the collegial focus and high school students' achievement

The Collegial Focus and High School Students' AchievementAuthor(s): Jeffrey Y. Yasumoto, Kazuaki Uekawa and Charles E. BidwellSource: Sociology of Education, Vol. 74, No. 3 (Jul., 2001), pp. 181-209Published by: American Sociological AssociationStable URL: http://www.jstor.org/stable/2673274 .

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The Collegial Focus and High School Students' Achievement

Jeffrey Y. Yasumoto University of Chicago

Kazuaki Uekawa University of South Florida

Charles E. Bidwell University of Chicago

The authors examine the consequences of teachers' collegial social relations for high school students' mathematics and science achievement. They present a growth model for achievement that incorporates student, teacher classroom, and department effects. Particular attention is given to mechanisms of collegial social control. Using data from a national sample of 52 public high schools and some

3,000 students, they found that when departmental faculties form collegial foci -that is, when they present a combination of communication density, intensity of instructional practice norms, and consistency of practice-the effects of their instructional practices on students' achievement growth intensify.

W _ ur purpose is to present evidence of the effects of high school faculty social organization on school production, extending an earlier

investigation by Bidwell and Yasumoto (1999) into the collegial social control of instruction in high school faculties. School production denotes the processes by which schooling generates the cognitive develop- ment or moral socialization for which a school is formally responsible. These processes are socially ordered, so that to understand school production sociological- ly, one must investigate relationships between structures of social relations in schools, instructional or other socialization processes, and a given student outcome.

The sociological literature on schools and schooling does not yet contain a com-

prehensive analysis that incorporates measures from each of these three sets of variables. Consider studies of curricular differentiation, arguably the principal current research focus in the sociology of education. This research has explored how classroom practices vary across ability groups or curricular tracks or levels, mediating curricular effects on students' academic achievement (e.g., Barr and Dreeben 1983; Gamoran and Mare 1989; Lee and Bryk 1988). However, for the most part, these studies have limited their attention to individual teachers working within their own classrooms or courses. Consequently, they have not explored systematically how the environing social organization of the school is implicated in curricular effects on student outcomes.

Sociology of Education 2001, Vol. 74 (Uuly): 181-209 181



182 Yasumoto, Uekawa, and Bidwell

Consider also the recently growing literature on collegial structures in schools (e.g., Johnson 1990; Little 1990; Louis and Marks 1998), which includes interesting applications of organizational learning concepts to schools (Leithwood and Louis 1998). This literature sensitizes sociologists of education to the importance of these structures for the way teachers work and to the ways in which informal structures of social relationships in schools may affect the conduct of both teachers and students in classrooms. However, it does not specifically address either the consequences for student outcomes or the mechanisms involved. Among these studies is an increasing number that have examined relationships between informal social relations within faculties and teachers' instructional beliefs and practices (e.g., Bidwell and Yasumoto 1999; McLaughlin and Talbert 1990; Page 1991; Rowan 1990, 1995; Rowan, Raudenbush, and Kang 1991; Siskin 1994). Neither these studies nor their classic predecessors (Lortie 1975; McPherson 1972; Waller 1932) have examined the consequences for students.

We attempted a more comprehensive analysis of school social organization, instruction, and student outcomes. Using data from a national sample of public high schools in the United States, we estimated the relationships between informal ties among faculty colleagues, their instructional practices, and students' academic achievement growth, with explicit attention to the mechanisms by which achievement growth is affected.

The recent studies of faculty social organization have shown that high school faculties form fairly strong networks of informal interaction, much of this interaction centered sub- stantively on the everyday work of teaching. These networks tend to follow structural lines provided by the division of faculty labor, differentiating especially into cohesive subgroups according to departmental membership or teaching field. The findings suggest that in these subgroups, teachers reflect collectively about the ends of their instructional activities and about effective ways of attain- ing these ends. In other words, faculty networks can provide necessary social capital for the social control of teaching, in the classical

sense that collective deliberation about the ends and means of action is a prime social control mechanism in modern societies (Janowitz 1975; Park and Burgess 1921).

THEORETICAL RATIONALE

Concern with socially ordered efforts by groups of teachers to solve day-to-day instructional problems is explicit in research by Rowan (1990) and Bidwell and Yasumoto (1999). Rowan began with the premise that teaching takes place in an environment of uncertainty because it is technically impre- cise, without well-specified rules and standards of performance, and because teachers face demands for the accomplishment of diverse, often contradictory or conflicting, instructional goals. He argued that teachers, finding no ready-made ways of resolving the consequent problems that they face in their classrooms, turn to colleagues in a search for solutions. In this way, collegial interaction centers on the endemic problems of teachers' classroom work.

Bidwell and Yasumoto (1999), in their study of high school faculties, introduced the idea of the collegial focus as a way to understand how faculty networks affect instruction. We summarize their theoretical argument and then draw out its implications for effects on achievement before we present our findings.

Social Control and Colleglal Foc Bidwell and Yasumoto (1999), applying Feld's (1981) social focus construct to networks of professional interaction in faculties, defined collegial foci as subgroups of frequently inter- acting faculty colleagues that are character- ized by local cultures of teaching practice.1 They reasoned that collegial foci are most likely to emerge within teaching fields. Like Rowan, they assumed that teaching is inher- ently problematic, in their view, because the difficulties that Rowan described are com- pounded by the complexity of instructional interaction in the classroom. When teachers teach the same subject in the same school, the classroom problems that they encounter



The Collegial Focus and High School Students' Achievement 183

should be alike. Under these conditions, teachers who are trying to find solutions should form nodes of problem-diagnosing and problem-solving interaction, interaction that should be facilitated when teaching fields are formally organized into departments and when shared offices or neighbor- ing classrooms provide physical proximity.

As the diagnoses and solutions take shape, contagion processes and selection into subgroup membership should lead to converg- ing views within these problem-solving subgroups about the nature of the problems and ways to solve them-that is, effective ways in the local situation to teach and manage the classroom. Specifically, interpersonal ties are channels of communication. Presumably, the denser the ties in a faculty subgroup, the greater the probability of frequent and accu- rate communication and the greater the accessibility of any member to monitoring by any other (if not direct observation of classroom work, then monitoring by self-report or reports by students and other third parties). Thus, the density of ties in a faculty subgroup should increase the subgroup's problem- diagnosing and problem-solving capacity and the capacity of its members to keep track of each other's work. Ties also are mediums of interpersonal influence. The denser and stronger the ties in a faculty subgroup, the greater its aggregate power to induce members to adopt preferred lines of classroom action, the greater the exposure of any member to such persuasion, and the greater the aggregate potency of the sanctions that members can apply to one another's instructional performance. These contagion processes should be reinforced by the selection of subgroup members, when disagreeing members leave and others, facing similar problems, join because they find a supportive and helpful set of colleagues in the subgroup.

As a consequence of communication, persuasion, and selection, subgroups of teachers should develop their own distinctive local cultures of practice-conceptions of appropriate teaching objectives, procedural rules, and standards for assessing results. Local cultures of practice do not arise de novo. When they occur within teaching fields, they are adaptations of the practice norms of the shared

teaching field to the particular situation of the local collegial subgroup. These local cultures of practice provide accounts of ways of teaching a subject that are likely to succeed in the local school setting and that are means toward preferred instructional objectives.2 They have a normative force that may derive, in part, from the cultural authority of the academic disciplines, but that is more immedi- ately the result, first, of members' identification with the subgroup and consequent internal sanctioning and, second, of external sanctioning by others in the subgroup.

In sum, collegially focal subgroups of faculty provide varieties of social capital that should sustain normatively forceful narratives of good teaching practice, encompassing aims, procedures, and standards of teaching. They should create the capacity to reach and maintain agreement about these local norms of practice through selection into the subgroup and socialization within it. They should provide the face-to-face interaction that allows ready discussion of the nature of teaching problems and their remedies and the internal and external sanctioning of instructional performance that builds compliance with the normative terms of these narratives.

Collegial Foci and Achievement As a result, we expect collegially focal faculty subgroups to intensify the achievement effects of the instructional practices of their members when these practices are normatively preferred in the subgroup. This effect should be observed at the level of the individual teacher or course and, in an aggregate rate of achievement, at the level of the subgroup. We expect this intensification effect because of the action of four mechanisms.

The first mechanism is simple problem- solving efficiency. If teachers in collegially focal subgroups are unusually good collectively at diagnosing and solving instructional problems, given dense communication links in the subgroup and locally specific norms and standards of practice, then their individual classroom performance should benefit.

The second mechanism is cumulative exposure. The normative force of local cultures of practice should result in a strain




toward pedagogical consistency for teachers individually and among the members of the subgroup. Once solutions to teaching problems are arrived at and become part of the local culture of practice, normative agreement in the collegially focal subgroup should result in the relatively uniform use of these solutions. This tendency toward consistency is also a tendency toward cumulation. That is, if a group of teachers has fixed on a locally effective teaching technique or set of techniques, then the more consistent the use of this practice or set of practices, the larger the intensification effect should be. This cumulative effect should occur both within courses (or classrooms) and across courses (or teachers). Note that we do not propose that consistency effects are necessarily specific to individual practices. Teaching may be particularly effective when complementary or reinforcing practices are combined. In this case, intensification should come about with consistent use of the set of practices.

