collaborative activities on complex tasks.

A substantial body of research documents the effectiveness of cooperative learning, in which children work with children to support each other's learning (Bossert, 1988). Despite the strength of the database sup- porting this conclusion, long-standing research programs (e.g., King, 1992; Webb, 1991) also provide the basis for an important qualification: Certain types of student interactions are essential to the effectiveness of cooperative learning.

Interactions That Support Learning Research offers guidance about which student behaviors within cooperative groups



184 THE ELEMENTARY SCHOOL JOURNAL

promote learning. Children who construct

explanations, which clarify processes, to

help classmates arrive at their own solutions learn more than children who simply tell classmates answers (Nattiv, 1994; Par- adis & Peverly, 1994; Swing & Peterson, 1982; Webb, 1989, 1991, 1992; Webb, Troper, & Fall, 1992). Theoretical support for this

phenomenon comes from a generative model of learning (Wittrock, 1989), which

posits that if new information is to be re- tained and meaningfully related to previously acquired knowledge, the learner must elaborate-or generate connections between that information and representations in memory. One strategy for encouraging learners to elaborate material is to have them explain it to others.

From the perspective of the recipient of those explanations, however, the simple provision of explanations is not sufficient to

promote learning. Rather, recipients per- form better when explanations are timely, relevant, correct, and elaborated (see Webb, Troper, & Fall, 1995) and when recipients have opportunities to apply explanations to novel material (King, 1989; Webb et al., 1995). The importance of timely, relevant, correct, and elaborated explanations finds

support in the teacher effectiveness literature (e.g., Good & Grouws, 1977); the im-

portance of applying explanations is consistent with a constructivist perspective on

learning (Vygotsky, 1978; Wertsh, 1984). Another line of research offering guid-

ance about productive student behaviors shows that children learn more when they engage in and resolve cognitive conflict with peers (e.g., Bearison, 1982; Doise &

Mugny, 1979; Mugny & Doise, 1978; Nas- tasi, Clements, & Battista, 1990). Grounding for such findings comes from sociocognitive theory, which, based on the work of Piaget (1928), posits that internal cognitive conflict arises when children express alternative perspectives. In resolving those disagreements, children explain and justify positions, question beliefs, seek new information, or adopt alternative frameworks and

conceptualizations (see Bell, Grossen, & Perret-Clermont, 1985; Brown & Palincsar, 1989; Glachan & Light, 1982; Tudge, 1989).

Unfortunately, observations reveal that students do not develop these effective interactional styles as a natural function of

participating in workgroups (Cooper &

Cooper, 1984; Fuchs, Fuchs, Bentz, Phillips, & Hamlett, 1994; Michaels & Bruce, 1991; Palincsar & Brown, 1989). Studies do, nevertheless, demonstrate that children can be

taught to be cooperative and helpful in

workgroups (Ashman & Gillies, 1997; Mesch, Lew, Johnson, & Johnson, 1986; Ya-

ger, Johnson, & Johnson, 1985), to provide elaborated (Swing & Peterson, 1982; Webb & Farivar, 1994) and conceptual (L. Fuchs et al., 1997) explanations, to offer peers opportunities to apply explanations (L. Fuchs et al., 1997; Webb et al., 1995), and to generate and resolve controversy (Johnson & Johnson, 1985; Smith, Johnson, & Johnson, 1981).

Structuring Activities to Elicit Productive Interactional Styles Research also indicates that certain cooperative learning structures may induce students to use productive interactional styles (for reviews, see Cohen, 1994, or Slavin, 1996). In the current study, we attempted to extend this database by conducting a field- based experiment examining the effects on student productivity of two workgroup features: structured interdependence and

workgroup size.

Structured Interdependence Structures that induce students to use

productive interactional styles include out- come interdependence, whereby individu- als achieve goals only if workgroup members also achieve goals (Deutsch, 1949; Johnson, Johnson, & Stanne, 1990) or rewards (O'Donnell, 1996; Slavin, 1996); means interdependence, whereby individ- uals achieve goals only when workgroup members share resources and roles (Ehrlich, 1991; Johnson & Johnson, 1992); and indi-

JANUARY 2000



PRODUCTIVITY 185

vidual accountability, whereby each student is accountable for learning (Slavin, 1996).

Unfortunately, structuring group work with an explicit role, goal, resource, and reward interdependence complicates practi- tioners' use of cooperative learning by re-

quiring substantial teacher training and commitment (Slavin, 1996). It is not surprising, therefore, that teachers typically con- duct cooperative learning in unstructured

ways that do not incorporate features that

promote the constructive interactional

styles research has identified (Antil, Jen- kins, Wayne, & Vadasy, 1998; Sharan, 1990).

Two features of the research base do, however, make it difficult to determine how

problematic teachers' unstructured imple- mentation is for promoting productive interactional styles within the context of current education practice. The first source of confusion stems from the increasing diver-

gence between the kinds of tasks used in today's classrooms for cooperative activities and the kinds of tasks used in cooperative learning research. With curricular reform over the past decade, classroom tasks have become increasingly complex and challenging, with greater application of

problem-solving skills and strategies (Goodman, 1995). These tasks contrast sharply with those incorporated in most cooperative learning studies, which typically have required simple recall, application of rote algorithms, or noncontroversial problem solving (see Cohen, 1994; Slavin, 1996).

This first problem is exacerbated by a second source of confusion in the available literature. In a careful analysis of that work, Cohen (1994) speculated that complex tasks, by definition, may require group interaction, because no individual has the knowledge necessary for problem solution. Given this inherent source of group interdependence, complex tasks may naturally motivate students to participate and cooperate (Hertz-Lazarowitz, 1989), elicit elaborated discussion (Nystrand, Gamoran, & Heck, 1991; Smith et al., 1981), and produce

cognitive conflict and resolution (Smith et al., 1981). In a recent literature review, Slavin (1996) also discussed this possibility, and Cohen went further to propose that structured interactions over complex tasks may actually constrain productive interaction. As described by Slavin as well as Co- hen, research is warranted to examine the tenability of this proposition.

Workgroup Size A variety of cooperative learning meth-

ods, all shown to be effective, rely on dyads (e.g., Aronson, 1978; Fantuzzo, King, & Heller, 1992; D. Fuchs, L. Fuchs, Mathes, & Simmons, 1997; Greenwood, Delquadri, & Hall, 1989; King, 1992) or small groups (e.g., Peterson & Swing, 1985; Slavin, Madden, &

Leavey, 1984; Webb et al., 1995). Although some (e.g., Damon, 1984; Sharan, 1980) have characterized the potential strengths and limitations of dyadic versus small-group compositions, validated methods vary in terms of their problem-solving approaches, the types of tasks they incorporate, and the interdependence structures they employ. This makes it impossible to formulate clear conclusions on the basis of the efficacy literature.

Moreover, few studies have experimen- tally manipulated the productivity of student interactions as a function of workgroup size while keeping other structural variables constant and while using complex tasks. In our literature review, for example, we identified only four relevant studies, which provided inconsistent findings. In the more pertinent investigations, Klingner and Vaughn (1996) found comparable effectiveness when reciprocal teaching was conducted in dyads and small groups; by contrast, Moody and Gifford (1990) docu- mented stronger learning for pairs over groups on laboratory chemistry exercises. In less pertinent, but related, studies, Jen- kins, Mayhall, Peschka, and Jenkins (1974) and Russell and Ford (1983) each docu- mented stronger achievement for students with mild disabilities when those children




worked on identically structured lessons in

pairs, with cross-age tutors, as opposed to small groups, with teachers. Unfortunately, this inconsistent and small database fails to

provide a sufficient basis for determining whether student productivity differs as a function of workgroup size. The Jenkins et al. and the Russell and Ford studies con- founded workgroup size with the mediator of instruction (teachers vs. peers). More- over, Klingner and Vaughn's findings can- not be compared to those of Moody and Gifford because one study was conducted in naturalistic classrooms during reading instruction, whereas the other occurred in science with older students. Therefore, em-

pirically based conclusions await further

study. Despite this absence of clear empirical

guidance, it is possible to construct some broad process distinctions between dyadic and small-group compositions. First, dyadic peer communication is bilateral, whereas group communication occurs bi-

laterally or via multilateral discussion (Sharan, 1980). Second, although high achievement status students in small

groups are afforded more action, performance, and evaluation opportunities (Ber- ger, Wagner, & Zelditch, 1985; Meeker, 1981), dyadic interaction may involve a more delicate balance of power (Hare, 1975), in which high achievement status members may dominate (McAuliffe & Dembo, 1994) to a greater extent. Third, re-

gardless of achievement status, dyads may permit more interaction per individual sim-

ply because fewer participants are involved (Webb, 1988). These process distinctions

may be used to argue for dyadic or for

small-group compositions. Clearly, research is needed to vary group size while

maintaining constant the other structural variables potentially associated with workgroup dynamics.

Purpose of This Study The purpose of this study, therefore, was to examine the effects of workgroup structure

and size on student productivity during co-

operative learning sessions involving com-

plex tasks. We relied on mathematics performance assessments as our complex tasks, we measured student productivity broadly, and we focused explicitly on the interactions of low-achieving students. A brief rationale for each of these study features follows.

Mathematics Performance Assessments Few studies have examined the effects

of cooperative learning when students work on complex, controversial tasks, which do not have a well-defined path to solution or a single correct answer (Cohen, 1994; Slavin, 1996). Despite this omission, the importance of studying complex tasks has increased recently. School reform is re-

directing educators to focus on complex problem solving within authentic contexts (Goodman, 1995); this mandate occurred at least in part because today's economy has increased demands for highly skilled work- ers who can apply knowledge flexibly to solve novel problems (Darling-Hammond, 1992; Mory & Salisbury, 1992).

In keeping with corresponding changes in school practices, we selected mathematics performance assessment as our complex task. This task has strong external validity with respect to current school reform (see Hambleton et al., 1995; Wiggins, 1989). Moreover, because our performance assessment (PA) task (a) required children to in-

tegrate and apply multiple mathematical skills and strategies to novel situations, (b) incorporated complicated verbal and

graphic as well as extraneous information, and (c) allowed more than one path to problem solution and more than one correct answer, it is more complex and controversial than those embedded in prior related work.

Broad Definition of Student

Productivity Alternative hypotheses are possible

about the effects of workgroup structure and size on student productivity on com-

JANUARY 2000



PRODUCTIVITY 187

plex tasks. With respect to structure, previous work on the importance of role, goal, resource, and reward interdependence on routine tasks suggests that structured interactions result in greater participation, collaboration, cooperation, and helpfulness (see Cohen, 1994; Slavin, 1996). By contrast, sociocognitive theory (Bell et al., 1985), along with the potentially natural sources of interdependence inherent in challenge (see Cohen, 1994), predicts that unstructured work on difficult tasks may produce more

cognitive conflict and better discussion. With respect to workgroup size, alter-

native hypotheses are also possible. On the one hand, with uneven achievement status, one student in a dyad may dominate interaction, resulting in unequal rates of participation, poor collaboration, and little cognitive conflict (see Damon, 1984); this

suggests the superiority of small groups. On the other hand, when structure is im-

posed via role, goal, reward, and resource

interdependence, an interchange between two, rather than four, students may facilitate participation, collaboration, helpfulness, cooperation, and explanations (see Slavin, 1996); this suggests the possibility of an interaction between workgroup size and structure.

Given these competing possibilities, we indexed student productivity broadly. We rated student participation, collaboration, cognitive conflict, quality of procedural and conceptual talk, and degree of helpfulness and cooperation. In addition to rating interactions along these dimensions, we characterized low-achieving students' participation, and we scored the quality of the work produced during the sessions.

Focus on Low-Achieving Students Research has demonstrated systematic

inequalities in participation among members of cooperative groups: low-status students interact less frequently and have less influence than do high-status students (Hoffman, 1973; Lindow, Wilkinson, & Pe- terson, 1985; McAuliffe & Dembo, 1994; Ro-

senholtz, 1985; Tammivaara, 1982), and academic achievement is the most powerful status characteristic (McAuliffe, 1991; Mc- Auliffe & Dembo, 1994). O'Connor and Jen- kins (1996) illustrated the deleterious effects associated with low achievement status when they observed students with disabilities participating in cooperative learning. Even with positive interdependence structure, individual accountability, and routine tasks, these students consistently made fewer contributions to the groups' work than did average-achieving students. Only five of 12 low-achieving students were clas- sified as successful participants.

