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Examining Connections Between Teacher Perceptions of Collaboration, Differentiated Instruction, and Teacher Efficacy


by Yvonne L. Goddard & Minjung Kim - 2018

Background/Context: Teacher collaboration, instructional practices, and efficacy are linked in various ways in the literature. For example, in schools where teachers reported greater use of differentiated instruction, team collaboration and culture were reportedly higher (Smit & Humpert, 2012). Further, teachers’ instructional mastery experiences lead to higher efficacy (Tschannen-Moran & McMaster, 2009). Tomlinson (1995) suggests that getting teachers to continue using differentiated instruction requires those teachers to experience quick success (i.e., mastery experiences that lead to increased efficacy). Bruce, Esmonde, Ross, Dookie, and Beatty (2010) found that teachers with high efficacy were more likely to try challenging instructional approaches that required taking risks in their classrooms and to use assessments. Based on our literature review, we hypothesized that teachers’ reports of their collaborative practices would be related to their teaching efficacy when mediated by their reported differentiated instruction use.

Purpose: The purpose of this study was to examine connections between teachers’ perceptions of their collaboration, their reported use of differentiated instruction (a particular instructional practice), and teacher efficacy in high-poverty rural schools in a Midwestern state.

Participants: Survey, demographic, and assessment data were collected for 95 elementary schools, 1,623 elementary teachers, and 4,167 students in rural high-poverty areas located in the northern regions of a Midwestern state.

Research Design: Data from the first year of a large-scale, longitudinal randomized control trial designed to evaluate the effects of a leadership training program were used for this study.

Data Collection and Analysis: Survey data containing collaboration, differentiated instruction, and teacher efficacy scales were collected from teachers during regularly scheduled faculty meetings. Demographic and achievement data were collected from a state accountability data system. We employed multilevel structural equation modeling (MSEM) to analyze our data, allowing us to take into account the nested structure of the data (i.e., teachers’ responses nested within schools).

Results: After controlling for school- and student-level characteristics, we found positive, statistically significant connections between teacher collaboration and teachers’ reports that they differentiated instruction (β =.43, p<.001) and between differentiated instruction and teacher efficacy (β =.38, p<.001).

Conclusions: The results are potentially significant for researchers and practitioners interested in approaches to improving teacher practices and strengthening efficacy beliefs. Our outcomes demonstrate the importance of teachers’ collaborative work around school improvement, curriculum and instruction, and professional development. Further, our work extends what is known about sources of teacher efficacy. Theoretically, via mastery experiences gained through collaboration and reports of using differentiated instruction in their classrooms, teachers’ efficacy beliefs were strengthened. In sum, district and school leaders, as well as policy makers, should recognize the kinds of supports that teachers need to improve instruction.



INTRODUCTION


Teachers naturally experience myriad demands on their time and responsibility for their students’ performance. Further, classrooms may be large and usually include academically and culturally diverse students. Regardless of classroom composition, teachers are accountable for student outcomes. Provided adequate supports, teacher accountability has the potential to improve student outcomes, especially if teachers are able to work together (Y. L. Goddard, Goddard, & Tschannen-Moran, 2007).


If teachers feel disconnected from their peers, however, or believe that their work is unimportant, their morale may be affected negatively and they may be more likely to leave the profession (Jones, 1958; Kinsey, 2006; Peterson, Park, & Sweeney, 2008). This phenomenon has been studied for many decades. In addressing teacher morale, Jones (1958) stated that “teachers must share the feelings of oneness and of operating as a unit” (p. 291). Similarly, many decades later Peterson et al. (2008) described morale as “an important indicator of group well-being” (p. 20). Thus, when teachers work together, they are likely to experience positive outcomes that may lead to improved morale and teacher efficacy. In fact, Peterson et al. examined various dimensions of morale, including many that relate to efficacy: confidence, resilience, and belief in the group’s capability to teach successfully (i.e., collective efficacy). An additional dimension is teachers sharing a common purpose, which may involve work around particular instructional practices.


We postulate, therefore, that when teachers work together on instructional practices, their efficacy may be affected positively. In fact, Takahashi’s (2011) case study involving four teachers in a junior high school suggests that teachers’ work together on instructional improvement is connected to their teaching efficacy and may lead to a self-perpetuating cycle that stands to improve efficacy over time. This is an important step toward our understanding of teachers’ work and efficacy beliefs. Even so, Takahashi noted the need for quantitative work examining teachers’ practices and their impact on efficacy beliefs.