While the effect of problem-solving efficiency should always be positive (the result of better choices and the better use of chosen procedures), the effect of cumulative exposure may be either positive or negative. Techniques that retard learning should be more strongly retarding the greater the exposure, just as those that promote learning should have stronger positive effects the greater the exposure. Moreover, a teacher who perseverates in the use of a single practice (e.g., teaching entirely by lecture) may weaken the effectiveness of the practice, whatever its instructional potential.

The third mechanism is pedagogical interference. Interference should occur less often than cumulative exposure, but it may be important. Some instructional techniques may interfere with others if they are experi- enced in the same course or even across courses in the same subject. For example, a technique that places high demand on students' energies (such as extensive reading in a topic or conducting independent research) may be effective. However, combining two such techniques (both extensive reading and an individual project, of substantially different content) may make excessive demands on students and reduce their overall levels of

motivation in the course. Interference should lower the achievement effects of positive teaching techniques, but it should not weaken the adverse effects of negative ones.

The fourth mechanism is the induction of trust among the subgroup members. A teacher in a collegially focal subgroup should be able to rely on the fact that his or her colleagues tend to use the same techniques in the same classroom situations as he or she. In many schools, students attempt to negotiate reduced academic standards to moderate their levels of effort (Bidwell 1965; Bidwell and Friedkin 1988; Stinchcombe 1964 Waller 1932). In these situations, teachers who pre- fer to make strong academic demands on students may be more willing to do so when they know that their colleagues make the same level of demand. Moreover, this united faculty front may moderate the consequences of students' resistance. If we assume further that demanding techniques generally have positive effects on students' achievement, then the trustworthiness of colleagues should intensify the effectiveness of such techniques.

A GROWTH-MODEL FRAME- WORK

We must stress that we do not posit collegially focal subgroups as the statistically normative state of high school faculties. Rather, we expect substantial variation, both within and between schools, in the degree to which collegially focal subgroups exist. We analyzed the relationships of this variation, as it occurred between the mathematics departments and between the science departments of our high school sample, and the magnitude of the effects of instructional practices on students' academic achievement in the two subject matters. Because of the cumulative nature of the proposed effects, we considered how collegial foci affect growth curves, rather than the mean achievement scores of students or schools. We used hierarchical growth models (Bryk and Raudenbush 1992) to track students' achievement scores over time, estimating their growth trajectories and effects on these trajectories.



The Collegial Focus and High School Students'Achievement 185

The Data Our data were collected in collaboration with the Longitudinal Study of American Youth (LSAY). LSAY followed two cohorts of students, one that entered the 7th grade and the other that entered the 10th grade in fall 1987. Our sample was the younger cohort, consisting of some 3,000 subjects from a national sample of 52 public high schools. We had six years of test-score information taken annually from fall 1987 (the 7th grade) to fall 1992 (the 12th grade). These scores, on achievement tests constructed for LSAY, were calculated using a three-parameter logistic item response theory (IRT) model.3 In addition to the science and mathematics tests, each fall the students were asked to complete survey questionnaires regarding their schooling and home experiences.

Teacher and class information was collected in the spring of each school year. At these times, the LSAY students' mathematics and science teachers were asked in some detail about the specific instructional techniques they used in the courses in which the LSAY students had been enrolled in that year. The teachers were asked to report how often or with how much emphasis they used 70 specific instructional techniques that cover a wide spectrum of pedagogical approaches.

We supplemented the LSAY data set for each school in the sample with data collected in spring 1993 and fall 1994. In spring 1993, we asked the LSAY teachers to report retro- spectively the frequency of their professional discussions with other teachers in their departments during the academic year just ending, that is, the last year that the LSAY students were enrolled in the school. In fall 1994, we asked the science and mathematics teachers not earlier surveyed to provide this same sociometric information. Each teacher was also asked to complete a questionnaire that substantially replicated the original LSAY teacher questionnaire and included items about teaching techniques used in what the teacher considered to be a key course among those that he or she offered.4

The supplemented LSAY data allowed us to examine how classroom-specific instructional experiences influenced academic achieve-

ment over the entire four years that the student-respondents were in high school. They also permitted us to analyze how learning took place under different social structural conditions, particularly in courses taught by teachers from departments that differed in the degree to which they formed collegial foci.5

The Model Students' academic achievement, both its level and its growth, is related to certain of their personal attributes and to such attributes of their courses as content and ability level, whatever the effects that faculty collegial relationships may have on these outcomes. Hierarchical modeling allowed us to control for attributes of both students and courses when we estimated the effects of departmental collegial foci on students' achievement levels and growth. For this purpose, we first estimated models of individual students' growth in mathematics and science achievement. These models include terms that represent the timing of test administration (in mathematics or science), the level of achievement in the subject during junior high school, the linear and nonlinear components of the student's growth curve, individual attributes of the student, and the subject matter and ability level of the mathematics or science courses that the student took in high school. Using this student-level model as a baseline, we turned, first, to models that evaluate the consequences of student and course attributes for mean achievement levels and growth patterns in mathematics or science and, then, addressing the main questions of our study, to models that estimate the effects of departmental collegial foci on achievement levels and growth, net of students' individual attributes and course taking.

Specifically, we used a three-level hierarchical linear model (HLM), which is a type of mixed coefficient model (Bryk and Raudenbush 1992). By using this model, we avoided the estimation problem caused by our complex sampling design of repeated test observations of students nested within mathematics or science departments. In the LSAY student sample, the mean test scores rose




until the 1 0th grade and then declined. Hence, we defined a basic quadratic growth model of the form:

ACHIEVEMENTtij = no + m, (YEAR) + t2(YEAR2) + 113 COV + e(tiJ) (1)

where ACHIEVEMENTt1j is the achievement at time t of student i in department j and e are independent and normally distributed with common variance a2.

Each observation represents a different year t, and each student i contributes five years of observations. YEAR indicates the year of test administration; the YEAR2 term is added to the model diminishing growth. no represents 10th-grade average achievement because YEAR is centered on the 1 0th grade. m, represents the growth rate, and the n2 quadratic term represents nonlinearity in the curve. 113 is a (q x 1) matrix representing the q effects of a (1 x q) matrix of time-varying covariates, COV. These covariates include the teaching practices, subject-matter content, and ability level of the mathematics or science courses in which the students had been enrolled during the school year just prior to a given year's fall test administration.

Now considering the three-level models, student test observations are nested within students, and students are nested within departments:

Level 1: ACHIEVEMENTtj = luoij +

l ii (YEAR) tij + (2ij YEAR!) tij + 113 ij COVtij + e

Level 2 (student mean): 7toij = Roj +

Bo1jCOV11j + roj

Level 2 (student growth): 7c1ij = l, Oj +

B, 1 jCOV21j + r1 1j (2)

Level 3 (department mean): Roj = 7000 + Fool COV3j + VOoj

Level 3 (department growth): Rloj= 7100 + r101COV4j+ v1oj (3)

At Level 1, we have an individual growth model of the academic achievement at time t of student i in department j. At Level 2, we

model the variation of n0 and ml. These models (Equations 2) specify that the 1 Oth-grade average score, n0, and growth rate, t1 are estimated separately for each department and are functions of COVI and COV2, matrices that contain student-level individual attributes, namely, socioeconomic status (SES), race-ethnicity, gender, and dropout and transfer status in the LSAY school. In substantive terms, it is this framework that allows us to ask what kinds of individual students in what kinds of courses performed well in terms of absolute achievement and growth.

The key propositions about the effects of collegial foci are tested at Level 3, the department level (Equations 3). Our indicator of the effects of departmental collegial foci on achievement growth is intrinsic to the estimation of the Level 3 models and is discussed in that portion of the analysis. As in the Level 2 formulation, at Level 3 average 10th-grade achievement and growth rate are estimated separately for each department. Variation in Roo and in %lo is modeled by department covariates contained in matrices COV3 and COV4. These covariates include departmental size, the school's per pupil expenditure, the school's urbanicity, and a series of terms for properties of the professional discussion network that linked departmental members. This format is used to explore the ways in which academic performance is associated with social organizational attributes of departments, so that we can estimate consequences of departmental collegial foci on achievement growth, 1l O (For an excellent review of modeling organizational characteristics for students' achievement in a growth model, see Bryk and Raudenbush 1992)

Decomposition of Variance An unconditional ANOVA model shows how mathematics and science achievement scores are distributed at the individual student and department levels. The average 10th-grade school mean, 7000, was estimated at 58.75 for mathematics and 57.50 for science. The standard deviation for 7000, is approximately 13 point. Because these scores are IRT precision scores, Level 1 variance is fixed at 1. The variance within departments, ro, is 1 36.5 and




136.8, and the variance between departments, vi3, is 25.6 for mathematics and 25.3 for science. For both mathematics and science, about 84 percent of the variance in achievement is between students, and 16 percent is between departments.