This problem of participatory inequality assumes even greater importance in light of three phenomena. First, amount of interaction has been shown to predict learning in

cooperative groups (Cohen, 1984; Webb, 1988). Second, teachers increasingly report using cooperative learning as a means of fa-

cilitating participation among students of diverse academic competence (Antil et al., 1998), even as the range of academic performance in typical classrooms grows (Hodgkinson, 1995; Stallings, 1995). Third, as the use of complex tasks for cooperative activities increases (Goodman, 1995), so may the risk of unsatisfactory levels of participation among low-achieving students, who may have less to contribute to nonrou- tine, challenging tasks. It is therefore unfortunate that research has failed to examine how variations in cooperative learning activities affect the productivity specifically of low-achieving students. In this study, we separated estimates of productivity for low- achieving students, for high-achieving students, and for workgroups as a whole. (To ensure an appropriate focus on low- and high-achieving students, we selected the lowest-and highest-performing student in each classroom. As shown in Table 1, low- achieving students averaged approximately 30 normal curve equivalents; high-achieving students, about 75 normal curve equivalents.) Results should help teachers determine optimal workgroup structure and size




TABLE 1. Schedule of Study Activities by Condition

Background

Collaborative Week Activity Individual Collaborative + Structure

1 Teacher workshop X X X 2 Student orientation to PA

structure and scoring X X X Student orientation to team building X X Student training in rules of participation X

2-5 Classroom PA-individual, no points X

2-5 Classroom PA-collaborative, no structured interdependence or points X

2-5 Classroom PA-collaborative, structured interdependence and points X

6 Videotaped PA-collaborative, no structure or points; all, including individual background groups, worked in pairs or groups X X X

for the collaborative activities they design, when complex tasks are the focus of group work and when low-achieving students are included.

Method Overview

Stratifying by grade, we randomly as-

signed 36 third- and fourth-grade classrooms to three background experience workgroup structures. In 12 classrooms, students worked individually. In another 12 classrooms, students worked collabora-

tively; preparatory work was limited to a lesson on workgroup cooperation, and work-

group interactions were unstructured. In the

remaining 12 classrooms, students also worked collaboratively; in addition to providing students with a lesson on workgroup cooperation, however, we structured the interactions of these students via role, goal, resource, and reward interdependence. In addition, stratifying by background experience condition and grade, we randomly assigned classrooms to dyadic or small-group compositions (in the individual background ex-

perience condition, workgroup size was not in effect during classroom sessions).

Following training, students completed four weekly classroom sessions under these conditions. Then, we videotaped one work-

group from each classroom as they com-

pleted a fifth session; these videotaped workgroups incorporated the lowest- and

highest-achieving students from each class.

Workgroups from individual background experience classrooms completed video-

taped sessions in pairs or small groups, de-

pending on their original group assign- ment. For this final session, we did not constrain the nature of student interactions. This allowed us to assess student productivity as a function of workgroup size and structural background experience, as well as the interaction between size and structure. In addition, we focused on how these structural variables affected the interactions of the low-achieving students. We hypoth- esized that varying workgroup sizes and

background experiences might provide participants with different strategies for

dealing with the ambiguities of an uncon-

JANUARY 2000



PRODUCTIVITY 189

strained workgroup experience. See Table 1 for a list of study activities by treatment.

Participants Teachers. From five schools in a south-

eastern urban school district, 36 general educators (18 at grade 3 and 18 at grade 4) participated. Every teacher used the district's mathematics basal program, Mathe- matics Plus (Burton et al., 1992). The central assumptions underlying this program are that solving problems related to everyday life should be the primary focus of mathematics instruction; reasoning about mathematics, rather than memorizing rules and procedures, helps children make sense of mathematics; mathematics is a way of thinking and a network of related ideas and concepts, as well as a vehicle for developing critical thinking, creative thinking, and decision-making abilities; manipulatives are a powerful tool to help children link concrete objects to pictorial representations and abstract symbols; and computational profi- ciency is a necessary tool for successful problem solving. Every lesson incorporates a high-interest theme to help children understand how mathematics applies to everyday life, questions to encourage students to talk about mathematics and develop mathematical communication and verbal problem-solving skills, manipulative activities, and paperwork activities.

Stratifying by grade level, we randomly assigned teachers (a) to individual classroom PA experiences, collaborative classroom PA experiences, or collaborative classroom PA experiences with structure and (b) to pairs or groups. In Table 2, we provide years teaching and highest degree earned for teachers by condition. Chi-square and analysis of variance (ANOVA) with two factors (workgroup size and classroom collaborative structure) indicated group compar- ability.

Students. At the beginning of the study, we asked teachers to rank order their students in terms of mathematics competence. We used the orderings to constitute work-

groups. Within each class, we organized groups so that each pair included a higher- and a lower-achieving student; each small group, so that it included one higher-, one lower-, and two middle-achieving students. Pairs included two girls, two boys, or one boy and one girl; groups included all girls, all boys, or two girls and two boys.

For the videotaped PA, we described the performance of one workgroup (i.e., pair or group) from each classroom. In constituting these videotaped workgroups at the beginning of the study, we omitted students who were chronically absent, spoke English as a second language, or had significant behavior problems (as reported by teachers). Vid- eotaped pairs were constituted with the highest- and the lowest-achieving students in each class; videotaped groups with the highest-, the lowest-, and the two middle- achieving students in each class. Teachers and research assistants were unaware of which students would complete the videotaped PAs. We coded videotaped interactions for the workgroup or the high-achieving (HA) student and for the low-achieving (LA) student. We treated achievement status (LA vs. workgroup/HA) as a factor.

For all analyses, we treated students from the same workgroup as dependent observations due to two common influences on their performance: (a) as members of the same classroom, they shared the same learning experience and participation his- tory, and (b) during the videotaped PA, the students worked together and thereby affected each other's behavior.

Demographic information on the HA and LA students is shown in Table 2. We conducted 2 (workgroup size) x 3 (background structure) x 2 (ability, HA vs. LA) ANOVAs with repeated measures on the last factor on math grade level (judged by teachers) and on the Comprehensive Test of Basic Skills (CTBS; administered by the district within 1 month of the videotaped PA). Effects were significant for student status: Effect sizes (ESs) were 1.69 for grade level and 2.91 for CTBS, with HA students per-




TABLE 2. Demographic Data by Condition

Conditions

Marginal Means

Size Background

Collaborative Pairs Groups Individual Collaborative + Structure

Variable X (SD) n X (SD) n X (SD) n X (SD) n X (SD) n

Teacher: Years teaching 12.47 (7.39) 10.89 (9.21) 9.13 (8.38) 14.33 (9.22) 11.58 (6.89) Education:

Bachelors 9 9 6 6 6 Masters 8 9 6 6 5 Ed.S./Ed.D. 1 0 0 0 1

Student: Math grade level:

HA 3.75 (.85) 3.71 (.44) 3.73 (.92) 3.82 (.56) 3.65 (.51) LA 2.38 (.82) 2.57 (.82) 2.67 (.89) 2.68 (.87) 2.10 (.57)

CTBS-NCE: HA 77.35 (16.58) 75.03 (18.50) 72.18 (20.63) 74.10 (19.53) 72.58 (16.26) LA 28.64 (15.65) 28.92 (14.51) 30.50 (17.91) 26.29 (14.80) 29.57 (11.06)

Male: HA 8 7 5 5 6 LA 10 11 8 8 5

Caucasian: HA 7 8 6 5 5 LA 9 10 6 7 6

NOTE.-HA is a high-achieving student; LA is a low-achieving student. CTBS-NCE is the Comprehensive Test of Basic Skills-Normal Curve Equivalents.

forming higher than LA students on both measures. These data substantiate the ap- propriateness of the relative and absolute (in terms of CTBS normal curve equivalent scores) achievement status designations for the HA and LA students. No other F value was significant. The gender and ethnicity of groups also were comparable as indicated by McNemar Tests.

Treatments Common treatment features. All class-

rooms, regardless of their experimental condition, shared five treatment features. First, all teachers attended a 2-hour, after- school workshop. At this workshop, we in- troduced the general purpose of the study: exploring children's performance on PAs. We presented the rationale for this general focus and provided an overview of study activities (series of lessons, weekly classroom PAs, and videotaped PA). We discussed how teachers in the same building

would be conducting related, but different treatments. We emphasized that teachers should avoid discussing treatment features with colleagues and implementing other PA-like activities during the study but should implement study conditions exactly as specified. We reminded them that after the study, we would invite them back to describe results and seek their input about the different treatments. Next, to gain familiar-

ity with PAs, teachers took one PA and scored their own performances. Then, for additional information on treatments, teachers broke into groups (individual, paired collaborative, small-group collaborative, paired collaborative with structure, and small-group collaborative with structure).

The second feature, common across all conditions, was that all students received a lesson that highlighted the structure and scoring of PAs. This scripted lesson, which was conducted by research assistants, cov-

JANUARY 2000



PRODUCTIVITY 191

TABLE 2. (continued)

Conditions

Cell Means

Pairs Groups

Collaborative Collaborative Individual Collaborative + Structure Individual Collaborative + Structure

X (SD) n X (SD) n X (SD) n X (SD) n X (SD) n X (SD) n

8.75 (5.38) 14.00 (9.92) 14.67 (5.75) 9.50 (11.19) 14.67 (9.40) 8.50 (6.98)

4 2 3 2 4 3 2 4 2 4 2 3 0 0 1 0 0 0

3.75 (1.28) 3.88 (.71) 3.63 (.55) 3.72 (.47) 3.75 (.42) 3.67 (.52) 2.83 (.75) 2.30 (.97) 2.00 (.63) 2.50 (1.05) 3.00 (.71) 2.20 (.55)

75.17 (21.23) 80.20 (18.45) 76.67 (17.57) 78.60 (21.71) 78.00 (22.95) 68.50 (18.52) 33.20 (17.53) 22.40 (13.58) 30.33 (13.58) 27.80 (16.32) 30.17 (14.70) 28.80 (13.99)

3 2 3 2 3 3 4 4 2 4 4 3

2 3 3 4 2 2 3 3 3 3 4 3

ered the following points: (a) how PAs are structured, (b) strategies for approaching PAs (i.e., as the PA is read aloud, read along and pay careful attention; as you work, go back and reread parts of the story and ask for help if you need help rereading; do the

questions in any order; show all your work, even easy work you figure in your head; do

every part you can; show what you know- use hard skills if you can); and (c) scoring procedures.

Third, preceding the videotaped PA, all students completed, at weekly intervals, four classroom PAs. These PAs were drawn from a pool of six alternate PA forms we had developed at third grade (see Fuchs et al., in press). Each PA began with a multi-

paragraph narrative describing the problem situation and presenting students with tab- ular and graphic information for potential application in the PA. The problem included four questions that provided students with opportunities to apply a core set

of skills deemed essential at third grade, to discriminate relevant from irrelevant information in the narrative, to generate information not contained in the narrative, to ex-

plain their mathematical work, and to

produce written communication related to the mathematics. Between each question we left adequate space for responses. Although half the participants were fourth graders, no student experienced a ceiling effect on

performance on the third-grade PAs. Every- one in the class completed one PA each week for 4 weeks prior to the videotaped PA. Research assistants read the PA aloud to the class and, along with the teachers, provided additional individual help with

rereading as requested. Students had 30 minutes to work on classroom PAs. (See Appendix C for a sample third-grade PA.)

Fourth, at the end of each PA session, all students removed PAs from their desks and independently took a quiz. Students were told that the purpose of the quiz was to pro-




vide them with feedback and that the quiz would not count as a grade. This quiz presented students with the PA they had just completed, but asked only one of the four

questions. After 3 minutes, quizzes were collected. Over the next week, research assistants scored quizzes, and immediately preceding the next week's PA, they re- turned quizzes, with feedback, to students. We limited quiz feedback to one question because of limitations on our capacity to score complete PAs for 36 classrooms in the week intervening between PAs. Each week, the quiz question was selected randomly from the four PA questions.

Fifth, after quizzes had been collected, teachers distributed to each student an answer key to all four questions on the PA students had just completed. Students com-

pared answers on their completed PAs to those on the answer key.

Treatment differences. In the individual condition, students completed the four

weekly classroom PAs individually. They took their first PA immediately after the scripted introduction on the structure and

scoring of PAs. Then they completed sub-

sequent PAs on the same day of the week, at weekly intervals.