The purpose of this paper, therefore, is to examine links between teachers’ reports that collaboration occurs in their schools, their reported use of differentiated instruction (a particular instructional practice) in their classrooms, and their teaching efficacy self-assessments. This paper extends current research by examining a mediated path in which we study the relationship between collaboration and teachers’ reported use of differentiated instruction in their classrooms and the link between differentiated instruction and teacher efficacy.


LITERATURE REVIEW


Our work is associated with social cognitive theory, in which Bandura (1997) postulated that of the four sources of efficacy beliefs (mastery experience, vicarious learning, social persuasion, and affective states), the most effectual source is enactive, or mastery, experience. Specifically, success fosters improved self-efficacy beliefs, while failure depresses them. We believe that when teachers collaborate to implement or improve a challenging approach to teaching, their teaching efficacy is likely to be affected positively. Further, if teachers are working collaboratively on instructional practices, their mastery experiences may be affected by their collaborative work, thus increasing their level of teaching efficacy. The next sections describe in some detail the three constructs that we examine in this study: teachers’ reports of their collaborative practices, differentiated instruction use, and teacher efficacy. Following separate treatment of these constructs, we examine links among the constructs in the extant literature and conclude by stating our hypothesis.


TEACHER COLLABORATION


When teachers work together, they may overcome the isolation that can result in stymied professional learning and practice (Bruce, Esmonde, Ross, Dookie, & Beatty, 2010; Hart, 1998). Having opportunities to work together may help teachers’ personal and professional growth and teaching efficacy. Collaboration, especially collaborative work that is focused on instructional support and professional development, has many documented benefits for teachers, including higher levels of trust (Tschannen-Moran, 2001), greater job satisfaction (Pounder, 1999), more positive affect toward teaching (Brownell, Yeager, Rennells, & Riley, 1997), improved teaching (Vescio, Ross, & Adams, 2008), and increased teaching efficacy (Shachar & Shmuelevitz, 1997). Issues of time and scheduling conflicts can be problematic, however (Berry, Daughtry, & Weider, 2009; Butler & Schnellert, 2012; Darling-Hammond & Richardson, 2009). Further, Bruce et al. (2010) emphasize that the levels of trust required to truly effect change via collaboration cannot be underestimated, because the move from isolated to public practice requires cultural shifts. In fact, Shachar and Shmuelevitz (1997) emphasize that implementing new instructional approaches that deviate significantly from whole-group teaching creates issues that teachers must work on collectively. Importantly, Kardos and Johnson (2007) and Youngs, Holdgreve-Resendez, and Qian (2011) found that first-year teachers are more likely to remain in the profession and in their schools when they collaborate for the purpose of instructional improvement.


Further, recent research has extended our knowledge about the effects of teacher collaboration on student achievement. Specifically, emerging evidence supports positive effects of teacher collaboration on student achievement (Y. L. Goddard et al., 2007; Moolenaar, Sleegers, & Daly, 2012; Supovitz, 2002; Supovitz & Christman, 2003; Vescio et al., 2008). Vescio et al. describe several studies documenting that changes in teachers’ collaborative practices resulted in improvements in their schools’ teaching and learning culture. Further, all eight studies examined by Vescio et al. demonstrated a positive link between teachers’ participation in professional learning communities and student achievement.


Supovitz (2002) and Supovitz and Christman (2003) found that when teachers worked together on instructional practices, students experienced improved achievement outcomes. In fact, across the two school districts studied by Supovitz and Christman, only those schools in which teachers focused their collaborative efforts on instructional practice demonstrated improvement in student achievement.


Y. L. Goddard et al. (2007) found a positive, statistically significant link between teachers’ reported collaboration and student achievement in math and reading on state-mandated assessments. Notably, they suggest that this link is likely indirect and that perhaps teachers’ instructional practices are affected by the learning that occurs as teachers collaborate; it is this practice-to-achievement link that is likely affected by collaboration.


Moolenaar et al. (2012) found that teachers’ collaboration networks did not lead directly to improved student achievement. However, these collaboration networks resulted in improved collective efficacy among teachers, which was associated with student achievement. Thus, collective efficacy served as a mediator between teachers’ collaborative practices and student achievement. This evidence supports the theory postulated by Y. L. Goddard et al. (2007) that the effects of collaboration on student achievement are likely indirect. The question that remains unanswered is what specific teacher practices might serve as effective mediators between collaboration and achievement.