RESULTS: STUDENT AND TEACHER EFFECTS

Estimating the Baseline Growth Model The baseline growth model provides a bench- mark for estimating the effects of collegial foci on the mathematics and science departments' production of achievement growth. This model includes covariates that measure individual students' attributes and the content and ability levels of either the students' mathematics or science courses, terms for the linearity and nonlinearity of the students' own growth curve, and a term for the students' average scores on the achievement tests in junior high school. These variables are ordered by block and described in Table 1. (Descriptive statistics for these variables and others used in later models, including means and standard deviations, are available from the first author on request.)

Tables 2 and 3 report parameter estimates for two stepwise series of four models each. One series of models predicts mathematics achievement growth, and the other predicts science achievement growth. Each series displays how the covariates change with successive controls, culminating in the baseline model. To let us see how the effects of these covariates change with successive controls, the variables enter in the blocks that are shown in Table 1: first, the student attributes (Model a); second, the variables that characterize a student's growth curve (Model b); third, the student's prior achievement (Model c); and, fourth, the course attribute measures (Model d, the baseline model).

Student Effects In Model a (Tables 2 and 3), we see positive effects of SES and negative effects of minority

status (except for Asians) on achievement growth. These effects are consistent with the literature on high school achievement (e.g., Berends, Lucas, and Sullivan 1999; Hauser 1998; Mare 1995). The achievement growth advantage for females in mathematics and the lack of a significant gender effect in science differ from previous findings of persis- tent small achievement advantages for males in high school mathematics and science. However, our results should be considered in the context of a more general trend toward gender parity in academic performance during the high school years (Gamoran 1999).

The student growth-curve terms that enter Model b do not represent students' characteristics in the strict sense. However, they are determinants of the shape of students' growth curve, so that it makes sense to discuss the parameter estimates for these terms here. The linear component of the growth model indicates that, on average, the students gained approximately 3 points a year in mathematics (13 = 2.95, p < .01) and 2 points a year in science (1 = 1.96, p< .01). However, the quadratic component is significantly negative, which confirms that these students' growth typically declined over time. Better students have steeper growth curves.6 Entering typical numbers makes these curves easier to grasp. Figure 1 shows typical growth curves for students of high, average, and low ability for mathematics and science.

In addition to modeling variation in the outcome means (estimated variances of 42.80 for mathematics and 48.20 for science), we examined variation in the growth curve. The estimated variances of the between-department growth slopes were CR22 (mathematics) = 2.816 and "R22 (science) = 3.98, with X2 statistics 450.026, df= 48, p < .0001 and X2 statistics 230.60, df = 48, p < .0001, respectively. These tests reject the null hypothesis that the estimated variances in growth slopes are zero. Hence, we infer that there is sufficient variability between departments to model the relationship between departmental collegial foci and growth rates. Table 4 gives the decomposition-of-variance figures.

Returning to Tables 2 and 3 and comparing Models a and c, with the introduction of




Table 1. Description of the Student and Course Variables

Variable Name Description

Block 1: Student Attributes SES A Level 2 measure of the SES of the student's family, calculat-

ed as the equally weighted average of composite parental education, composite parental occupational prestige, and the score on an index of household possessions.

Hispanic, Black, Asian A set of Level 2 dummy variables indicating race-ethnicity. White is the omitted category.

Race-ethnicity missing A Level 2 dummy variable indicating missing race-ethnicity data.

Female A Level 2 dummy variable indicating gender, with male the omitted category.

Transfer-leave A Level 1 time-varying dummy variable indicating that the student had dropped out, transferred, or otherwise left the LSAY school.

Block 2: Growth Components Year 10 A Level 1 linear growth-model term, centered on year 10.

Year 1 02 A Level 1 quadratic growth-model term, centered on year 10.

Block 3: Prior Achievement Prior achievement A Level 2 measure of prior mathematics or science achieve-

ment. It is the average of Grades 7 and 8 IRT test scores.

Block 4: Course Attributes Mathematics

A set of Level 1 time-varying dummy variables indicating mathematics course content. Algebra 1 is the omitted category

Junior high school: Basic, average, high

High school: Prealgebra, geometry, Algebra 2, trigonometry, calculus, no math course taken

Science A set of Level 1 time-varying dummy variables indicating science course content. General science is the omitted category.

Biology, Biology 2, chemistry, physics, advanced chemistry or physics, no science course taken

Level A Level 1 time-varying measure for the mathematics or science course in which the student was enrolled, based on the teacher-reported ability level (1 = lowest, 3 = middle, 5 = highest).

Course missing; level missing A set of Level 1 time-varying variables indicating missing data for mathematics course enrollment and science course enrollment.




Table 2. Quadratic Models of Growth in Mathematics Achievementa

Model a: Model b: Model c: Model d: Student Attributes GrowthCurve Prior Achievement Baseline Model

Level 2 explained variance 10.2% 17.0% 66.0% 68.4% Level 3 explained variance 44.5% 54.1% 82.7% 83.1%

Student mean: Hoj Base (Grade 10) 58.63** 62.56** 11.60** 14.12**

(0.64) (0.59) (0.91) (0.91) SES 4.15** 4.05** 1.21 ** 1.03**

(0.31) (0.30) (0.20) (0.1 9) Hispanic -4.79** -4.41 ** -1.10k* -1.01 *

(0.80) (0.77) (0.51) (0.49) Black -4.45** -4.21 ** -0.01 -0.09

(0.78) (0.75) (0.50) (0.48) Asian 4.94** 5.22** 2.90** 2.63**

(1.33) (1.28) (0.84) (0.81) Indian -4.34* -4.1 1 * -1.27 -1.10

(1.78) (1.72) (1.13) (1.09) Race-ethnicity missing -5.76** -4.24** -1 .63* -1 .60*

(1.09) (1.05) (0.70) (0.68) Female 1.07** 0.89* 0.05 0.00

(0.43) (1.05) (0.27) (0.26) Prior achievement 1.00* 0.94**

(0.02) (0.02) Transfer-leave 6.62** -0.25 -0.05 -0.05

(0.15) (0.16) (0.16) (0.17) Year 2.96** 0.44** 0.66**

(0.03) (0.16) (0.18) Prior achievement 0.05** 0-03**

(0.00) (0.00) Year2 -0.71** 0.08 0.06

(0.02) (0.12) (0.13) Prior achievement -0.02** -0.01 **

(0.00) (0.00) Level 0.1 9**

(0.05) Level missing 0.81 **

(0.1 9) No course taken -2.1 0**

(0.37) Basic junior high -1.52**

(0.18) Average junior high -1.99**

(0.20) High junior high -1.56**

(0.28) Prealgebra -1 .27**

(0.13) Geometry 1.39**

(0.15) Algebra 2 1.53**

(0.1 9) Trigonometry 3.88**

(0.33) Calculus 0.15

(1.11) Course missing -0.68

a Metric coefficients (standard errors). * p < .05, ** p < .01 (two-tailed tests).




Table 3. Quadratic Models of Growth in Science Achievementa

Model a: Model b: Model c: Model d: Student Growth Prior Baseline

Attributes Curve Achievement Model

Level 2 explained variance 9.6% 16.1% 63.6% 64.4% Level 3 explained variance 46.8% 57.8% 83.8% 83.5%

Student mean: foij5 Base (Grade 10) 58.46 61.54** 14.94** 15.25**

(0.63) (0.58) (0.94) (0.94) SES 4.11 ** 3.95** 1.03** 0.97**

(0.31) (0.30) (0.21) (0.21) Hispanic -5. 10** -4.78** -1.27* -1.25*

(0.80) (0.78) (0.53) (0.53) Black -5.01 ** -4.89** -0.70 -0.73

(0.78) (0.75) (0.52) (0.51) Asian 2.40 2.44 2.12* 2.00*

(1.34) (1.29) (0.87) (0.86) Indian -3.15 -2.99 -0.01 0.04

(1.81) (1.75) (1.19) (1.18) Race-ethnicity missing -4.87** -3.82** -1.78* -1.84*

(1.11) (1.07) (0.73) (0.73) Female -0.06 -0.71 1.00** 0.95*

(0.43) (0.42) (0.29) (0.28) Prior achievement 0.89** 0.88**

(0.02) (0.02) Transfer-leave 5.03** 0.20 0.22 0.25

(0.18) (0.19) (0.18) (0.18) Year 1.96** -1.24** -0.79**

(0.03) (0.17) (0.17) Prior achievement 0.06** 0.05**

(0.00) (0.00) Year2 -0.76** -1.76** -1.60**

(0.02) (0.13) (0.13) Prior achievement 0.02** 0.01 **

(0.00) (0.00) No course taken -1.32**

(0.21) Biology ? 39**

(0.14) Biology 2 0.83**

(0.32) Chemistry 2.13**

(0.23) Physics 3.49**

(0.39) Advanced 2.65**

(0.91) Course missing 0.70

(0.43)

a Metric coefficients (standard errors). * p < .05, ** p < .01 (two-tailed tests).