In both collaborative conditions, students completed the four weekly classroom PAs in pairs or groups. During week 2, research assistants conducted a 20-minute training session on workgroup cooperation that addressed the following points: (a) talk only to workgroup members, only about work, in a soft "inside" voice; (b) be considerate, pa- tient, and kind toward workgroup members; (c) be a good participant; (d) ask for help, offer to help others, and make sure all

workgroup members understand; and (e) encourage workgroup members to join in and be good listeners. This lesson, which was scripted and relied on posters (that re- mained posted in the classes for the study duration), presented information and elic- ited frequent student responding. After this training session, students in the collaborative condition completed their first PA.

They completed subsequent PAs at weekly intervals.

In the collaborative with structure condition, research assistants also conducted one 60-minute training session on rules of participation. The rules of participation re-

quired students to assume four roles: reader, monitor, checker, and writer. In

groups, each student assumed one role for the first PA question, and then students alternated roles as they completed the four PA questions. In pairs, students assumed two roles for each question (reader/checker and writer/monitor) and alternated dual roles for each question. Readers read each

question out loud and helped the team find

important information for answering the

question. Monitors made sure team members maintained workgroup cooperation and followed the rules of participation, identified team members in need of help and decided who should provide that help, and reminded team members to participate. Checkers helped the team decide on the steps required to answer the question, made sure each math step was written on individual worksheets, checked members' individual answers, and helped determine the team's group answer and settle disagreements. Writers wrote the team answer on the team answer sheet, explained the team answer and checked agreement with it, and

changed the team answer as needed. The

scripted lessons presented information, incorporated positive and negative videotaped illustrations of responsibilities, and provided opportunities for students to discuss those videotaped illustrations. After the second lesson, students in the structured collaboration condition completed their first classroom PA and then completed subsequent classroom PAs at weekly intervals.

The collaborative with structure condition also incorporated the following features. First, as students worked on the classroom PAs, their workgroup received points for cooperating and following the rules of participation. Second, workgroups received

JANUARY 2000



PRODUCTIVITY 193

points for their members' performance on the weekly quizzes (each individual's score, 1-5, corresponded with the number of points that individual contributed to the workgroup's total). Third, following the last classroom PA, teachers announced the high-scoring workgroup; this workgroup selected a reward from a menu the class had collaboratively put together with teacher input prior to the first training session. The entire class received this reward.

Measures To study the nature of students' inter-

actions, we structured a videotaped PA outside classrooms 1 week after the last classroom PA had been completed. The data for this study were collected from the videotaped sessions.

We used one third-grade alternate-form PA that had not previously been used as a classroom PA. A research assistant, familiar to the students, walked with the students from the classroom to a familiar room where video equipment and a table with two or four chairs and a microphone (taped to the side of the table) had been arranged; on the table was a box that held an array of manipulative materials. When the students entered the room, the research assistant asked them to sit at the table. For pairs, LA students sat on the left; for groups, LA and HA students sat in the middle of the group with the LA student to the left of the HA student.

The research assistant gave each student one copy of the PA and said,

I'm going to read this problem to you. You read along silently as I read aloud. In a few minutes, I'm going to ask you to help each other learn how to do this type of problem. When one of you doesn't understand something, the other [another] student should provide help. I'm hoping that when you finish working together, each of you will know how to do this kind of problem on your own. So, you need to work together and help each other to make sure that both [all] of you

know how to do this type of problem. Listen as I read the problem out loud.

After the research assistant had read the problem, she said, "Right now, I want you to think carefully about some good ways to help each other work together on this problem. I'll give you a few minutes to think about this. Tell me if you want me to read any part of the problem aloud again. This is thinking time; do not start writing. Also, this is the only time I can help you with rereading; so, ask for help if you need it."

The research assistant gave the students 2 minutes to review the problem, provided help as requested with rereading, and said, "I'm going to videotape you as you work. Later, I'll study the videotapes to understand how students help each other in math." The research assistant then gave each student a pencil and placed a group answer sheet in the middle of the table. Then, the research assistant said,

This is the math problem you just looked over. Now, I want you to work together on this problem. Do your best to make sure that both [all] of you learn as much as possible about how to do this type of problem. You can work together in any way you think will be helpful to make sure both [all] of you learn as much as possible about how to do this type of problem. You can use your individual worksheets in any way you want; write your name on your individual worksheet now. However you use your individual worksheet, I want you to write your group answers on the group answer sheet; write each of your names on the group answer sheet now. Try to do your best. You'll have 15 minutes to work on the problem together. If you don't finish in the 15 minutes, that's OK. It's more important for everyone to understand what you do finish than to complete all the questions. If you do finish before 15 minutes, though, that's OK too. Just let me know and I'll tell you to stop at that time. Begin now.

If a student asked whether he or she should use the classroom roles and structures, the




research assistant said, "Do whatever you think will be most helpful." When the students indicated they were finished or after 15 minutes, whichever occurred first, the research assistant said, "You've done a nice job. Thank you."

On the basis on these videotaped tutoring sessions, we derived four types of information: ratings of student interactions, characterizations of LA students' participation, scores reflecting the quality of the PA work generated, and classifications of workgroups' background experience structures. In addition, we identified representative videotapes to illustrate effects for the workgroup size factor.

Ratings of students' interactions. Two authors cooperatively developed a coding scheme and rated the tapes. These raters were not involved in data collection and were blind to students' identities and to students' classroom PA conditions. After watching two pairs of sessions, judged by research assistants to represent the most complex set of interactions, the two raters developed a scale to rate the quality of the students' interactions and an operational procedure for collecting the rating data.

Each rating scale item was scored on a 5- or 6-point Likert scale (see Table 3 for list of items). One item addressed participation, the extent to which most children participated in the math work (1 = not at all; 5 =

very much). One item addressed collaboration, the proportion of students involved in and the quality of the collaboration over the math work (1 = not at all; 5 = very much). Four items addressed cognitive conflict: the amount to which students disagreed in their approach to the problem and, when disagreement did occur, the extent to which students offered alternative solutions/perspectives on solving the problem; the extent to which they participated in negotiating, arguing, and reacting to ideas; and the extent to which they successfully resolved cognitive conflict (1 = not at all; 5 = very much). On each participation, collaboration, and cognitive conflict item, one rating

described the performance of the workgroup (pair or group); another rating described the performance of the LA student. Four items (two for the HA student and two for the LA student) addressed the quality of the student's talk in terms of procedural explanations and conceptual explanations (0 = not at all; 1 = poor; 5 = excellent). Four items (two for the HA student and two for the LA student) addressed the student's affect in terms of the degree to which the student was helpful and cooperative (1 = not at all; 5 = very much).

To collect the ratings, we used the following procedure. We counterbalanced the order in which the tapes were viewed with respect to grade level, classroom background structure, and workgroup size. The two raters watched each session together. The unscored individual and group PA answer sheets that had been worked during the interaction were displayed on a table so that each rater could view these documents as he or she viewed the videotaped interaction. They watched the tape in its entirety; parts were reviewed as requested by either rater; then, each rater independently circled one number for every item on the rating scale and wrote a few sentences character- izing the LA student's participation. Then, raters revealed their item-by-item ratings and discussed rationales and disagreements. When raters were convinced to alter ratings based on this discussion, they sig- naled changes by placing a triangle (rather than a circle) on revised scores.

For each item, on both pre- and postdiscussion ratings, we calculated percentage of agreement in the following way. First, we divided the full range of the scale (i.e., 100) by one less than the number of points on the Likert scale; second, we subtracted the difference between the two observers' scores; third, we multiplied the difference between the scores by one less than the number of points on the Likert scale; finally, we subtracted this product from 100. So, for example, on rating scale items where the Likert points ranged from 0 to 5 (so that there were

JANUARY 2000



PRODUCTIVITY 195

TABLE 3. Percentage of Agreement by Item, Before and After Discussion

Before After

Item X (SD) X (SD)

Participation: Extent most children participate in math work 88.19 (12.66) 93.75 (10.98) Extent LA participates in math work 85.28 (19.71) 93.75 (10.98)

Collaboration: Amount and quality of collaboration 87.50 (16.37) 96.53 (8.77) Of time spent collaborating, extent of LA

participation 84.72 (14.97) 94.44 (10.54)

Cognitive conflict: Extent students disagree in approach 85.00 (15.10) 92.14 (11.78) Extent LA disagrees in approach 86.43 (15.27) 90.71 (12.26) When conflict occurs, extent students offer

alternative solutions/perspectives 82.57 (18.57) 90.00 (12.43) When conflict occurs, extent LA offers alternative

solutions/perspectives 83.57 (16.11) 89.29 (15.06) When conflict occurs, extent students negotiate,

argue, react to ideas 88.00 (15.20) 93.57 (11.09) When conflict occurs, extent LA negotiates, argues,

reacts to ideas 83.14 (13.94) 91.14 (13.23) When conflict occurs, extent students achieve

resolution 83.86 (16.59) 91.43 (12.04) When conflict occurs, extent LA achieves resolution 82.14 (17.88) 92.00 (12.23)

Talk: Quality of procedural explanations:

HA 85.71 (14.20) 96.00 (8.12) LA 86.29 (14.37) 93.71 (10.60)

Quality of conceptual explanations: HA 85.71 (12.55) 92.86 (11.46) LA 90.86 (16.02) 95.00 (10.15)

Affect: Quality of affect in terms of helpfulness:

HA 81.94 (16.49) 92.36 (11.68) LA 88.75 (17.90) 96.53 (8.77)

Quality of affect in terms of cooperativeness: HA 83.33 (16.90) 91.67 (11.95) LA 86.81 (14.00) 97.22 (7.79)

6 points on the scale), and for scores of 3 and 4 provided by two raters, this procedure would result in the following calculations: First, divide 100 by 5 (1 less than 6) to get 20; second, subtract the two scores to get a difference of 1; third, multiply 1 by 20; finally, subtract 20 from 100. This yielded an agreement score of 80%. In Table 3, percentages are shown for each rating scale item. The av-

erage prediscussion percentage of agreement was 85.59 (SD = 6.90); postdiscussion, 93.30 (SD = 4.32). The data entered into analysis were the postdiscussion ratings averaged across the two raters.

LA students' levels of participation. When a set of ratings had been completed,

but prior to the viewing of the next video and before the debriefing discussion, raters wrote a few sentences to characterize the LA student's participation. Subsequently, the two raters' characterizations were combined and typed without reference to students' background experience or work-

group size. To capture the level of the LA students' participation, two licensed and experienced teachers who had not been involved in other data-reduction functions studied the characterizations and developed a hierarchical coding scheme with eight categories (ordered from most to least desirable): problem-solving collaborator, computational collaborator, nonmathemat-




ical collaborator (e.g., contributed nonmathematical information such as how to

spend additional money), helper (e.g., wrote others' answers on group worksheet), parallel worker, ignored participant (i.e., asked for help or attempted interaction but was ignored), minimal participant (e.g., copied others' answers on individual worksheet), and unengaged pupil (i.e., off-task). Then, two research assistants uninvolved in other data-reduction activities coded each characterization into the category that best captured the characterization; if two cate-

gories described participation equally well, research assistants assigned the more desirable category. Research assistants agreed on 31 of 36 decisions and resolved disagreements through discussion. We attached to each category a number to indicate its desirability (1 = problem-solving collaborator; 8 = unengaged pupil).

Classifications of classroom PA structure conditions. Immediately after a tape had been rated and the LA student's participation characterized, but before debriefing discussion occurred, each rater classi- fied the session as individual, collaborative, or collaborative with structure.

Quality of work generated. Each work-

group's collective answer sheet was scored

according to a rubric adapted from the Kan- sas Quality Performance Accreditation (Kansas State Board of Education, 1991). This rubric structured scoring along four dimensions (conceptual underpinnings, computational applications, problem-solving strategies, and communicative value); each dimension was scored on a 6-point Likert- type scale (0 = no relevant response; an an- chor was provided for every odd number on the scale). Two scorers who were blind to study conditions and had not been involved in any other coding function used this rubric to score the PAs independently. On each item, scorers earned 100% agreement when they awarded identical scores; for each deviation of 1 point on the scale, they lost 20 percentage points. For example, if scorers awarded scores of 2 and 3, they

earned 80% agreement; scores of 2 and 5, 40% agreement. For each protocol, we av-

eraged agreement across the four dimensions. Across 20% of protocols, agreement was 96.3%.