In sum, teacher collaboration has been linked to positive outcomes for teachers and to improved student achievement. Questions about the mediating effects of instructional practices remain, however. Although there are many instructional practices that might be influenced by collaboration, we chose to examine differentiated instruction because of its burgeoning use, focus on meeting students’ diverse academic needs, and emerging research support.


DIFFERENTIATED INSTRUCTION


When teachers truly differentiate instruction for their students, they are knowledgeable about each student’s strengths, needs, and interests and are able to plan instruction based on this information. Grouping is flexible and designed for varied purposes, ranging from one-on-one, to small-group, to whole-group instruction. Purposeful grouping based on interests or abilities may allow students to work with various classmates or to focus on specific skill development. Also, students may have choices among approaches for accessing information, topics, and/or assignments. To make informed instructional decisions, teachers use assessments to gather information about student progress and determine next steps to assure progress for each student and for the entire class simultaneously. Instruction is dynamic and based upon a solid curricular foundation. Differentiated instruction requires time and reflection to be implemented well (Lawrence-Brown, 2004; Pettig, 2000; Tomlinson, 1999, 2000; Tomlinson et al., 2003).


When teachers differentiate, instruction is purposeful, flexible, and respectful. As teachers become more familiar with their students’ peculiarities, they are increasingly able to plan instruction designed to improve student outcomes. Additionally, the learning environment is as important as the content and instructional approaches.


Although differentiated instruction is becoming increasingly popular as an educational practice, few studies have examined its effects on student achievement. In fact, descriptions of differentiated instruction seem to vary between commercial products, professional development, and theoretical perspectives. We chose to examine differentiated instruction from a theoretical perspective to keep our work aligned closely with the origins of the construct (e.g., Tomlinson et al., 2003). Further, we agree with Hall, Strangman, and Meyer (2002), who stressed the need to examine the effects of differentiated instruction as a “package” rather than referring to the effects of the constructs upon which it is based (e.g., Vygotsky’s zone of proximal development; Gardner’s theory of multiple intelligences).


Recent studies found connections between differentiated instruction—as a package—and positive student outcomes. For example, Y. L. Goddard, Goddard, and Kim (2015) found positive, statistically significant links between differentiated instruction and students’ mathematics and reading achievement. Further, VanTassel-Baska et al. (2008) used the Classroom Observation Scale—Revised and a parallel assessment, the Student Observation Scale, to measure differentiated instruction in classrooms. Items on these assessments that were related to differentiated instruction focused on flexible grouping, task choice, and task engagement requiring interpretation and problem solving. These authors linked teachers’ use of differentiated instruction to student engagement. Tieso (2005), who measured differentiated instruction by examining teachers’ grouping practices and curricular adjustments, demonstrated a link between differentiated instruction and students’ mathematics achievement. Ernest, Thompson, Heckaman, Hull, and Yates (2011) worked closely with 35 teacher education candidates who were assigned to K–12 classrooms across various subjects in rural, urban, and suburban settings. Teacher education candidates were required to log their differentiated instruction methods across the four domains described by Tomlinson (2000): content, product, process, and learning environment. Over the course of 5 weeks, the candidates wrote and revised lesson plans to include differentiated instruction across those four domains in their lessons. Success was significant and quick; these teachers were involved in intensive mastery experiences, and their students experienced academic gains on various teacher-designed assessments.


Teachers who differentiate instruction report that doing so requires a shift in their thinking about instruction and meeting students’ needs (Ernest et al., 2011). In fact, some educators indicate that teachers are not likely to begin or continue using differentiated instruction without support (Pettig, 2000; Westberg & Archambault, 1997).


In sum, differentiation is not a quick fix or an easy solution to education, but emerging evidence suggests that it may be effective. Our choice to focus on one specific instructional practice in schools, teachers’ reports that they differentiated instruction, was purposeful.


First, differentiated instruction can be implemented in many ways; thus, while it is a unique instructional approach, it is simultaneously a broad construct in which teachers have autonomy regarding design and implementation. Because differentiated instruction can be defined and executed in various ways, we chose a particular approach to examining it based on its theoretical constructs. We specifically chose to focus on teachers’ self-reported use of assessments, student choice, flexible grouping, and assignment selection based on students’ interests, needs, and skills.


Second, differentiating instruction takes time to implement across lessons, units, and subjects and is likely to challenge teachers’ instructional approaches as well as their considerations of students’ needs and interests. We postulate, therefore, that teachers’ use of differentiated instruction may provide mastery experiences that could lead to enhanced teaching efficacy. In fact, Wertheim and Leyser (2002) found that more efficacious teachers expressed intent to use instructional approaches designed to meet learners’ various needs.