Table 4. Three-Level Analysis of Variance: Achievement Growth Model b

Fixed Effect Coefficient SE t-ratio

Mathematics Mean year 10, y0oo 14.400 .958 15.100 Growth rate, y1oo 0.510 .244 2.100

Prior achievement, Yilo 0.030 .003 7.970 Year2, 7200 -.230 .162 -1.420

Prior achievement, Yg210 -.008 .003 -3.090

Science Mean year 10, y000 15.290 .930 16.35 Growth rate, yl10 -.642 .244 -2.63

Prior achievement, yllo 0.041 .003 11.65 Year2, 7200 -1.630 .159 -10.24

Prior achievement, yg210 0.013 .002 5.048

Variance Random Effect Component df X2 p value

Level 1 Temporal variation, etij 1.00

Level 2 (students within departments)

Mathematics Student year 10 score, roij 42.80 2753 19669.56 <.0001 Student growth rate, r1ij fixed Student year2,r2ij fixed

Science Student year 10 score, rojj 48.20 2756 19710.00 <.0001 Student growth rate, r1 j fixed Student year2,r2ij fixed

Level 3 (between departments)

Mathematics Department mean, uooj 2.816 48 450.026 <.0001 Department mean growth, u1oj 1.08 48 1243.34 <.0001 Department mean year2, U20j 0.544 48 633.06 <.0001

Science Department mean, uooj 3.98 48 230.60 <.0001 Department mean growth, u1oj 1.22 48 11 33.52 <.0001 Department mean year2, u20j 0.26 48 398.10 <.0001




Figure 1. Average Achievement Growth in Mathematics and Science for High-, Average-, and Low-Performing Intake Students

Mathematics Growth Scence Growth

i .. , . .w % .v B. ., .. .. . ,. ., s' ,, fi~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~. .... .. 85.00 85.00

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controls for the components of the growth curve and for prior achievement, the effect of students' SES on the 1 Oth-grade score remains positive and significant for both mathematics and science (R = 1.03, p < .01, mathematics; R = 0.97, p < .01, science). Probably because of the control for prior achievement, differences at year 10 between white students and minority students and between males and females weaken substantially. The difference between blacks and Native Americans is no longer significant in either mathematics or science, although Hispanics and those with missing data for race-ethnicity still lag by 1 point (p < .05) in both subjects. The Asian advantage drops from 5 points to 3 points in mathematics, and the 2-point Asian science advantage becomes statistically significant. The female advantage in mathematics virtually disappears, although it emerges in science. This final student model explains 66.0 percent and 63.6 percent of student variation (Level 2 R2) and 82.7 percent and 83.8 percent of between-department variation (Level 3 R2) on the intercepts for mathematics and science, respectively.

For the most part, the contributions of the time-varying covariates that measure course content and ability level are significant when these covariates are introduced in Model d, adding or subtracting approximately 1 point each.7 This baseline model explains 68.4 percent and 64.4 percent of student variation

(Level 2 R2) and 83.1 percent and 83.5 percent of between-department variation (Level 3 R2) on the intercepts for mathematics and science, respectively.

Effects of Teachers' Instructional Practices Next we analyze the dimensions of individual teachers' instructional practices and their effects on the achievement growth of the students who were enrolled in the teachers' courses. The specific practices measured in LSAY range from those characteristic of teacher-centered instruction (e.g., time spent lecturing, time spent leading whole-class discussions, and time spent in science courses conducting demonstrations) and reliance on rote teaching (e.g., time spent on review, time spent teaching basic facts, and time given to seat work) to teaching for understanding or authentic teaching (e.g., stress on problem solving and time given to individual research projects). (See the Appendix for a description of these variables.)

Confronted by the diverse array of 70 practice items in LSAY, we looked for latent constructs that would provide a clear, eco- nomical picture of the pedagogical domain that these items measure. From these items, we were able to form three acceptable scales, on the basis of an initial latent factor analysis and subsequent Rasch model analysis (Wright



The Colleqial Focus and Hiqh School Students' Achievement 193

and Masters 1982).8 Two of these scales, one for mathematics and the other for science, contain items measuring teachers' efforts to enrich the standard curriculum. The third is composed of items that measure the science teachers' emphasis on teaching experimental methods and skills. Because these scales do not exhaust the core domain of instructional practice in either mathematics or science, we devote our analysis to the individual practices and use findings about one of the scales, Science Enrichment, as a convenient illustra- tion of our results.

Because our primary interest is in faculty social organizational influence on school production, rather than in the effectiveness of specific instructional techniques, we briefly summarize our findings about the effects of these practices on achievement. With controls for our array of student attributes and for course content and level, 54 out of the 70 practices (77 percent) had significant effects on growth: 42 significant positive effects (15 for mathematics and 27 for science, p < .05) and 12 negative significant effects (8 for mathematics and 4 for science, p < .05). On average, exposure to a teacher's practice affects 10-15 percent of a student's yearly achievement growth. For example, science enrichment is positive and significant and can improve students' scores, with effect sizes on the order of .22 (R = .09, p < .05).9 Because the science scores gained, on average, about two points each year, an effect size of this magnitude corresponds to about 10 percent of the annual science achievement growth. Other practices, such as time devoted to coverage, review, and introducing new materials, were also positive and significant (p < .05), with effect sizes on the order of Ito 3 of a point for both mathematics and science.

RESULTS: COLLEGIAL FOCI AND ACHIEVEMENT

Now we address our main questions: whether departmental collegial foci affect students' academic achievement growth and whether these effects result from their consequences for instructional practice. The evidence comes

from a series of models that add departmental variables to the baseline model. Table 5 describes these department-level measures.

Recall that collegial foci form through the interplay of individuals' activities at work, their interpersonal ties in the workplace, and agreement about norms and standards of practice. They are more likely to form under conditions of physical proximity than otherwise. Therefore, the most appropriate test of collegial focus effects on growth is through a multiplicative interaction term. In the case of high school departments, a three-way interaction term is adequate: the interaction of our department-level measures of the density of professional discussion relationships, the mean score on a given instructional practice, and the consistency with which the practice is used. Similarity of instructional activities and physical proximity are implicit because we are exploring the incidence of collegial foci among the teachers within subject-special- ized departments.

In this three-way interaction term, the level of interaction density indicates the probability of communication, collective problem solving, and monitoring. Multiplying by the mean of practice anchors this structural potential to specific content, that is, a specific instructional practice. Multiplying by the consistency score provides evidence that the content-specific structural potential has been realized in consistent use of the practice in the department.

The postulated effects of collegial foci on instruction and on achievement growth arise, to some degree, from both the pairwise and the threefold multiplicative relationships among interaction density, the practice mean, and consistency.10 Therefore, as our indicator of the presence of a significant focus effect on achievement growth, we use the comparative fit of two departmental (Level 3) models. One, which we call the no-focus model, is a linear model that includes terms for the main effects of density, the mean, and consistency. The other, the focus model, is a multiplicative model that includes as well terms for the two-way and three-way interactions of these variables. We use a multipara- meter test of the fit of each model and a likelihood ratio test that compares the difference




Table 5. Description of Department Variables

Variable Name Description

Department size (log) The natural logarithm of the number of department faculty. Grand-mean centered with original SD.

Expenditures per pupil Total expenditures per pupil, 1988-89. Grand-mean centered with SD of 1.

Urban A dummy variable for the school district, with 1 = urban.

Rural A dummy variable for the school district, with 1 = rural.

Density (D) For the departmental professional discussion network: the percentage of connected dyads out of the total possible dyads. Grand-mean centered.

Practice mean (M) Departmental mean of a given teaching practice.a Grand-mean centered.

Practice consistency (C) The reciprocal of the SD of the practice score distribution. Grand-mean centered.

D x M 2-way interaction of density and mean.

C x M 2-way interaction of consistency and mean.

D x C 2-way interaction of density and consistency.

D x M x C 3-way interaction of density, mean, and consistency.

aSee the Appendix for a description of the practice variables.

in the models' deviance scores to a chi-square distribution with four degrees of freedom (Bryk and Raudenbush 1992). A comparison in favor of the focus model is our indicator of a significant focus effect.

Our theory predicts that teachers in collegially focal departments, more often than others, use practices that are locally effective, use them consistently and with precision (as a result of collegial coaching and control), and do so in a context in which the practices of the entire faculty subgroup are also consistent and, therefore, are mutually reinforcing. Consequently, we expect a high proportion of the effects of collegial foci to be positive- either increasing the beneficial results of gen-

erally effective instructional practices for students' achievement growth or weakening or reversing the adverse consequences of practices that otherwise would retard growth.

Our findings accord with these expectations. Of the 70 specific practices that LSAY measured, 53 (76 percent) showed significant focus effects. Given the broad pedagogical spectrum that these practices cover, this percentage is striking. Although there are excep- tions, the trend of the focus effects is clear. The effect is likely to be positive, with a curvilinear form in which the growth curve accel- erates upward.

In Figure 2, the Science Enrichment scale illustrates this trend. The figure displays the




Figure 2. Science Enrichment Growth Curves: Comparing Focus and No-focus Models

Science Enrichment

3.50 . w......... . .. - -v__-------_. n. ................ .. ............. ..... .... . _............. . . .... ~b .A. .