As demonstrated on 362 students with this PA (see Fuchs et al., in press), alternate form/test-retest reliability for the conceptual underpinnings, computational applications, problem-solving strategies, and communication scoring dimensions, respectively, was .66, .76, .69, and .66. Correlations with the CTBS ranged from .62 to .68; with the performance assessments of the Iowa Tests of Basic Skills, .60 to .67.

Representative videotape sessions. To illustrate the workgroup size effect, we identified videotapes representative of the interactions within pairs and within small groups. To accomplish this, we did the fol-

lowing. First, for each workgroup, we computed an average rating score across all the

rating variables. Second, on this new, com-

posite variable, we computed a mean for the pairs condition and identified the pair whose score was closest to this mean; we repeated this second step for the small

groups condition. Finally, we transcribed the dialogue from these two interactions

through the PA's second question.

Results Ratings of Students' Interactions and Representative Transcripts Means and standard deviations on the

rating scale items are shown in Table 4. The first two columns show marginal means for the workgroup size conditions, the next three columns show marginal means for the background structure conditions, and the next six columns show the means for the cells. Under each variable, the three rows, respectively, show the mean for the workgroup or the HA, the mean for the LA, and the marginal mean across the workgroup/ HA and the LA.

On each item, we conducted a 2 (workgroup size) x 3 (background structure) x 2 (ability, i.e., LA vs. workgroup or HA)

JANUARY 2000



PRODUCTIVITY 197

ANOVA, with repeated measures on the last factor. In this section, we report F val- ues for the ANOVAs and describe follow- up (Fisher's least significant difference) tests for significant effects; when interactions supersede main effects, we report follow-up tests for interactions only. We also include effect sizes (ESs; difference between the means, divided by the pooled standard deviation; see Hedges & Olkin, 1985).

Participation. The ANOVA produced the following effects: for workgroup size, F(1, 30) = 2.49, ns; for background structure, F(2, 30) = .93, ns; for ability, F(1, 30) = 13.39, p < .01; for workgroup size x background structure, F(2, 30) = 3.95, p < .05; for workgroup size x ability, F(1, 30) = .06, ns; for background structure x ability, F(2, 30) = .54, ns; and for the three-way interaction, F(2, 30) = .24, ns.

Across background structures and across workgroup sizes, the participation of workgroups (X = 4.01, SD = 1.03) ex- ceeded that of LA students (X = 3.60, SD = 1.15); ES = .65. Follow-ups to the workgroup size x background structures interaction indicated that students with independent classroom PA experiences participated more in pairs than in groups (ES = .86); by contrast, students in the two collaborative background experience groups participated comparable amounts in pairs and groups (ESs for collaborative and collaborative with structure, respectively, were .00 and -.32).

Collaboration. The ANOVA produced the following effects: for workgroup size, F(1, 30) = 2.88, ns; for background structure, F(2, 30) = .76, ns; for ability, F(1, 30) = 6.50, p < .05; for workgroup size x background structure, F(2, 30) = 2.07, ns; for workgroup size x ability, F(1, 30) = 6.50, p < .05; for background structure x ability, F(2, 30) = .36, ns; and for the three-way interaction, F(2, 30) = .30, ns. Follow-ups to the workgroup size x ability interaction indicated that the workgroups collaborated comparable amounts in pairs and groups

(ES = .23), whereas the LA students collaborated more when in pairs than in groups (ES = .78).

Cognitive conflict. For amount of disagreement, ANOVA produced the following effects: for workgroup size, F(1, 30) = .33, ns; for background structure, F(2, 30) = 1.60, ns; for ability, F(1, 30) = 11.77, p < .01; for workgroup size x background structure, F(2, 30) = 1.49, ns; for workgroup size x ability, F(1, 30) = 9.43, p < .01; for background structure x ability, F(2, 30) = .90, ns; and for the three-way interaction, F(2, 30) = .98, ns. Follow-ups to the workgroup size x ability interaction indicated that the workgroups disagreed more in groups than in pairs (ES = .52), whereas the LA students disagreed comparable amounts whether in pairs or in groups (ES = .13). Disagreement occurred for five of the six workgroups in every condition except for the individual classroom PA treatment, which worked in groups for the videotaped PA; in this condition, disagreement occurred for six of the six workgroups.

For offering alternative perspectives, we found no statistically significant effects. The ANOVA produced the following effects: for workgroup size, F(1, 30) = .99; for background structure, F(2, 30) = 2.27; for ability, F(1, 30) = 3.73; for workgroup size x background structure, F(2, 30) = 1.69; for workgroup size x ability, F(1, 30) = 2.69; for background structure x ability, F(2, 30) = .90; and for the three-way interaction, F(2, 30) = 1.47.

For negotiating, ANOVA produced the following effects: for workgroup size, F(1, 30) = 2.24, ns; for background structure, F(2, 30) = 2.32, ns; for ability, F(1, 30) = 3.65, ns; for workgroup size x background structure, F(2, 30) = 3.29, p < .05; for workgroup size x ability, F(1, 30) = 7.71, p < .05; for background structure x ability, F(2, 30) = 1.40, ns; and for the three-way interaction, F(2, 30) = 1.27, ns. Follow-ups to the workgroup size x background condition interactions indicated no effect for background condition when students worked in




TABLE 4. Ratings of Student Interactions by Condition

Conditions

Marginal Means

Size Background


Variable X (SD) X (SD) X (SD) X (SD) X (SD)

Participation: Workgroup 4.25 (.94) 3.78 (1.09) 3.67 (1.37) 4.13 (.96) 4.25 (.62) LA 3.86 (1.05) 3.33 (1.21) 3.33 (1.39) 3.79 (1.01) 3.67 (1.07) Workgroup/LA 4.06 (.96) 3.56 (1.09) 3.50 (1.34) 3.96 (.95) 3.96 (.78)

Collaboration: Workgroup 3.28 (1.20) 3.03 (1.01) 2.88 (1.25) 3.33 (.86) 3.25 (1.20) LA 3.28 (1.22) 2.31 (1.27) 2.50 (1.41) 3.13 (1.25) 2.75 (1.34) Workgroup/LA 3.28 (1.77) 2.67 (1.04) 2.69 (1.30) 3.23 (.97) 3.00 (1.14)

Cognitive Conflict: Amount of disagreement:

Workgroup 2.41 (.96) 3.00 (1.33) 2.14 (.60) 3.13 (1.43) 2.83 (1.19) LA 2.35 (1.07) 2.19 (1.37) 1.91 (.92) 2.63 (1.33) 2.25 (1.34) Workgroup/LA 2.38 (.98) 2.60 (1.28) 2.02 (.72) 2.88 (1.29) 2.34 (1.20)

Offer alternative perspectives: Workgroup 2.20 (.84) 2.88 (1.18) 1.73 (.47) 3.10 (1.08) 2.90 (1.05) LA 2.21 (1.03) 2.35 (1.51) 1.81 (.80) 2.65 (1.33) 2.28 (1.48) Workgroup/LA 2.20 (.83) 2.67 (1.27) 1.81 (.57) 2.88 (1.07) 2.56 (1.21)

Negotiate: Workgroup 1.93 (.84) 2.91 (1.21) 1.64 (.64) 3.05 (1.14) 2.70 (1.16) LA 2.11 (1.15) 2.27 (1.49) 1.81 (1.10) 2.45 (1.34) 2.22 (1.48) Workgroup/LA 2.05 (.94) 2.67 (1.25) 1.78 (.78) 2.75 (1.10) 2.42 (1.29)

Resolve: Workgroup 2.03 (.77) 2.34 (.96) 1.73 (.47) 2.35 (1.08) 2.55 (.83) LA 2.25 (.99) 1.88 (1.29) 1.63 (.79) 2.30 (1.21) 2.22 (1.33) Workgroup/LA 2.17 (.85) 2.12 (1.08) 1.72 (.57) 2.33 (1.09) 2.33 (1.02)

Talk: Procedural:

HA 3.35 (1.26) 2.31 (.93) 2.59 (1.28) 2.88 (1.15) 2.96 (1.27) LA 2.50 (1.00) 1.61 (1.09) 2.00 (1.47) 2.25 (.66) 1.88 (1.21) HA/LA 2.93 (.97) 1.96 (.63) 2.29 (1.31) 2.56 (.66) 2.42 (.83)

Conceptual/ problem-solving: HA 3.29 (1.41) 2.22 (.84) 2.55 (1.59) 2.67 (1.01) 3.00 (1.22) LA 2.09 (1.12) 1.44 (.73) 1.91 (1.30) 1.92 (.90) 1.46 (.69) HA/LA 2.69 (1.06) 1.83 (.54) 2.23 (1.36) 2.29 (.69) 2.23 (.70)

Affect: Helpfulness:

HA 3.58 (1.14) 2.78 (1.05) 3.04 (1.27) 3.25 (1.01) 3.25 (1.25) LA 3.92 (.90) 2.83 (1.51) 3.13 (1.35) 3.62 (1.21) 3.83 (1.52) HA/LA 3.75 (.90) 2.81 (.93) 3.08 (1.22) 3.44 (.72) 3.31 (1.12)

Cooperativeness: HA 3.50 (1.08) 2.89 (.85) 3.08 (1.28) 3.17 (.65) 3.33 (1.07) LA 4.14 (.90) 3.22 (1.22) 3.38 (1.26) 3.83 (1.05) 3.83 (1.17) HA/LA 3.82 (.90) 3.06 (.84) 3.23 (1.22) 3.50 (.68) 3.58 (.89)

NOTE.-LA is a low-achieving student; HA is a high-achieving student.

pairs; by contrast, when working in groups, students negotiated more in the collaborative than the individual background condition. Follow-ups to the workgroup size x

ability interaction indicated that although workgroups negotiated more in groups

than in pairs (ES = .96), LA students negotiated comparable amounts whether in

pairs or groups (ES = .12). In terms of conflict resolution, ANOVA

produced the following effects: for workgroup size, F(1, 30) = .05, ns; for back-

JANUARY 2000



PRODUCTIVITY 199


Conditions

Cell Means

Pairs Groups


x (SD) X (SD) X (SD) X (SD) X (SD) X (SD)

4.50 (.84) 4.08 (1.24) 4.17 (.82) 2.83 (1.33) 4.17 (.68) 4.33 (.41) 4.25 (.99) 3.83 (1.03) 3.50 (1.18) 2.42 (1.11) 3.75 (1.08) 3.83 (1.03) 4.37 (.89) 3.96 (1.10) 3.83 (.97) 2.63 (1.16) 3.96 (.87) 4.08 (.61)

3.58 (1.28) 3.25 (.88) 3.00 (1.52) 2.17 (.75) 3.42 (.92) 3.50 (.84) 3.42 (1.43) 3.50 (1.05) 2.92 (1.28) 1.58 (.58) 2.75 (1.41) 2.58 (1.50) 3.50 (1.34) 3.38 (.89) 2.96 (1.36) 1.88 (.56) 3.08 (1.10) 3.04 (1.01)

2.30 (.91) 2.42 (1.11) 2.50 (1.00) 2.00 (.00) 3.83 (1.44) 3.17 (1.37) 2.50 (1.06) 2.50 (1.26) 2.08 (1.02) 1.42 (.38) 2.75 (1.51) 2.42 (1.68) 2.40 (.96) 2.46 (1.19) 2.29 (.95) 1.71 (.19) 3.29 (1.35) 2.79 (1.45)

1.80 (.57) 2.30 (.76) 2.50 (1.12) 1.67 (.41) 3.90 (.65) 3.30 (.91) 2.25 (.87) 2.50 (1.37) 1.90 (.89) 1.38 (.48) 2.80 (1.44) 2.75 (2.06) 2.13 (.60) 2.40 (1.04) 2.20 (.93) 1.50 (.41) 3.35 (.96) 3.50 (.79)

1.70 (.84) 2.20 (.91) 1.90 (.89) 1.58 (.49) 3.90 (.55) 3.00 (1.51) 2.50 (1.22) 2.30 (1.35) 1.60 (.89) 1.13 (.25) 2.60 (1.47) 3.00 (1.83) 2.19 (.97) 2.25 (1.12) 1.75 (.87) 1.38 (.25) 3.25 (.92) 3.25 (1.34)

1.80 (.57) 2.10 (.89) 2.20 (.91) 1.17 (.41) 2.60 (1.29) 2.90 (.65) 2.25 (.65) 2.40 (1.14) 2.10 (1.25) 1.00 (.00) 2.20 (1.40) 2.38 (1.60) 2.13 (.52) 2.25 (1.00) 2.15 (1.05) 1.31 (.24) 2.40 (1.28) 2.56 (1.09)

3.40 (1.34) 3.58 (1.11) 3.08 (1.49) 1.92 (.80) 2.17 (.68) 2.83 (1.13) 3.10 (1.60) 2.50 (.32) 2.00 (.63) 1.08 (.20) 2.00 (.83) 1.75 (1.67) 3.25 (1.41) 3.04 (.49) 2.54 (.93) 1.50 (.42) 2.08 (.41) 2.29 (.78)

3.60 (1.71) 3.00 (1.26) 3.33 (1.51) 1.67 (.82) 2.33 (.61) 2.67 (.88) 2.80 (1.48) 2.08 (.86) 1.50 (.77) 1.17 (.41) 1.75 (.99) 1.42 (.66) 3.20 (1.51) 2.54 (.83) 2.42 (.83) 1.42 (.38) 2.04 (.46) 2.04 (.56)

3.92 (1.02) 3.42 (1.02) 3.42 (1.46) 2.17 (.82) 3.08 (1.07) 3.08 (1.11) 3.92 (1.02) 4.08 (.66) 3.75 (1.08) 2.83 (1.21) 3.17 (1.51) 3.00 (1.90) 3.92 (.90) 3.75 (.81) 3.58 (1.10) 1.25 (.89) 3.13 (.49) 3.04 (1.17)

3.67 (1.33) 3.33 (.61) 3.50 (1.34) 2.50 (1.00) 3.00 (.71) 3.17 (.82) 4.00 (1.10) 4.17 (.75) 4.25 (.99) 2.75 (1.17) 3.50 (1.26) 3.42 (1.28) 3.83 (1.16) 3.75 (.59) 3.88 (1.20) 2.63 (1.03) 3.25 (.72) 3.29 (.70)

ground structure, F(2, 30) = 1.17, ns; for ability, F(1, 30) = 1.51, ns; for workgroup size x background structure, F(2, 30) = .93, ns; for workgroup size x ability, F(1, 30) =

5.71, p < .05; for background structure x

ability, F(2, 30) = .20, ns; and for the three-

way interaction, F(2, 30) = .46, ns. Follow- ups to the workgroup size x ability interaction failed to identify any significant effects. Nevertheless, for the workgroup, the ES for workgroup size was -.36, favoring groups over pairs; for LA students, the




ES for workgroup size was .32, favoring pairs over groups.

Talk. On procedural talk, ANOVA produced the following effects: for workgroup size, F(1, 30) = 13.47, p < .01; for background structure, F(2, 30) = .18, ns; for abil-

ity, F(1, 30) = 9.59, p < .05; for workgroup size x background structure, F(2, 30) = 2.56, ns; for workgroup size x ability, F(1, 30) = .07, ns; for background structure x ability, F(2, 30) = .45, ns; and for the three- way interaction, F(2, 30) = .74, ns.

On conceptual talk, ANOVA produced the following effects: for workgroup size, F(1, 30) = 10.24, p < .01; for background structure, F(2, 30) = .03, ns; for ability, F(1, 30) = 19.65, p < .001; for workgroup size x background structure, F(2, 30) = 2.56, ns; for workgroup size x ability, F(1, 30) = .84, ns; for background structure x ability, F(2, 30) = 1.64, ns; and for the three-way interaction, F(2, 30) = .04, ns.

On both pairs of items (procedural talk and conceptual talk), the workgroup size main effect revealed that the quality of student talk was higher in pairs than in groups (ESs = 1.21 for procedural talk and 1.08 for

conceptual talk), and the ability main effect indicated that the quality of the work-

group's talk was higher than that of the LA students (ESs = .55 for procedural talk and .77 for conceptual talk).

Affect. On helpfulness, ANOVA produced the following effects: for workgroup size, F(1, 30) = 9.47, p < .01; for background structure, F(2, 30) = .46, ns; for ability, F(1, 30) = .58, ns; for workgroup size x back-

ground structure, F(2, 30) = 1.39, ns; for

workgroup size x ability, F(1, 30) = .29, ns; for background structure x ability, F(2, 30) = .13, ns; and for the three-way interaction, F(2, 30) = .20, ns.

On cooperation, ANOVA produced the following effects: for workgroup size, F(1, 30) = 6.51, p < .05; for background structure, F(2, 30) = .51, ns; for ability, F(1, 30) = 6.66, p < .05; for workgroup size x background structure, F(2, 30) = .56, ns; for workgroup size x ability, F(1, 30) = .66, ns;

for background structure x ability, F(2, 30) = .33, ns; and for the three-way interaction, F(2, 30) = .10, ns.

On both pairs of items, the main effect for workgroup size revealed that student affect was rated more positively in pairs than groups (ESs = 1.03 for helpfulness and .87 for cooperation). In addition, the ability main effect indicated that LA students were rated as more cooperative than were HA students (ES = .44).

LA Students' Levels of Participation On LA students' levels of participation,

a 2 (workgroup size) x 3 (background structure) ANOVA revealed the following: for workgroup size, F(1, 30) = 21.70, p < .001; for background structure, F(2, 30) = .31, ns; and for the interaction, F(2, 30) = .22, ns. Mean scores (lower scores represent more desirable levels of participation) for pairs and groups, respectively, were 2.83 (SD = 1.72) and 5.89 (SD = 2.03); ES = 1.63. Mean scores for individual, collaborative, and collaborative with structure

workgroups, respectively, were 4.50 (SD = 2.47), 4.00 (SD = 2.30), and 4.58 (SD = 2.64); ES comparing individual with collaborative = .21, individual with collaborative with structure = .03, and the two collaborative conditions = .23. Within the individual condition, mean scores for pairs and groups, respectively, were 2.67 (SD = 1.21) and 6.33 (SD = 1.97); within the collaborative conditions, 2.67 (SD = 1.97) and 5.33 (SD = 1.86); and within the collaborative with structure condition, 3.17 (SD = 2.14) and 6.00 (SD = 2.45). See Table 5 for characterizations by condition.

Classifications of Classroom PA Experience Conditions For each of the two raters, we ran a two-

way contingency table: one dimension was the workgroup's actual condition; the other dimension, the rater's classification. These contingency tables produced a statistically significant chi-square value for each rater, (4, N = 36) = 15.01 and 20.18, indicating a

JANUARY 2000



PRODUCTIVITY 201

TABLE 5. Low-Achieving Students' Characterizationsa by Condition

Pairs Groups

Collaborative Collaborative Characterizations Individual Collaborative + Structure Individual Collaborative + Structure

Problem-solving collaborator 2 2 1 1 0 0

Computational collaborator 1 2 2 0 0 0

Nonmathematical collaborator 0 0 1 0 1 1

Helper 1 1 2 0 1 0 Parallel worker 1 0 0 0 2 1 Ignored

participant 1 1 0 0 0 0 Minimal

participant 0 0 0 5 1 2 Unengaged pupil 0 0 0 0 1 2

aNumbers in table are frequencies.

strong relation between the actual and clas- sified conditions.

Raters achieved greatest accuracy when classifying videotapes in the collaborative with structure condition. One rater coded nine of 12 sessions correctly, mistaking one session for the collaborative condition and two sessions for the individual condition; the second rater coded 10 of 12 correctly, mistaking two for individual. Raters also coded collaborative sessions with fair accuracy. One rater coded seven of 12 sessions correctly, mistaking two sessions as collaborative with structure and three sessions as individual; the second rater coded eight of 12 sessions correctly, mistaking one for collaborative with structure and three for individual. Both raters were least accurate when coding individual sessions. Each clas- sified five of 12 correctly; one rater mistook one session for collaborative with structure and six sessions for collaborative; the second rater mistook two sessions for collaborative with structure and five sessions for collaborative.

The two raters agreed on the classroom PA experience conditions for 32 of 36 videotaped sessions. Among the 32 agreements, 23 (72%) of the raters' designations were accurate. The incorrect agreements were as follows: four occurrences of raters

coding unstructured conditions as individual, three occurrences of raters coding individual conditions as unstructured, and two occurrences of raters coding individual conditions as structured.

Quality of Work Generated See Table 6 for PA means and standard

deviations. The first two columns show marginal means for the workgroup size conditions, the next three columns show marginal means for the background structure conditions, and the next size columns show means for the treatment cells. A series of 2 (workgroup size) x 3 (background) structure ANOVAs was conducted.

On conceptual underpinnings, ANOVA produced the following effects: for workgroup size, F(1, 30) = 4.51, p < .05; for background structure, F(2, 30) = .14, ns; and for workgroup size x background structure, F(2, 30) = 1.47, ns. The significant main effect for workgroup size favored pairs over groups (ES = .82).

On computational applications, problem-solving strategies, and communication, respectively, ANOVAs produced the following nonsignificant effects: for workgroup size, F(1, 30) = 3.20, 2.90, and 1.40; for background structure, F(2, 30) = .70, .20, and 1.36; and for workgroup size x back-




TABLE 6. Videotaped Performance Assessment Scores by Condition

Marginal Means

Size Background


Variable X (SD) X (SD) X (SD) X (SD) X (SD)

Conceptual underpinnings 3.56 (1.36) 2.50 (1.24) 3.00 (1.89) 3.20 (1.32) 3.13 (.84) Computational applications 3.13 (1.45) 2.33 (.79) 2.60 (1.51) 3.10 (1.37) 2.63 (.74) Problem-solving strategies 3.63 (1.63) 2.58 (1.38) 3.00 (2.00) 3.10 (1.60) 3.50 (1.07) Communication 2.50 (1.55) 1.83 (1.11) 2.80 (1.62) 1.80 (1.32) 2.00 (1.07)

ground structure, F(2, 30) = .78, .95, and .95. Workgroup size effects on computational applications and problem-solving strategies scores approached statistical sig- nificance (.09 and .10, respectively), with ESs again favoring pairs over groups (.71 and .70, respectively).

Transcripts of Representative Dyad and Small Group See the Appendix for transcripts of rep-

resentative workgroups illustrating student interactions within pairs and within small

groups (both of which coincidentally were in the structured collaboration background condition). These transcripts run through the PA's second question.

In the small group, the LA student's level of participation was minimal; she ful- filled the role of "reader" for the first question but contributed little more to the problem-solving collaboration. In fact, much of her time was spent copying the HA's re-

sponses and looking up. She failed to com-

plete even the computational steps of the

problems, and the few attempts she made to enter the interaction were ignored. In- stead, the HA, although appropriately re-

sponsive to the other workgroup participants, dominated the problem-solving activity and interacted primarily with one middle achiever. When the other middle achiever requested help, the HA seemed ea- ger to provide enough guidance so that the middle achiever could formulate a correct response. The quality of the HA students'

procedural and conceptual talk was awarded 3s on the rating scale; that of the LA student, is.

By contrast, within the dyad, the LA

generated his own work, entirely in re-

sponse to the HA's explanations for how to

proceed with the problem solving. Both students relied on the structured collaboration's rules of participation in that, once

they agreed on the problem-solving approach (entirely determined by the HA), each worked the problem, and then they compared answers. If their answers were the same, they continued; if not, they re- worked the problem. Although many of the HA's explanations focused on the LA's

computational work, the HA did offer the LA alternative strategies for making correc- tions and did provide a conceptual rationale for each step of the work. The quality of the HA student's procedural and conceptual talk was rated with 4s; the LA student's

procedural and conceptual talk, respectively, was rated as 2 and 1. Clearly, com-

pared to the small group, the LA in the dyad spoke more, produced more work, and received a greater number of explanations directed at the LA student's specific difficulties.