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! v 1.00 G;rowth 0.5+ G .9o MEAN 0.5 * CONSISTENCY + 03* DENSITY .0.3 - (MEAN X DENSITY) - 0.4 * (MEAN X CONSISTENCY) -0.1 (CONSISTENCY X DENSISTY)

0.50 . + 0.2 (MEAN X CONSISTENCY X DENSITY)

O.OD F. -1, 4 1F 1. I. 2 -2 -1. -1.6 -1.4 -1.2 -1 -0.8 -0.6 -0.4 -0.2 0 0,2 0A 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Standard deviation change In all three main effects ........................................................................................................................................................................................................................................................

comparative predictive power of the focus and no-focus models. It plots the change in the growth curve that each model predicts. In this calculation, the values of the component variables of the interaction terms are expressed in standard deviation units of their main effects. To highlight the difference between the focus and no-focus models, in the figure we present the difference in the two models' estimates for a science department with scores on density, the practice mean, and consistency that were at least one standard deviation above the mean of the corresponding score distribution.

In Figure 2, the multiplicative focus model significantly improves predictive power (p < .001) by comparison with the linear no-focus model. In the no-focus model, a one standard deviation increase in each of the three main effects results in a 24 percent increase in the growth slope (from 2.07 to 2.55), while in the focus model, the same increase in the main effects produces a 46 percent increase in the growth slope (from 2.1 7 to 3.1 6). The no-focus model is conceptually incomplete and not as predictive because it is missing the multiplicative interaction terms that measure significant curvilinear effects.

The comparative predictive power of the focus and no-focus models can be shown fur-

ther by calculating the typical growth slopes that result when each of the three main effects (density, the practice mean, and consistency) is varied by either 1.0 or 1.5 standard deviation units. Continuing the Science Enrichment example, with a 1.0 standard deviation change in the main effects, the no- focus model predicts an average 8 percent increase in the growth curve, while the focus model predicts an average 20 percent increase. As the collegial focus strengthens, this difference becomes more pronounced. At the 1.5 standard deviation criterion, the linear no-focus model predicts only an average 12 percent increase in growth, while the multiplicative focus model produces a substantially larger average increase of 41 percent, indicating an intensification of instructional effectiveness associated with departmental collegial foci.

Now consider Table 6, which extends this comparison of typical growth slopes to a sub- set of 31 of the specific teaching practices that LSAY measured. These practices are those with significant positive effects on the growth slope that were significantly strengthened (according to our comparative-fit criterion) by the presence of a departmental collegial focus. Thirteen of these practices are in mathematics, and 18 are in science. This table, like




Table 6. Intensification Effects for Individually Positive Practices (Average Changes in Achievement Growth Curves) by Changes in the Main Effects of Density, Practice Mean, and Consistency

Mathematics Science

Amount of Increase in Each Main Effect Focus No Focus Focus No Focus

1.0 standard deviation 20% 8% 27% 17%

1.5 standard deviations 41% 12% 50% 25%

the Science Enrichment example, shows the greater predictive power of the focus model. The no-focus model substantially underesti- mates the growth associated with collegially focal departments (i.e., departments at or above the 1.5 standard deviation criterion).

The differences between the two models are striking because any effect that changes a growth slope alters a student's entire achievement trajectory. In this way, the effect of consistent departmental practice cumulates over time, so that over four years, a student benefits from collegially focused instructional practice. If, as seems likely, collegial foci have rea- sonably pervasive effects on the instructional practices of a departmental faculty, then these cumulative growth benefits will add up impressively. These results indicate the positive consequences for achievement growth of a high rate of collegial interaction when it reinforces consistent practice.

Now consider the full set of comparisons between the focus and no-focus models of effects on the growth slope. For the Science Enrichment scale and each of the 70 LSAY mathematics and science practice measures, Table 7 presents the pertinent parameter estimates for the two models. In addition to the variables shown in Table 7, these models include controls for department size and for the school's urbanicity and expenditures per pupil. Of the 58 individual practices that dis- played significant positive effects on achievement growth, the growth effects of 29 were boosted by the presence of a departmental collegial focus. (For mathematics, these practices were subject applications, seat work, discussing television, leading discussions, dis-

cussing magazines, basic facts and principles, business applications, supplementary materials, increasing awareness, homework assigned, textbook coverage, and small- group work. For science they were teaching applications, discussing inventions, written reports, explain reasoning, women in science, lecturing, review, observation skills, returning homework, lab techniques, testing, prepare for further study, science biographies, environmental issues, discussing careers, presenting new material, and increasing interest.) In addition, of the 14 practices with negative main effects on growth, 7 were substantially weakened, and the negative main effects were offset, for the most part, by a positive focus effect. (For mathematics, the practices were discussing careers, returning homework, and classroom discipline. For science, they were seat work, discussing television, basic facts and principles, and textbook coverage.)

Although our data do not allow us to measure directly the mechanisms that we posited to account for the intensification effect of collegial foci, some conjectural interpretations may let us infer their action. The coefficients in Table 7 suggest that the observed intensifying focus effects (measured by comparing the focus and no-focus models) were strongly influenced by the interaction of the density of discussion relationships and the consistency of the practices used in the collegially focal departments. This result suggests that cumulative exposure to collegially consistent, supported, and monitored practice may have been the central mechanism involved in the reinforcement of effective instructional techniques. More speculative still, this consistency of practice among the mem-




Table 7. Focus Models of Achievement Growth

Practice Effect on Mean Consistency Density Focus Terms AchievementGrowth (M) (C) (D) D x M C x M C x D D x C x M

Positive with Positive Focus Effect

Mathematics Subject applications 0.23 *** -0.04 0.11 **

1 .04*** 0.16 1.21 *** -0.64*** -0.21 ** -0.32** 0.20**

Subject awareness -0.05+ 0.1 7*** 0.09* -0.42*** -0.41 *** 0.20* -0.06 0.30*** 0.04 -0.01

Business applications 0.1 2*** -0.01 0.1 2*** 0.66*** 1.23*** 0.89*** -0.40*** -0.59*** -0.77*** 0.35***

Leading discussions 0.21 *** -0.08** 0.1 0*** 1 .29*** 1 .95*** 0.51 ** -0.28*** -1.1 8*** -0.77*** 0.46***

Mathematics enrichment 0.22*** -0.1 8*** 0.08** -0.02 -0.90** 0.14 -0.03 0.1 8** 0.03 0.01

Basic facts and -0.32*** 0.55*** -0.03 principles -0.35** 1.18 ** -0.22 0.01 -0.26** -0.12 0.07

Small-group work 0.1 6*** 0.1 2*** 0.08* 0.49*** 0.52** 0.98*** -0.33*** -0.1 5* -0.38*** 0.1 4***

Discussing magazines 0.24*** -0.06* 0.03 -0.01 ** -0.53** -0.35 0.06** 0.08 0.1 9*** 0.00

Seat work 0.1 3*** -0.09** 0.11 *** 0.01 -0.72*** -0.86*** 0.1 6** -0.08 0.39*** 0.01

Supplementary materials -0.03 -0.04 0.11 *** 0.14 0.83*** 0.68*** -0.1 6** -0.33*** -0.53*** 0.1 9***

Discussing television 0.30*** -0.26*** -0.06+ 1 .04*** 0.03 -0.83*** -0.03 -0.51 *** 0.15+ 0.11 ***

Homework assigned 0.1 9*** 0.02 0.11 *** 1 .72*** 1 .46*** 1 .68*** -0.71 *** -0.77*** -0.73*** 0.37***

Textbook coverage 0.1 2*** -0.1 8*** 0.1 1 *** 0.34*** 0.68*** 0.84*** -0.26*** -0.26*** -0.62*** 0.22***

Science Teaching applications 0.1 7*** 0.20*** 0.1 4***

-1.61 *** -0.87+ -2.03*** 0.65*** 0.13 0.50*** -0.10 Science biographies 0.01 0.01 0.09**

-1.24*** 0.01 -0.70*** 0.45*** 0.04 0.02+ -0.04 Environmental issues -0.02 0.25*** 0.09**

-1.1 6*** -1.1 7** -0.30+ 0.21 ** 0.76*** 0.25* -0.1 4** Explain reasoning 0.34*** 0.27*** 0.1 5***

0.72** 0.35 -0.13 -0.05 -0.23 + 0.08 0.03 Science enrichment 0.00 0.39*** 0.11 ***

0.94** 0.53+ 0.27 -0.31 ** -0.42** -0.06 0.1 5** Prepare for further

study 0.02 0.1 1*** 0.10** -0.55** 0.65* 0.22+ 0.00 -0.27* -0.35*** 0.1 9***

Increasing interest 0.24*** 0.09** 0.05 -2.48*** -1 .33*** -1.1 2*** 0.69*** 0.92*** 0.36*** -0.22***

Discussing inventions 0.02 0.30*** 0.1 7*** 0.87** 0.39 0.36 -0.26** -0.30** -0.02 0.11 **