Discussion The videotaped generalization sessions, which provided the database for this study, were unconstrained: we did not prompt workgroups to use any styles or methods of interaction. Workgroups did, however, ap-

JANUARY 2000



PRODUCTIVITY 203


Cell Means

Pairs Groups


X (SD) X (SD) X (SD) X (SD) X (SD) X (SD)

3.67 (1.75) 4.00 (1.22) 3.00 (1.00) 2.00 (1.83) 2.40 (.89) 3.33 (.58) 3.17 (1.72) 3.60 (1.67) 2.60 (.89) 1.75 (.50) 2.60 (.89) 2.67 (.58) 3.50 (1.97) 4.00 (1.73) 3.40 (1.34) 2.25 (2.06) 2.20 (.84) 3.67 (.58) 3.17 (1.60) 2.40 (1.67) 1.80 (1.30) 2.25 (1.71) 1.20 (.45) 2.33 (.58)

proach the videotaped PA sessions with

varying classroom histories. Some groups had only individual experience; others had unstructured collaborative experience with

training in workgroup cooperation; and some, in addition to training in workgroup cooperation, had collaborative experience with structured interdependence. We hy- pothesized that these varying background experiences might provide students with different strategies for dealing with the am-

biguities of an unconstrained workgroup experience.

And, not surprisingly, these back-

ground experience conditions did influence the methods by which students interacted. Two independent coders, blind to back-

ground structure conditions, correctly clas- sified a majority of workgroups with structured collaborative experience, and they mistook only 12% of the remaining work-

groups as structured. In addition, coders correctly identified most of the 12 work-

groups with unstructured collaborative ex-

perience. When errors did arise, they typically centered on workgroups with individual histories that the coders classi- fied nearly equally as individual or unstructured. These classifications provide evidence that students trained and practiced in the interdependence structure did tend to rely on some features of that structure during the unconstrained, generalization session. Moreover, students in other conditions did not spontaneously develop salient features of the interdependence structure.

What is more surprising is that despite students' apparent reliance on the interde-

pendence structure, the quality of their interactions did not exceed those of students in the unstructured experience condition. Across the many dimensions on which interactions were rated, no significant work-

group structure main effects emerged. Moreover, a small mean ES of .15 actually favored workgroups with unstructured histories. Corroborating evidence was provided in LA students' levels of participation, where modest effects again favored unstructured over structured experience (.23).

In spite of these minimal differences between unstructured and structured experiences, the rating data, although not statis-

tically significant, suggested that

workgroups with collaborative experience, regardless of whether it was structured or unstructured, did interact more effectively than students without collaborative experience. These mean ESs on rating data were .48 and .62.

Altogether, these findings suggest that experience with collaborative groups, whether it be structured or unstructured, may enhance the quality of students' interactions over complex tasks. Contrary to demonstrated effects on relatively routine tasks (e.g., Ehrlich, 1991; Johnson et al., 1990; Slavin, 1996), however, explicit interdependence structures may be unnecessary on more challenging, controversial tasks. In fact, results provide mild support for Co-




hen's (1994) proposition that complex tasks

may provide a natural source of group in-

terdependence, which motivates students to participate and cooperate (Hertz-Laza- rowitz, 1989), elicits discussion (Smith et al., 1981), and generates cognitive conflict and resolution (Smith et al., 1981). From the perspective of the classroom teacher, whose

tendency is to implement cooperative learn-

ing without interdependence structures (Antil et al., 1998; Sharan, 1980; Slavin, 1996), these findings may be welcome. Of course, inferential statistical theory makes it

impossible to prove an absence of differences; consequently, readers are cautioned to interpret ESs as only suggestive and pre- liminary. Additional research is warranted.

In contrast to the lack of clear differences for background experience, a persuasive pattern of findings did emerge for work-

group size. Several main effects favored dyadic over small-group compositions, re-

gardless of workgroup structure or the focus of the data collection (LA vs. HA/ workgroups). Pairs were rated statistically and substantially higher than groups on

procedural and conceptual talk (ESs = 1.21 and 1.08) as well as helpfulness and cooperation (ESs = 1.03 and .87). The quality of the PA work generated during the video-

taped sessions also was higher in pairs than in groups (ESs = .82 on conceptual under-

pinnings, .71 on computational applications, .70 on problem-solving strategies).

Moreover, a series of statistically significant effects indicated that LA students ben- efited differentially in dyadic compositions. The level of their participation was greater in pairs than in groups (ES = 1.63). In addition, dyads produced higher collaboration ratings for LA students (ES = .78); by contrast, other workgroup members collaborated comparably in dyads and small

groups (ES = .23). These results lend support to dyadic

compositions, which may afford children with low-achievement status greater opportunity to participate and collaborate. This effect may accrue because dyadic conver-

sation is bilateral rather than multilateral (Sharan, 1980), or because dyads provide greater opportunity, or more actual time, for each individual to participate (see Webb, 1988). In addition, in contrast to dyads, small groups offer students greater choice about potential collaborators. As shown in the LA students' levels of participation data, which favored dyadic com-

positions, such choice may reduce LA students to menial or nonexisting roles.

Of course, these findings do not detract from previous work illustrating the deleterious effects of low achievement status on

equality of workgroup interactions (Hoff- man, 1973; McAuliffe & Dembo, 1994; Ro- senholtz, 1985; Tammivaara, 1982). Rather, as demonstrated in this study, LA students, across background structures and work-

group sizes, participated less than other

workgroup members (ES = .65) and exhib- ited lower-quality procedural and conceptual talk (ESs = .55 and .75). Lower participation rates are consistent with earlier work (e.g., Lindow et al., 1985; O'Connor & Jenkins, 1996). Lower-quality talk is pre- dictable: compared to lower-achieving pupils, high-ability students have greater oral

language facility (Feldhusen & Treffinger, 1980; King, 1989), have more experience providing explanations (Nattiv, 1994; Peter- son, Janicki, & Swing, 1981; Webb, 1982), and provide conceptually richer and pro- cedurally stronger explanations than do

lower-achieving pupils-even on more

simple mathematical content (Fuchs et al., 1996). The current study does, nevertheless, illustrate how certain workgroup arrangements, such as workgroup size, may ame- liorate some of the unfortunate effects associated with low achievement status.

It is important to note that results do not

permit unqualified support for dyadic ar-

rangements. On cognitive conflict ratings, some findings suggested the desirability of small groups over dyads-at least for average or high achievers. Workgroups generated greater disagreement and negotiation in groups than in pairs (ES = .52), even

JANUARY 2000



PRODUCTIVITY 205

though LA students participated in this dis-

agreement and negotiation comparably- and minimally-across workgroup sizes (ES = .13). In a similar way, a statistically significant interaction suggested a differing pattern of conflict resolution as a function of workgroup size for students with varying achievement status: ESs favored conflict resolution in small groups for average and

high achievers (ES = .36), but favored conflict resolution in dyads for LA students (ES = .32). Of course, cognitive conflict and resolution are desirable, because in expressing and resolving disagreement, students ex-

plain and justify positions, question beliefs, seek new information, or adopt alternative frameworks and conceptualizations (e.g., Bell et al., 1985; Tudge, 1989).

Although findings suggest that constructive disagreement may occur more fre-

quently for average and high achievers in

groups, but more often for low achievers in

dyads, readers are cautioned to consider a limitation in interpreting these findings. In this study, when working in small groups, high achievers had available average achievers with whom to disagree. By contrast, in dyads, high achievers had available only low achievers. High achievers may have viewed low achievers as less attractive than average achievers for potential part- ners in cognitive conflict because of more dramatic differences not only in cognitive capacity but also in achievement status (Mc- Auliffe, 1991). It is possible that, if this study had incorporated dyads with high and average achievers or with two high achievers, dyadic arrangements may have favored cognitive conflict and resolution for high and low achievers alike. In fact, previous work (Bell et al., 1985; Fuchs, Fuchs, Hamlett, & Karns, 1998; Mugny & Doise, 1978; Nastasi et al., 1990; Phelps & Damon, 1989) has demonstrated that, on complex, authentic problem-solving tasks, high- achieving, elementary-age students work more productively and effectively-and generate greater cognitive conflict-when paired with fellow high achievers than with

lower-achieving classmates. Therefore, additional work contrasting workgroup productivity as a function of workgroup size, while systematically controlling students' achievement status, is necessary to sort out the potential effects of workgroup size for higher-achieving students. In the mean- time, current findings should be general- ized only to heterogeneously constituted

groups. In a related way, before summarizing

conclusions, it may be useful to remind readers that this study, which incorporated several strong features, also suffers from important weaknesses. With respect to

strengths, we boosted external validity by using a PA task resembling those incorporated in current school reform activities. Second, the design offered several controls:

incorporating students in an individual

background experience condition allowed us to consider the effects of collaborative

backgrounds while controlling for experience with PA; by using workgroup as the

analytic unit, the statistical analysis directly compared the interactions of LA students to their classmates; and coders were blind to

background experience conditions. Third, our coding methods yielded multidimen- sional descriptions of performance, provided by independent coders.

Despite these strengths, it is important for readers to interpret findings with at least three problems in mind. First, external validity of findings is constrained by the arti- ficiality associated with videotaping children outside classroom settings and by our decision to constitute dyads and small groups in an extreme way, which maxi- mized differences in ability (i.e., by grouping highest- with lowest-achieving students in each classroom). Additional research should extend results by analyzing children's naturalistic interactions during classroom groupwork, conducted in dyads as well as small groups, with a range of for- mats for constituting workgroups' ability compositions. Second, although we did examine the quality of students' PA work gen-




erated during the interactions, which is suggestive of learning, we did not investigate the effects of ability group composition on

long-term achievement. Therefore, no conclusions about how much students learn as a function of workgroup structure or size can be drawn. Third, as noted, workgroup size effects must be interpreted in light of the achievement status mix in dyads as opposed to groups.

With these strengths and limitations in mind, some important and practical, albeit tentative, conclusions are possible. As teachers formulate decisions about how to

arrange cooperative learning activities, they inevitably struggle not only with the con- straints imposed by available time and

training but also with the requirement that

they balance the needs of the low- and high- achieving students in their classrooms. With respect to the demands associated with workgroup structure, findings suggest explicit interdependence structures may not be essential to workgroup productivity when complex, controversial tasks are involved. In terms of workgroup size, results are mixed. On the one hand, findings reveal that on complex tasks, LA participants may profit more from working in dyads than in

groups. By contrast, for other workgroup members, cognitive conflict and resolution are facilitated in small groups.

The set of findings on workgroup size, combined with previous work showing su-

perior interactions on complex tasks when HA students work with fellow HA rather than LA peers (Fuchs et al., 1998), suggests that high achievers, when working on com-

plex material, should have ample opportunity to work in small groups with fellow

high achievers so that cognitive conflict and resolution can occur. Nevertheless, current findings, in combination with previous work showing that LA students learn routine tasks better when explanations are provided by high- rather than average-achieving classmates (Fuchs et al., 1996), also suggest the importance of teachers consid- ering when and how dyadic, mixed-ability

group compositions facilitate student learn-

ing. It appears that heterogeneous dyads may be used effectively on complex tasks to enhance productivity for LA students. Al-

though better articulated rules for constituting workgroup structure and size await future research, current findings highlight the fact that varying arrangements will accomplish different objectives for different children. Consequently, teachers must be

prepared to vary the kinds of groupwork they employ and to constitute group structures in conjunction with clear objectives for what those activities are designed to accomplish.

Appendix A

Representative Transcript: Small Group (Structured Collaboration) LA: OK. (Reads.) How much money do you

have for school clothes? MA1: OK. We're going to add. HA: $105. MA1: $105. (Everyone writes.) HA: Plus ... MA1: Plus... HA: $97. (Everyone writes. LA looks at HA's

paper.) MA1: 5 plus 7 ... 5 plus 7 is ... (LA counts on

fingers.) HA: $202. MA1/MA2: $202. HA: And label it, too. $105 is from the money

mom saved. Then, ... (LA looks at HA's paper.)

MA1: Wait. (Everyone writes. LA looks at HA's paper.)

HA: $97 is from washing cars. (Everyone writes. LA looks up.)

HA: Now, we have to write it down on the group sheet. (HA writes; others watch.)

MA1: OK. Come on. Wait. (MA1 corrects paper; MA2 takes group sheet and checks it.)

MA2: (Reads.) How much will you spend on your first shopping trip when you buy the things your mom says you have to buy? (HA and MA1 help with decoding.)

HA: Let's see. Jeans cost $17, and we're going to buy four pairs of jeans.

MA1:So, write 17 plus 17 plus 17. (Everyone writes.)

HA: Plus 17. Then, you're going to buy six shirts and they're $7. (MA1 and HA write. MA2 looks at HA's paper. LA looks up.)

JANUARY 2000



PRODUCTIVITY 207

MA1: How many? HA: Six. (Everyone writes.) OK. And then. (HA

waits while MA1 and MA2 write and while LA counts on her fingers.) You're going to buy 10 socks, and those are $8 and four in each pack. So, ...

MA1: Two pairs. HA: No. That would only be eight. But then, 3

... that would be 8, 4, and 3 times is 12. MA1: Yeah, so ... LA: Yeah, I ... MA2: No. MA1: 17 plus (MA2 and LA look at each other

and shake heads no. MA2 points to own paper to show LA something.)

HA: 8 um... MA1: Four in a sack and how many do we need?

10 pairs? HA: 12. MA1: So... HA: We need 10 pairs and then ... MA1: 4, 8, uh ... HA: I guess we should just buy 12 pairs. That

would be 4 times 8. (LA looks at HA's paper. Everyone writes.)

MA1: 8 times 8 plus 8. How many 8s? HA: Then, we have to buy some shorts. We buy

two pairs. That's 6 plus 6. (LA looks at HA's paper and writes.)

LA: OK. That's 17. HA: 17? MA1: 17. MA2: Is it 14? (HA and MA1 work. MA2 holds

head. LA is off-task; then, counts on fingers; then, smiles and laughs. Then, MA2 is off-task while others write. Then, all write.)

HA: 154. LA: One hundred fifty what? MA2: 154. (Everyone writes.) HA: Then, we still got to label them. (LA copies

from HA; others write.) HA: Pants, shirts (as writing). All the 8s. MA1: Wait. The 8s are for the socks. HA: No. The 6 ... yeah, yeah. MA2: I don't understand. HA: What do you need help with? MA2: What do I do here? HA: We got to label. Let's see. No. Two. Let's

see jeans. How many jeans do we buy? LA: Let's see. (Points to own paper. No one

looks.) HA: We buy four pairs of jeans. 17 plus 17 plus

17 plus 17. MA1: It's too much. (Shows HA her paper.) HA: (to MA1) That's OK. (to MA2) You got to

put 17 four times. 17 plus 17 four times. You got to erase that cause you got to write some more.

MA2: (Erases.) Cause you got a lot of ... right there.

MA1: Put it on this. (Picks up group answer sheet.)

HA: And, then shirts. You put 1, 2, 3, 4, 5, 6. Put six 7s for the shirts because we got six pairs of shorts. Wait.

MA2: I already got it. I need to write ... HA: Wait. Um. That's shirts. Got six 7s. You got

to write how much all the shirts cost. (Points to MA2's paper.)

MA2: 1, 2, 3, 4. HA: Oh, you already did the problem? MA2: Yeah. HA: Oh. OK. Now, you got to label it. That's

for the jeans. It's spelled j-e-a- MA1: n-s. HA: Yeah. MA2: Jeans is right there. HA: Yeah. Then, there's the 7s is all for the

shirts. OK. Then, shorts. We bought two pairs. And, that's all the total. OK. You're almost done? (Talking to MA1.)

MA1: I just need a label. HA: OK. LA: (Referring to reading the question.) I sup-

posed to do the first one. HA: You did do the first one. LA: Did it over there. Not there. (Pointing to

group worksheet.) (All continue on to third question.)

Appendix B

Representative Transcript: Pair (Structured Collaboration) HA: OK. At first, how much money do you

have for the school clothes. So, over here, it says you saved $105 and you have $97 from washing cars. So, let's add that together and if we come up with the same number, we'll write that down.

LA: OK. (Both work. LA counts on fingers.) Are you through?

HA: Yeah. Are you? LA: Yeah. HA: You got 202, right? LA: Yeah. HA: OK. We'll put that on our team answer

sheet. (HA writes. LA watches.) HA: OK. Read it. LA: (Reads.) What will you buy and how much

will you spend on your first shopping trip when you buy the things your mom says you have to buy? Show all your work.

HA: OK. If you scan that (points to first page of PA), it says your mom says you must buy 4 pairs of jeans, 6 shirts, 10 pairs of socks, 2 pairs of shorts, and 1 pair of shoes. So,




we have to multiply 17 times 4, and if we come up with the same answer, we'll put that down. (Both work.)

LA: OK. HA: Are you done? What'd you come up with? LA: 64. HA: I came up with 67. Because what you have

to do is 17 times 3 is 21 and 7 more to 21. OK. Let's do it again and if we come up with the same answer, we'll write it down.

LA: OK. (Both work.) Are you done? HA: Are you? LA: Yeah. I came up with 68. OK. Let's do it

again one more time and if we come up with the same answer that will be what we put down. (Both work.)

HA: 68. Do you agree? LA: Yeah. HA: OK. Put that down on the team answer

sheet. (HA writes.) Next, it says you need six shirts and one shirt costs $7. So, we'll multiply 7 times 6. (Both work.)

LA: I don't know my times that well. HA: If you know your 5s, you can multiply 7

times 5 and then add 7 more. LA: 35 times 6? HA: No. 35 plus 6. (Both work.) LA: 41. HA: I came up with 42. OK. That's a 7. (Points

to LA's paper.) Now, you can add it up. See what you get. (Both work.)

LA: Now I'm at 42. HA: Is 42 OK to write down? LA: Yes. HA: Next, it says you need 10 pairs of socks.

One pair of socks ... one pack of socks is $8, and there are four in each one. If you get two of them, you'll spend $16, but you'll only get 8. And, if you get three of them, you'll get 12 pairs of socks and you'll spend $24. So, we'll get the closest amount. See, eight will be two less than we need, and 12 will be two more. But, you want to stick with 12?

LA: Yeah. HA: OK. Let's multiply 8 times 3, and if we

come up with the same answer, we'll put that down. (Both work.)

LA: What if I don't know my times? HA: 8 times 2 is 16. 16 plus 8? LA: (counting on fingers) 16 plus 8. 8 plus 6 is

14. Carry 1. That makes 2. 24. HA: OK. That's what I came up with. You want

me to put that down? LA: Yeah. HA: (writes). Next it says shorts. One pair of

shorts is $6 and we need two pairs. OK. Multiply 6 times 2. That's easy.

LA: What'd you come up with?

HA: I came up with $12. LA: Me, too. HA: OK. We agree. So, I can put that down

right there? LA: Yeah. HA: Next, it says shorts and shoes. So what

kind of shoes do you want to buy from here (points to chart): Nike, Adidas, Con- verse, or Reebok?

LA: I think we should buy Nike. HA: OK. 10 and half off is $5. So, we'll spend

$40 on shoes. OK, we'll ... on shoes. OK? And then, let's multiply 5 times 9 ... 5 times 8. And, if we come up with the same answer, we'll put that down. (Both work.) OK. You come up with 40?

LA: Yup. HA: So, I should just write that down here?

Now, it says how much money will you spend on the things. We have to take all our answers and add them together.

LA: Yeah. HA: And, if we come up with the same answer,

we'll write that down. (Both work.) LA: How much did you come up with? HA: 186. LA: I came up with 184. HA: OK. 8 plus 2 is 10. 10 plus 4 is 14. 14 plus

2 is 16. Look. (Points to LA's paper.) OK? LA: OK. HA: Let's add them all up again and if we come

up with the same answer, we'll write that down. (Both work.) I came up with 186.

LA: That's what I came up with. HA: OK. You want me to put that on our team

answer sheet? LA: Yeah. HA: OK. It's your turn to write now. (Both con-

tinue on to the third question.)

Appendix C

One Grade 3 Performance Assessment

Name Date

Teacher Grade 3 PA# E

Shopping for School Clothes

School is about to start, and it's time to shop for school clothes. Your mom makes a list of clothes that you must buy, and she asks you to think of other things you want for school. You and your mom decide that you'll make two shopping trips.

On the first trip, you'll buy the clothes she says you need. Your mom says that you must buy

JANUARY 2000



PRODUCTIVITY 209

four pairs of jeans, six shirts, ten pairs of socks, two pairs of shorts, and one pair of shoes. On the second trip, you'll buy the things you want.

Your mom has saved one hundred five dollars to spend on your clothes. You earned ninety- seven dollars for clothes by washing cars. You washed twenty-three cars.

Regular Shoe Prices (See Key) Nike •••

Adidas g•• Converse •• Reebok ggg

Key: Each 8 means $10. All shoes on sale for 1/2 the price on the chart.

Clothing Prices

1 Pair of Jeans $17

1 Shirt $7

1 Pair of Shorts $6

1 Pack of Socks (4 pairs in a pack) $8

(1) How much money do you have for school clothes?

(2) What will you buy and how much will you spend on your first shopping trip (when you buy the things your mom says you have to buy)? Show all your work.

(3) On your second shopping trip, you'll buy the other things you want for school. What will you buy and how much will you spend? What bills can you give the clerk to pay for these things?

(4) School sweatshirts cost $12. After your shopping trips, will you have enough money to buy one? Explain how you got your answer.

Note

Inquiries should be sent to Lynn S. Fuchs, Box 328 Peabody, Vanderbilt University, Nash- ville, TN 37203.

References

Antil, L. R., Jenkins, J. R., Wayne, S. K., & Va- dasy, P. F. (1998). Cooperative learning: Prevalence, conceptualizations, and the relation between research and practice. Amer- ican Educational Research Journal, 35, 419-454.

Aronson, E. (1978). The jigsaw classroom. Beverly Hills, CA: Sage.

Ashman, A. F., & Gillies, R. M. (1997). Children's cooperative behavior and interactions in trained and untrained work groups in regular classrooms. Journal of School Psychology, 35, 261-279.

Bearison, D. J. (1982). New directions in studies of social interaction and cognitive growth. In F. C. Serafica (Ed.), Social-cognitive development in context (pp. 199-221). New York: Guilford.

Bell, N., Grossen, M., & Perret-Clermont, A. (1985). Sociocognitive conflict and intellec- tual growth. In M. W. Berkowitz (Ed.), Peer conflict and psychological growth (New Direc- tions for Child Development, No. 29, pp. 41- 54). San Francisco: Jossey-Bass.

Berger, J., Wagner, D. B., & Zelditch, M. (1985). Introduction: Expectations states theory: Re- view and assessment. In J. Berger & M. Zeld- itch, Jr. (Eds.), Status, rewards, and influence (pp. 1-72). San Francisco: Jossey-Bass.

Bossert, S. T. (1988). Cooperative activities in the classroom. Review of Research in Education, 15, 225-250.

Brown, A. L., & Palincsar, A. S. (1989). Guided cooperative learning and individual knowledge acquisition. In L. B. Resnick (Ed.), Knowing, learning, and instruction: Essays in honor of Robert Glaser (pp. 393-451). Hills- dale, NJ: Erlbaum.

Burton, G. M., Kaplan, J. D., Hopkins, M. H., Johnson, H. C., Kennedy, L. M., & Schultz, K. A. (1992). Mathematics plus. Orlando, FL: Harcourt Brace Jovanovich.

Cohen, E. G. (1984). Talking and working together: Status interaction and learning. In P. Peterson, L. C. Wilkinson, & M. Hallinan (Eds.), Instructional groups in the classroom: Organization and processes (pp. 171-188). Or- lando, FL: Academic Press.

Cohen, E. G. (1994). Restructuring the classroom: Conditions for productive small groups. Re- view of Educational Research, 64, 1-35.

Cooper, C. R., & Cooper, R. G. (1984). Skill in peer learning discourse. In S. A. Kucza (Ed.), Discourse development (pp. 89-102). New York: Springer-Verlag.

Damon, W. (1984). Peer education: The un-




tapped potential. Journal of Applied Develop- mental Psychology, 5, 331-343.

Darling-Hammond, L. (1992, April). Reframing the school reform agenda: Developing capacity for school transformation. Paper presented at the annual meeting of the American Educational Research Association, San Francisco.

Deutsch, M. (1949). A theory of cooperation and competition. Human Relations, 2, 129-152.

Doise, W., & Mugny, G. (1979). Individual and collective conflicts of centrations in cognitive development. European Journal of Social Psy- chology, 9, 105-108.

Ehrlich, D. E. (1991). Moving beyond cooperation: Developing science thinking in interdependent groups. Unpublished doctoral dissertation, Stanford University, Stanford, CA.

Fantuzzo, J. W., King, J. A., & Heller, L. R. (1992). Effects of reciprocal peer tutoring on mathematics and school adjustment: A compo- nent analysis. Journal of Educational Psychol- ogy, 84, 331-339.

Feldhusen, J. F., & Treffinger, D. J. (1980). Crea- tive thinking and problem solving in gifted education. Dubuque, IA: Kendall/Hunt.