Lab techniques 0.18*** 0.00 0.08* 2.57*** 2.95*** 1.66*** -0.86*** -1.50*** -0.99*** 0.52***

Lecturing -0.1 2*** 0.36*** 0.03 0.63+ 0.46 0.36 -0.29* -0.29 -0.08 0.11 +

Observation skills 0.38*** -0.7* 0.10Q** 0.05 -1.59** -0.09 0.00 0.53* 0.27+ -0.08




Table 7 (continued)


Returning homework 0.29*** 0.01 0.00 -0.97*** 0.51 -1 .08*** 0.48*** 0.28 0.15 -0.10

Written reports 0.03 0.1 5*** 0.11 *** 0.64* -0.14 0.27 -0.24** -0.17 0.05 0.09*

Review 0.15*** 0.18*** 0.11 *** 1 .95*** 1.71 *** 1.1 2*** -0.63*** -1 .04*** -0.57*** 0.40***

Women in science 0.07* -0.02 0.1 0** -1 .58*** -1 .67*** -2.06*** 0.74*** 0.41 ** 0.71 *** -0.21 ***

Testing -0.02 0.1 9** 0.1 4*** 1 .27*** 0.40 0.99*** -0.51 *** -0.02 -0.21 * 0.1 0*

Presenting new material -0.04 0.23*** 0.1 0** 1 .89*** 2.94*** 1.41 *** -0.52*** -1 .07*** -0.74*** 0.29***

Discussing careers 0.02 0.1 4*** 0.11** 2.72*** 1 .46*** 1 .35*** -0.84*** -1.1 2** -0.42*** 0.34***

Negative with Positive Focus Effect

Mathematics Discussing careers 0.09*** -0.32*** 0.1 0***

-1.1 8*** -1 .56*** -1 .54*** 0.59*** 0.47*** 0.59*** -0.1 9*** Classroom discipline -0.25*** -.0.25*** 0.1 5***

-0.17 -0.25+ 0.07 -0.1 8* -0.29** -0.07 0.23*** Returning homework 0.1 5*** -0.26*** 0.06+

0.22 -0.23 0.42* -0.1 4* 0.00 -0.18 0.06+

Science Textbook coverage -0.1 7*** 0.05 0.07+

-1 .09*** -0.56 -0.48* 0.26** 0.25 0.14 -0.06 Seat work -0.32*** 0.1 8*** 0.01 ***

-2.73*** -1 .98*** -1 .66*** 0.79*** 0.98*** 0.71 *** -0.32*** Basic facts and

principles -0.61 *** 0.21 *** -0.01 -0.66* 0.23 -0.19 0.00 -0.05 -0.01 0.02

Discussing television -0.1 5*** -0.09* 0.05 0.00 -0.19 0.21 -0.11 0.05 0.01 0.02

Positive with Focus Not Significant

Mathematics Prepare for further study 0.1 2** -0.01 0.1 0**

-0.02 -0.17 -0.21 * 0.1 4** 0.06 0.20+ -0.08*

Presenting new material 0.02 0.06* 0.09** -1 .04*** -1.11 *** -1.21 *** 0.59*** 0.53*** 0.61 *** -0.29***

Increasing interest 0.1 2*** 0.00 0.1 0*** -1.1 0*** -1 .45*** -0.76*** 0.46*** 0.72*** 0.44* -0.24***

Using computers 0.06 0.33*** 0.07* -0.68*** -0.47*** -0.63*** 0.35*** 0.48*** 0.39*** -0.22***

Review 0.1 5*** 0.04 0.1 3*** 0.55*** -0.20 0.79*** -0.41*** 0.12 -0.07 0.05

Science Homework assigned 0.09+ 0.08 0.09**

1 .90*** 0.81 *** 0.78*** -0.47*** -0.55*** -0.1 6** 0.1 3**




Table 7 (continued)

Practice Effect on Mean Consistency Density Focus Terms AchievementGrowth (M) (C) (D) DxM CxM CxD DxCxM

Demonstrating experiments 0.08** 0.30*** 0.1 8***

1.1 7*** 0.86* 0.44* -0.27** -0.45** -0.1 0*** 0.11 ** Student experiments -0.1 5*** 0.42*** 0.1 4***

1.25** 0.44 0.77* -0.42*** -0.20 -0.02 0.07 Science experiments 0.32*** 0.47*** 0.11 **

0.69+ -0.04 -0.26 -0.02 0.05 0.26** -0.05 Small-group work 0.1 6*** 0.05 0.08*

-1.50*** -1.50*** -1.29*** 0.77*** 0.83*** 0.74*** -0.40*** Use teaching machines 0.50*** 0.51 *** 0.05

0.46+ 0.77** 0.31+ 0.01 0.44 -0.08 -0.15+ Discussing magazines -0.1 5*** 0.24*** 0.07*

-0.38 -1.06* -0.22 0.07 0.43* 0.39** -0.1 2*

Oral reports 0.20*** 0.11 ** 0.08* -2.39** -2.85*** -1 .88*** 0.90*** 1.31 *** 0.95*** -0.44***

Science projects 0.05 -0.11** 0.1 0** -0.04 -0.12 -0.03 0.08 0.11 0.07 -0.07

Supplementary materials 0.1 0** 0.21*** 0.09** -0.30 -0.42 -0.29+ 0.12 0.18 0.1 7* -0.05

Scientific writing 0.48*** 0.55*** 0.1 0** -0.13 -0.63* -0.30 0.1 5* 0.65*** 0.31 *** -0.1 6***

Individualized instruction -0.08* 0.06+ 0.09**

-3.21 *** -3.81 *** -1 .84*** 0.80*** 1 .90*** 0.97*** -0.47*** Correcting homework -0.43*** 0.43*** 0.07*

-0.63* 4.52*** 0.47** 0.08 -0.89*** -0.92*** 0.1 9** Experiment reports 0.1 6*** 0.1 2*** 0.04

0.97* 0.74* 0.60** -0.30* -0.20 -0.23* 0.09 Problem solving 0.1 7*** 0.06+ 0.1 0**

0.39 -0.33 0.57 * -0.17 0.17 -0.02 0.00

Positive with Negative Focus Effect

Mathematics Correcting homework -0.04 0.03 0.1 0**

-0.28* -0.66** 0.01 0.10+ 0.33*** 0.33*** -0.1 5*** Lecturing 0.11 *** -0.14*** 0.11 ***

-1.59*** -2.65*** -1.54*** 0.70*** 1.08*** 1.1 6*** -0.50*** Problem solving 0.04 0.1 6*** 0.09**

-0.20 -1 .47*** -0.28 0.00 0.43*** 0.50*** -0.1 3*** Science Subject awareness -0.1 3*** 0.08* 0.1 0**

-0.92** -1.00** -0.08 0.27* 0.89*** 0.35*** -0.29*** Using computers 0.25*** -0.05 0.06+

0.40 -0.38 0.84*** -0.02 1 .00*** 0.15 -0.35*** Leading discussions 0.08* 0.25*** 0.02

-0.62* -1.50** -0.68*** 0.25** 0.57** 0.62*** -0.21 ***

Showing films -0.1 5*** 0.1 3** 0.06 -0.99*** -0.24 -0.14 0.26** 0.49** 0.10 -0.1 5**

Discussing current issues -0.01 0.1 4*** 0.11 ***

1 .29*** 1 .89*** 1 .04*** -0.38*** -0.61 ** -0.50** 0.1 7**




Table 7 (continued)


Negative with Negative Focus Effect

Mathematics Skills and computation -0.29*** -0.1 3*** 0.1 6***

-1.20*** -0.21 -1 .31 *** 0.75*** 0.12+ 0.35*** -0.20*** Individualized instruction -0.02 -0.28*** 0.1 2***

0.15 -0.54* 0.58** -0.1 8* 0.12 -0.01 0.01 Use teaching machines -0.27*** 0.02 0.1 4***

-1 .47*** -0.69*** -0.80*** 0.51 *** -0.30 0.31 *** -0.02 Daily routines -0.34*** -0.09+ 0.1 6***

-0.23 -0.20 0.28 -0.06 0.08 0.06 -0.05 Testing -0.23*** -0.1 6*** 0.1 0***

-1 .29*** -1.1 9*** -1 .00*** 0.52*** 0.53*** 0.49*** -0.26***

Science Classroom discipline -0.25*** -0.08 0.11 ***

2.89*** 2.50*** 2.25*** -0.96*** -0.83*** -0.76*** 0.28*** Daily routines -0.25*** 0.06 0.1 5***

1 .59*** 1 .58*** 1 .38*** -0.55*** -0.54** -0.41 *** 0.1 5***

*p < .05, ** p < .01,*** p < .001, + p < .10.

bers of collegially focal departments may have been reinforced by trust that one's own practices aligned with those of colleagues, particularly when the practice or practices were likely to induce students' resistance.