Fuchs, D., Fuchs, L. S., Mathes, P. G., & Sim- mons, D. (1997). Peer-assisted learning strategies: Making classrooms more responsive to diversity. American Educational Research Journal, 34, 174-206.

Fuchs, L. S., Fuchs, D., Bentz, J., Phillips, N. B., & Hamlett, C. L. (1994). The nature of student interactions during peer tutoring with and without training and experience. Amer- ican Educational Research Journal, 31, 75-103.

Fuchs, L. S., Fuchs, D., Hamlett, C. L., & Karns, K. (1998). High-achieving students' interactions and performance on complex mathematical tasks as a function of homogeneous and heterogeneous pairings. American Edu- cational Research Journal, 35, 227-268.

Fuchs, L. S., Fuchs, D., Hamlett, C. L., Phillips, N. B., Karns, K., & Dutka, S. (1997). Enhanc- ing students' helping behavior during peer- mediated instruction with conceptual mathematical explanations. Elementary School Journal, 97, 223-249.

Fuchs, L. S., Fuchs, D., Karns, K., Hamlett, C. L., Dutka, S., & Katzaroff, M. (1996). The relation between student ability and the quality and effectiveness of explanations. American Educational Research Journal, 33, 631-664.

Fuchs, L. S., Fuchs, D., Karns, K., Hamlett, C. L., Dutka, S., & Katzaroff, M. (in press). The importance of providing background information on the structure and scoring of performance assessments. Applied Measurement in Education.

Glachan, M., & Light, P. (1982). Peer interaction

and learning: Can two wrongs make a right? In G. Butterworth & P. Light (Eds.), Social cognition: Studies of the development of under- standing. Chicago: University of Chicago Press.

Good, T., & Grouws, D. (1977). Teaching effects: A process-product study in fourth grade mathematics classes. Journal of Teacher Edu- cation, 28, 49-54.

Goodman, J. (1995). Change without difference: School restructuring in historical perspective. Harvard Educational Review, 65, 1-28.

Greenwood, C. R., Delquadri, J. C., & Hall, R. V. (1989). Longitudinal effects of classwide peer tutoring. Journal of Educational Psychology, 81, 371-383.

Hambleton, R. K., Jaeger, R. M., Koretz, D., Linn, R. L., Millman, J., & Phillips, S. E. (1995). Re- view of the measurement quality of the Kentucky Instructional Results Information System (Final Report). Prepared for the Office of Educa- tional Accountability, Kentucky General As- sembly.

Hare, A. P. (1975). Handbook of small group research. New York: Free Press.

Hedges, L. V., & Olkin, I. (1985). Statistical methods for meta-analysis. Orlando, FL: Academic Press.

Hertz-Lazarowitz, R. (1989). Cooperation and helping in the classroom: A contextual approach. International Journal of Educational Re- search, 13, 113-119.

Hodgkinson, H. L. (1995, October). What should we call people?: Race, class, and the census for 2000. Phi Delta Kappan, 77, 173-179.

Hoffman, D. E. (1973). Students' expectations and performance in a simulation game. Unpublished doctoral dissertation, Stanford University, Stanford, CA.

Jenkins, J. R., Mayhall, W. F., Peschka, C. M., & Jenkins, L. M. (1974). Comparing small group and tutorial instruction in resource rooms. Exceptional Children, 40, 245-250.

Johnson, D. W., & Johnson, R. T. (1985). Class- room conflict: Controversy versus debate in learning groups. American Educational Re- search Journal, 22, 237-256.

Johnson, D. W., & Johnson, R. T. (1992). Positive interdependence: Key to effective cooperative groups. In N. Miller & R. Hertz-Laza- rowitz (Eds.), Interaction in cooperative groups: The theoretical anatomy of group learning (pp. 174-199). New York: Cambridge University Press.

Johnson, D.W., Johnson, R.T., & Stanne, M. (1990). Impact of goal and resource interdependence on problem-solving success. Jour- nal of Social Psychology, 129, 507-516.

Kansas State Board of Education. (1991). Kansas

JANUARY 2000



PRODUCTIVITY 211

Quality Performance Accreditation. Topeka: Author.

King, A. (1989). Verbal interaction and problem- solving within computer-assisted cooperative learning groups. Journal of Educational Computing Research, 5, 1-15.

King, A. (1992). Facilitating elaborative learning through guided student-generated question- ing. Educational Psychologist, 27, 111-126.

Klingner, J. K., & Vaughn, S. (1996). Reciprocal teaching of reading comprehension strategies for students with learning disabilities who use English as a second language. Ele- mentary School Journal, 96, 275-293.

Lindow, J. A., Wilkinson, L. C., & Peterson, P. L. (1985). Antecedents and consequences of verbal disagreements during small-group learning. Journal of Educational Psychology, 77, 658-667.

McAuliffe, T. J. (1991, April). Status rules of behavior in scenarios of cooperative learning groups. Paper presented at the annual meeting of the American Educational Research Association, Chicago.

McAuliffe, T. J., & Dembo, M. H. (1994). Status roles of behavior in scenarios of peer learning. Journal of Educational Psychology, 86, 163- 172.

Meeker, B. F. (1981). Expectation states and in- terpersonal behavior. In M. Rosenberg & R. H. Turner (Eds.), Social psychology: Socio- logical perspectives (pp. 290-319). New York: Basic.

Mesch, D., Lew, M., Johnson, D. W., & Johnson, R. (1986). Isolated teenagers, cooperative learning, and the training of social skills. Journal of Psychology, 120, 323-334.

Michaels, S., & Bruce, C. (1991). Discourses on the seasons (Technical report). Champaign: Uni- versity of Illinois, Reading Research and Education Center.

Moody, J. D., & Gifford, V. D. (1990, November). The effect of grouping by formal reasoning ability level, group size, and gender on achievement in laboratory chemistry. Paper presented at the annual meeting of the Mid-South Educa- tional Research Association, New Orleans.

Mory, E., & Salisbury, D. (1992, April). School restructuring: The critical element of total system design. Paper presented at the annual meeting of the American Educational Research Association, San Francisco.

Mugny, G., & Doise, W. (1978). Socio-cognitive conflict and structure of individual and collective performances. European Journal of So- cial Psychology, 8, 181-192.

Nastasi, B. K., Clements, D. H., & Battista, M. T. (1990). Social-cognitive interactions, motiva- tion, and cognitive growth in Logo program-

ming and CAI problem-solving environ- ments. Journal of Educational Psychology, 82, 150-158.

Nattiv, A. (1994). Helping behavior and math achievement gain of students using cooperative learning. Elementary School Journal, 94, 285-297.

Nystrand, M., Gamoran, A., & Heck, M. J. (1991). Small groups in English: When do they help students and how are they best used? Madison: University of Wisconsin, Center on the Or- ganization and Restructuring of Schools.

O'Connor, R. E., & Jenkins, J. R. (1996). Cooper- ative learning as an inclusion strategy: A closer look. Exceptionality, 6, 29-52.

O'Donnell, A. M. (1996). Effects of explicit incen- tives on scripted and unscripted cooperation. Journal of Educational Psychology, 88, 74-86.

Palincsar, A. S., & Brown, A. L. (1989). Class- room dialogues to promote self-regulated comprehension. In J. Brophy (Ed.), Advances in research on teaching (Vol. 1, pp. 35-71). New York: JAI Press.

Paradis, L. M., & Peverly, S. (1994, April). The effects of knowledge and task on students' peer- directed questions in modified cooperative learning groups. Paper presented at the annual meeting of the American Educational Re- search Association, New Orleans. (ERIC Document Reproduction Service No. ED 371 027)

Peterson, P. L., Janicki, T. C., & Swing, S. R. (1981). Ability x treatment interaction effects on children's learning in large-group and small-group approaches. American Edu- cational Research Journal, 18, 453-473.

Peterson, P. L., & Swing, S. (1985). Students' cog- nitions as mediators of the effectiveness of small-group learning. Journal of Educational Psychology, 77, 299-312.

Phelps, E., & Damon, W. (1989). Problem solving with equals: Peer collaboration as a context for learning mathematics and spatial concepts. Journal of Educational Psychology, 81, 639-646.

Piaget, J. (1928). Judgment and reasoning in the child. London: Routledge & Kegan Paul.

Rosenholtz, S. J. (1985). Treating problems of academic status. In J. Berger & M. Zelditch, Jr. (Eds.), Status, rewards, and influence (pp. 445- 470). San Francisco: Jossey-Bass.

Russell, T., & Ford, D. F. (1983). Effectiveness of peer tutoring vs. resource teachers. Psychol- ogy in the Schools, 20, 436-441.

Sharan, S. (1980). Cooperative learning in small groups: Recent methods and effects on achievement, attitudes, and ethnic relations. Review of Educational Research, 50, 241-271.

Sharan, S. (1990). Cooperative learning and help-




ing behavior in the multi-ethnic classroom. In H. C. Foot, M. J. Morgan, & R. H. Shute (Eds.), Children helping children (pp. 151-176). Chichester: Wiley.

Slavin, R. E. (1996). Research on cooperative learning and achievement: What we know, what we need to know. Contemporary Edu- cational Psychology, 21, 43-69.

Slavin, R. E., Madden, N.A., & Leavey, M. (1984). Effects of team-assisted individuali- zation on the mathematics achievement of academically handicapped and nonhandi- capped students. Journal of Educational Psy- chology, 76, 813-819.

Smith, K., Johnson, D. W., & Johnson, R. T. (1981). Can conflict be constructive? Contro- versy versus concurrence seeking in learning groups. Journal of Educational Psychology, 73, 651-663.

Stallings, J. A. (1995). Ensuring teaching and learning in the twenty-first century. Educa- tional Researcher, 24(6), 4-8.

Swing, S. R., & Peterson, P. L. (1982). The rela- tionship of student ability and small group interaction to student achievement. American Educational Research Journal, 19, 259-274.

Tammivaara, J. S. (1982). The effects of task structure on beliefs about competence and participation in small groups. Sociology of Education, 55, 212-222.

Tudge, J. (1989). When collaboration leads to re- gression: Some negative consequences of socio-cognitive conflict. European Journal of So- cial Psychology, 19, 123-138.

Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes. Cam- bridge, MA: Harvard University Press.

Webb, N. M. (1982). Peer interaction and learning in cooperative small groups. Journal of Educational Psychology, 74, 642-655.

Webb, N. M. (1988, April). Peer interactions and learning in small groups. Paper presented at the annual meeting of the American Educa- tional Research Association, New Orleans.

Webb, N. M. (1989). Peer interaction and learning in small groups. International Journal of Educational Research, 13, 21-40.

Webb, N. M. (1991). Task-related verbal interaction and mathematics learning in small groups. Journal for Research in Mathematics Education, 22, 366-389.

Webb, N. M. (1992). Testing a theoretical model of student interaction and learning in small groups. In R. Hertz-Lazarowitz & N. Miller (Eds.), Interactions in cooperative groups: The theoretical anatomy of group learning (102- 119). New York: Cambridge University Press.

Webb, N. M., & Farivar, S. (1994). Promoting helping behavior in cooperative small groups in middle school mathematics. Amer- ican Educational Research Journal, 31, 369-395.

Webb, N. M., Troper, J., & Fall, J. R. (1992, April). Effective helping behavior in cooperative small groups. Paper presented at the annual meeting of the American Educational Research Association, San Francisco.

Webb, N. M., Troper, J., & Fall, J. R. (1995). Con- structive activity and learning in collaborative small groups. Journal of Educational Psy- chology, 87, 406-423.

Wertsch, J. V. (1984). The zone of proximal development: Some conceptual issues. In B. Ro- goff & J. V. Wertsch (Eds.), Children's learning in the "zone of proximal development" (pp. 7- 18). San Francisco: Jossey-Bass.

Wiggins, G. (1989). A true test: Toward more authentic and equitable assessment. Phi Delta Kappan, 70, 703-713.

Wittrock, M. C. (1989). Generative processes of comprehension. Educational Psychologist, 24, 345-376.

Yager, S., Johnson, D. W., & Johnson, R. T. (1985). Oral discussion, group-to-individual transfer, and achievement in cooperative learning groups. Journal of Educational Psy- chology, 77, 60-66.



Documents

Effects of Workgroup Structure and Size on Student Productivity during Collaborative Work on Complex Tasks