Our theory also predicts that interference will result in negative effects of collegial foci. When interference occurs, a practice, whatever its own instructional benefits may be, draws on students' time, effort, or motivation in a way that adversely affects the time, effort, and motivation available for other beneficial instructional activities. Our findings reveal negative focus effects for 8 of the 60 practices that had positive main effects on achievement growth. Here, the overall result was to weaken the growth benefit conferred by the practice, a pattern consistent with interference. In three of these instances, the negative focus effect was a consequence particularly of the negative interaction of density and the practice score mean. This finding is consistent with departmental overemphasis on the practice-a general tendency toward its use by departmental members, reinforced by collegial interaction. This interpretation is particularly plausible for mathematics departments that emphasized instruction in mathematical problem solving and for science departments

that relied heavily on discussion. In each case, students may have been diverted from other activities, like listening to lectures or performing experiments, which, as our evidence shows, also promoted achievement growth.

However, these results are ambiguous. The dense interaction associated with these adverse focus effects may indicate an active departmental response to an instructional problem-the apparent ineffectiveness of a supposedly effective method. Moreover, at least some of the observed dampening effects of collegial foci on generally effective practices may reflect tensions between the occu- pationally normative and the locally effective and the efforts of collegially focal departments to resolve these tensions. For example, teaching students the higher-order mental skills involved in mathematical or scientific problem solving and teaching by discussion are certainly among those instructional practices that are currently espoused by leading specialists and organizations in both mathematics and science education. Nevertheless, what is normative in a teaching field need not translate readily into a locally effective practice in a particular school.

Seven additional practices had negative main effects on achievement growth that




were intensified by the presence of a departmental collegial focus. Here, we may be observing the results of error or conservatism, probably reinforced by cumulative exposure. Members of collegial foci are not inerrant problem solvers. In some instances, members of collegially focal departments may mistake the parameters of the local situation and then situate their erroneous solutions within the local culture of practice. Others may adhere strongly to practices that are normative in the teaching field, but are not locally effective. In such instances, collectively consistent use and strong collegial support and monitoring would intensify adverse effects on achievement growth (as, perhaps in the instances of the use of personal computers or other com- puting equipment in mathematics classes). In other situations, collegially focal departments may cling to outmoded, no longer effective, but traditionally used practices, forming something like cohesive "defended pedagogical communities" (cf. Suttles 1972). It is interesting that of the seven practices in Table 7 for which negative main effects are intensified by collegial foci, four are those in which the focus effect can be attributed most strongly to the negative interaction of discussion density and the practice mean. Intuitively, one would expect to find this pattern in such defended communities.

CONCLUSION

Our results support the theoretical stance that we have taken. When the mathematics and science departments of the LSAY high schools formed collegial foci, the effects of instructional practice on students' achievement growth were intensified. These findings are consistent with our characterization of collegially focal departments, and collegial foci more generally, as problem-solving communities. They underscore Podolny and Baron's (1997) emphasis on the importance of strong ties in the workplace, which ease the flow of information, provide collective ability to respond quickly and flexibly when problems of practice occur, and create the capacity to ensure consistent performance throughout a work group. The problem-solving communi-

ties that we have identified formed within teaching fields, so that they evidently were communities of cospecialists. They also centered on specific teaching methods, so that they evidently were communities of shared professional belief and practice. However, in the absence of direct measures of interaction in more and less collegially focal departments, this interpretation remains inferential.

Our findings suggest that collegial foci produce intensification effects at least as much by virtue of the consistency with which their members collectively use preferred teaching practices as by virtue of efficient problem solving. Nonetheless, because our findings do not reveal the specific mechanisms involved, we cannot evaluate the way various of the mechanisms that we have posited acted, singly or in combination, to affect students' achievement-departmental members' identification with the departmental subgroup, the reinforcement of practice by trust that all would engage in the same practice or practices, shared knowledge of what colleagues were doing in their classes, interpersonal support for the use of a preferred practice, and external sanctioning in dense networks of strong ties.

Intensification effects may be particularly strong when the members of a collegially focal department fix on and then consistently use clusters of complementary teaching practices.11 In our original analysis, using the entire teacher sample, the teaching practice items did not have strong dimensionality. However, in a further exploratory analysis, we found that for teachers in the collegially focal departments, the practice items could be reduced to a small number of statistically acceptable scales. This finding encouraged us to explore the possibility that problem solving in collegial foci involves assessing the local effectiveness of suites of teaching practices- that is, the possibility that local cultures of teaching practice center on coherent pedagogical approaches that entail complementary or reinforcing sets of classroom techniques.

We also have preliminary evidence that the stronger effect of collegially focal departments is on the consistency of instructional practice between teachers, not on the consistency with



202 _ Yasumoto, Uekawa, and Bidwell

which teachers individually use instructional methods from day to day or course to course. That is, it appears that the principal effect of collegial focus on achievement growth is direct, rather than indirect via the teaching practices of individual teachers. We found that the parameter estimates for the focus terms are little altered when measures of individual teacher practices enter our growth models. Perhaps, then, the social control of instruction in the collegial foci of schools has two chief facets: (1) efficient problem solving and (2) the capacity to maintain agreement about ways to teach and then to sustain a high level of compliance with consensually validated practice norms and standards. In this way, informal relationships among faculty colleagues may compensate when the segmental division of instructional labor weakens the formal coordination of teachers' work.

We have stressed the importance of the strong ties that characterize collegial foci. When faculty subgroups differentiate so that strong ties cluster within common domains of work, for example, by differentiating along departmental lines, there should be beneficial effects for the entire organization. Problem solving in such structures is likely neither to disrupt work routines elsewhere nor to dis- play the slow response that often accompa- nies problem solving in relatively large or diverse work groups. Nevertheless, subgroup- specific adaptations may be contradictory in ways that weaken the pedagogical effectiveness of an entire faculty-for example, a highly punitive approach to enforcing academic standards in Department X that alienates students so that they do not respond to more supportive forms of teaching in Department Y. In addition, as we have noted, once local cultures of practice institutionalize, they may inhibit responses to emerging problems, becoming sources of rigidity rather than adaptation. In situations like these, boundary- spanning ties, although they are likely to be weaker than those within subgroups, may be important and well worth study to the extent that they provide for communication, coordination, and brokering of conflicts over practice between subgroups.

Our findings should encourage further studies of the conditions under which colle-

gial foci emerge and stabilize. In addition to dimensions of the division of labor, including the intensity of faculty specialization (e.g., according to department or grade level), both faculty size and the frequency and severity with which new teaching problems appear should be considered. Presumably, the relationship between size and the incidence of collegial foci is linear, with small faculties as a whole as potential foci, while the likelihood that collegial foci will emerge at the subgroup level increases as faculties get larger. The relationship between the severity and frequency of a problem and the appearance and stabi- lization of collegial foci may be curvilinear. If groups of teachers experience success in solving a difficult problem, this experience may form the core of a local culture of practice that resists change and provide the basis for the corresponding cohesion of the group as collegially focal. At the same time, frequent and severe problems may create a situation that is sufficiently daunting to discourage collective problem solving and retard the forma- tion of collegial foci.

The relationship between incentives for collaboration with colleagues and both the incidence of collegial foci and their tendency to form within faculty specialties should also be investigated. For example, according to Coleman (1997), feedback loops in public schools that connect outputs of students' achievement with consequences for teachers, either individually or collectively, are typically long and unresponsive. If this characterization is correct, it should be no surprise that collegial foci tend to be concentrated among faculty subgroups composed of departmental colleagues or teachers of the same school grade. Coleman proposed various incentive systems intended to create shorter, more responsive feedback loops, thereby inducing school-level collaboration. Incentive systems similar to those that Coleman proposed are now beginning to appear in public education, perhaps creating an opportunity to analyze relationships between these systems and the tendency for collegial foci either to repro- duce or to cross-cut the formal differentiation of teachers' roles.

Our theoretical argument employs a number of key constructs that remained unmea-




sured in the present study, in particular, local cultures of practice, problem-diagnosing and problem-solving interaction, and intensification mechanisms. Further research on collegial foci should be designed to permit more direct measurement of central constructs like local cultures of practice, problem solving, and intensification mechanisms, especially through case studies of theoretically exem- plary settings. The relationship between the formal division of faculty labor (e.g., levels of specialization and interdependence) and informal collegial structures like those we have explored also calls for further inquiry. Clearly, our study, coupled with the literature on high school departments, suggests the inadequacy of inferring from the formally segmental division of faculty labor that collegial social structures and collegial control over teachers' work have little significance for understanding how schooling affects students' achievement. Our research points to significant social organizational mechanisms through which teachers' work may be ordered and controlled.

NOTES

1. Their treatment of the collegial focus and its consequences for practice is similar to Podolny and Baron's (1997) more general discussion of relationships among strong ties, interaction content, and expectations for role performance in the workplace.

2. Compare Siskin's (1994:180-81) argument that when high school departments (or subgroups within departments) develop structural cohesion, it is likely to center on the pedagogical values and norms of the teaching field, hence their "ethnocentrism."

3. See the LSAY codebook (Miller, Suchner, Hoffer, Brown, and Pifer 1991:46-77) for a discussion of the use of IRT.

4. We used these retrospective data on discussion networks on the assumption that such networks are stable. In their earlier study of teachers' networks, Bidwell and Yasumoto (1999) found that teachers' discussion networks are highly stable over a several years' period. The stability of networks should be enhanced when faculties themselves are sta-

ble. In the 52-school LSAY sample, the average tenure of members of 26 of the mathematics departments and 27 of the science departments was at least 10 years, with 10 years the modal average for the mathematics departments and 12 years the modal average for the science departments. We also assumed that teachers' instructional practices are relatively stable.

5. Although our analysis is specific to the four years of high school, to lengthen and anchor the growth curves, we calculated the growth curves using the test scores for grades 8-12. This procedure had no substantive implications for our findings.

6. An analysis not reported here provided some evidence of a ceiling effect for mathematics scores. However, we found that the top 5 percent of students show less diminishing growth than do average students. Hence, we inferred the absence of a severe ceiling effect. Furthermore, because the highest students show a consistently positive growth curve for science, we concluded that there is no ceiling effect for science.

7. Algebra taken in grade 12, as opposed to the typical 1 Oth-grade enrollment, is a sig- nal of comparatively low ability or motivation. Therefore, we tested for year-by-course type interactions. We did not find any significant interactions and decided that we could parsi- moniously use ability level for mathematics instead. Moving two ability levels adds or subtracts around .40 points in mathematics growth (R = .19, p < .01). For science, we used a separate advanced chemistry or physics dummy variable to indicate ability level.

8. Ideally, scale construction proceeds from conceptualizing what is to be measured to creating questions that measure the construct to empirical confirmation in the collected data. The LSAY data were not original- ly collected for our purposes, so we started by using factor and principal component analysis to explore the correlations among the questionnaire items about teaching practices.

9. The effect size is the coefficient multi- plied by a predictor two standard deviations above the mean of its distribution. Following convention, we contrast the difference between subjects who are one standard devi-




ation above the mean with those who are one standard deviation below the mean for the effect. Cohen (1990) and Rosenthal (1990) both advocated the use of effect sizes that allow an effect to be measured in standard- ized units.

10. The focus effects on the intercept are

interesting because they can reveal relationships between the incidence of collegial foci and achievement. However, to highlight our principal findings, we do not discuss the results for the intercept.

11. We are grateful to Robert Dreeben for suggesting this possibility.

APPENDIX

Description of Practice Variables

Mathematics Practices

Subject applications Teach applications of the subject in science: What emphasis?a

Homework assigned How many hours of homework did you assign for this class in a typical week?b

Subject awareness Increase awareness of importance of the subject in daily life: What emphasis?

Business applications Learning about applications of mathematics in business and industry: What emphasis?

Discussing careers Discuss career opportunities in scientific and techno- logical fields: How often?C

Correcting homework What percentage of homework assignments did you correct and return to students?

Textbook coverage What percentage of the textbook will you cover this year?

Leading discussions Leading discussions: How much time?

Classroom discipline Getting students to behave: percentage of class time

Skills and computation Develop skills and computation techniques: What emphasis?

Mathematics enrichment Rasch score (of discussing television, discussing careers, subject applications, business applications, subject awareness, increasing interest, discussing magazines, supplementary materials)

Basic facts and principles Teach math facts and principles: What emphasis?

Prepare for further study Prepare students for further study in the subject: What emphasis?

Small-group work Students work in small groups or laboratory: How much time?

Individualized instruction Providing individualized discussion: How much time?




Increasing interest Increase students' interest in mathematics: What emphasis?

Lecturing Lecturing to the class: How much time?

Use teaching machines Having students use teaching machines or computer- assisted instruction

Discussing magazines Discuss current magazine articles or books related to the subject: How often?

Presenting new material Presenting new material: percentage of class time

Returning homework What percentage of the homework assignments do you correct and return to students?

Review Review or students' practice of skills: percentage of class time

Daily routines Daily routines (setting up, cleaning up, passing out materials, taking attendance): percentage of class time

Seat work Having students do seat work on homework, work- book, or text assignment: How much time?

Problem solving Develop problem-solving/inquiry skills: What emphasis?

Supplementary materials Have students read supplementary materials: How often?

Discussing television Discuss television programs about the subject: How often?

Testing Testing or other forms of evaluation: percentage of class time

Using computers Use computers: How often?

Science Practices

Teaching applications Teach applications of the subject in science: What emphasis?

Homework assigned How many hours of homework did you assign for this class in a typical week?: Hours

Subject awareness Increase awareness of importance of the subject in daily life: What emphasis?

Science biographies Learning biographies of the subject: What emphasis?

Discussing careers Discuss career opportunities in scientific and techno- logical fields: How often?

Correcting homework What percentage of homework assignments did you correct and return to students?

Using computers Use computers: How often?




Textbook coverage What percentage of the textbook will you cover this year?

Demonstrating experiments Demonstrate an experiment or lead students in systematic observation of class: How often?

Leading discussions Leading discussions: How much time?

Classroom discipline Getting students to behave: percentage of class time.

Environmental issues Learning about applications of science to environmental issues: What emphasis?

Student experiments Have students do an experiment or systematic observation class: How often?

Explain reasoning Have students explain the reasoning they used to arrive at an answer: How often?

Experiment reports Require students to turn in written reports on experiments or systematic observation.

Science experiments Rasch score (of explain reasoning, lab techniques, problem solving, scientific writing, demonstrating experiments, student experiments, experiment reports, small-group work, observation skills)

Basic facts and principles Teach math facts and principles: What emphasis?

Showing films Show films, filmstrips, or videotapes: How often?

Prepare for further study Prepare students for further study in the subject: What emphasis?

Small-group work Students work in small groups or laboratory: How much time?

Individualized instruction Providing individualized discussion: How much time?

Increasing interest Increase students' interest in mathematics: What emphasis?

Discussing inventions Discuss political debates over new inventions and technologies: How often?

Discussing current issues Discuss current issues and events in the subject: How often?

Lab techniques Develop skills in lab techniques: What emphasis?

Lecturing Lecturing to the class: How much time?

Use teaching machines Having students use teaching machines or computer- assisted instruction: How much time?

Discussing magazines Discuss current magazine articles or books related to the subject: How often?

Presenting new material Presenting new material: percentage of class time

Observation skills Develop systematic observation skills: What emphasis?




Oral reports Have students give oral reports: How often?

Science projects Have students independently design and conduct their own science projects: How often?

Returning homework What percentage of the homework assignments do you correct and return to students?

Written reports Require written reports on outside readings: How often?

Review Review or students' practice of skills: percentage of class time

Daily routines Daily routines (setting up, cleaning up passing out materials, taking attendance): percentage of class time

Seat work Having students do seat work on homework, work- book, or text assignment: How much time?

Problem solving Develop problem-solving/inquiry skills: What emphasis?

Supplementary materials Have students read supplementary materials: How often?

Women in science Learning about women in science: What emphasis?

Scientific writing Develop scientific writing skills: What emphasis?

Discussing television Discuss television programs about the subject: How often?

Testing Testing or other forms of evaluation: percentage of class time

Science enrichment Rasch score (based on subject awareness, environmental issues, discussing careers, discussing current issues, discussing inventions, discussing magazines, discussing television, supplementary materials)

a This item and similar items asked for the usual emphasis given to the practice: none, minor, moderate, major.

bThis item and similar items asked for the actual number of hours usually given to the practice.

CThis item and similar items asked for the usual frequency of the practice: daily, almost every day, once a week, once a month, very rarely, never.




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Jeffrey Y. Yasumoto, MA, is a doctoral student, Department of Sociology, University of Chicago. His main fields of interest are organizations and social networks. He is currently coauthoring a book on how teachers' networks affect students' achievement.

Kazuaki Uekawa, Ph.D., is Research Associate, David C. Anchin Center and the College of Education, University of South Florida, Tampa. His main fields of interest are social stratification and social networks. He is currently conducting a comparison of national educational systems in terms of stratification mechanisms and analyses of adolescents' behavioral problems from social network and cross-cultural perspectives.

Charles E. Bidwell, Ph.D., is William Claude Reavis Professor Emeritus of Sociology and Education, University of Chicago. His main fields of interest are sociology of educational organization and education in the life course. He is currently conducting an analysis of the relationships between high school social organization and school production, in collaboration with Anthony Bryk, Kenneth Frank, Jeffrey Yasumoto, and Kazuaki Uekawa.

Grant SES-8803225 from the National Science Foundation, and grants from the Spencer Foundation and the University of Chicago School Mathematics Research Fund supported this research. The authors alone are responsible for the article's contents. The authors are especially grateful for the ideas and criticism of Anthony Bryk, Kenneth Frank, Daniel McFarland, Barbara Schneider, Susan Stodolsky, Yeow Meng Thum, Zalman Usiskin, and members of the Sociology of Education Brown Bag and Social Organization of Competition Workshops at the University of Chicago. Address all correspondence to Jeffrey Yasumoto, Department of Sociology, University of Chicago, 1126 East 59th Street, Chicago, IL 60637; e-mail: [email protected].



the collegial focus and high school students' achievement

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