TEACHER EFFICACY


Teacher efficacy refers to teachers’ beliefs in their own ability to generate desired student outcomes. Many factors may impact teachers’ beliefs in their capability to educate all students successfully (Tschannen-Moran & McMaster, 2009; Tschannen-Moran & Woolfolk Hoy, 2007). One element may involve teachers’ work together, especially if that work is focused on and results in improving instructional practices.


Teacher efficacy has been associated with organized and planful teaching (Allinder, 1994), trust (Da Costa & Riordan, 1996), and teacher satisfaction (Lee, Dedrick, & Smith, 1991). More importantly, teacher efficacy has significant research support regarding its effects on increased student achievement (Ashton & Webb, 1986; Tschannen-Moran & McMaster, 2009; Tschannen-Moran, Woolfolk Hoy, & Hoy, 1998). Conversely, low teacher efficacy has been associated with reduced levels of student achievement and efficacy, resulting in a “self-perpetuating cycle” that can lead to depressed student outcomes (Takahashi, 2011).


In addition to teaching efficacy effects on teacher and student outcomes, researchers are beginning to examine potential efficacy-shaping sources (mastery/enactive experiences, social/verbal persuasion, vicarious experiences, affective states) in an effort to understand what factors are important to building and supporting teaching efficacy. For example, Tschannen-Moran and Woolfolk Hoy (2007) surveyed novice and career teachers and found that verbal persuasion, one of the four postulated sources of efficacy beliefs, was more salient for novice teachers than career teachers, while mastery experiences had the greatest impact on both novice and career teachers. Additionally, Tschannen-Moran and McMaster (2009) found that mastery experiences, when paired with coaching to implement a new reading instruction strategy, were more powerful than other sources of efficacy beliefs.


In sum, teacher efficacy is a long-standing construct that has significant research supporting its effects on teachers and students. Emerging research supports mastery experiences as the most influential efficacy-shaping source for novice and experienced teachers. This is important, because changing teachers’ efficacy beliefs may have tremendous impact on their students’ achievement. In fact, Takahashi (2011) argues the importance of learning how to change efficacy beliefs, most notably via a sociocultural perspective in which teacher colleagues engage in shared decision making focused on improving teaching practices and student outcomes. We agree, so we set out to examine the links between teachers’ reported engagement in collaborative work focused on instructional practice and their sense of efficacy. Next, we examine links in the literature between these three constructs.


LINKING COLLABORATION, DIFFERENTIATED INSTRUCTION, AND TEACHER EFFICACY


Teacher collaboration, instructional practices, and efficacy are linked in various ways in the literature. For example, Parise and Spillane (2010) found that teachers’ self-reports of their on-the-job learning opportunities, including collaborative work, were positive, statistically significant predictors of teachers’ reported changes in their math and English language arts instructional practices. In fact, the strongest predictor of changes in instructional practices was teachers’ collaborative discussions. Smit and Humpert (2012) found that in schools where teachers reported greater use of differentiated instruction, team collaboration and culture were reportedly higher. Further, Butler and Schnellert (2012) conducted case studies involving teachers’ work together. Among other findings, they discovered that most teachers who worked together to improve student outcomes reported getting to know their students better and working harder to meet students’ particular needs. Specifically, 94% of teachers reported learning more about their students as part of their collaborative inquiry processes. Notably, this is an important step toward differentiating instruction, as teachers must be familiar with their students’ needs, skills, and interests. In fact, Fabrocini (2011) conducted case studies in which she found that structured collaborative meetings resulted in teachers’ increased use of differentiated strategies to meet the needs of their diverse learners.


In addition to differentiated instruction, teachers’ collaborative practices have been linked to their teaching efficacy. For example, Shachar and Shmuelevitz (1997) found that when teachers collaborated to improve instruction they were more likely to resolve that they were capable of improving student outcomes. In other words, their efficacy was enhanced. Supovitz (2002) examined changes in culture, instructional practices, and effects on student achievement. While his measures of instructional practice were broad, he found important connections between school community (fostered by teacher collaboration) and teachers’ reports of improved school environments and teaching efficacy. Importantly, when teachers were efficacious, they were more likely to change their instructional approaches significantly. Bruce et al. (2010) summarized teacher efficacy literature indicating that teachers with high efficacy were more likely to try challenging instructional approaches that required taking risks in their classrooms and to use assessments.


Thus, teachers’ instructional changes and their sense of teaching efficacy are intertwined. Tschannen-Moran and McMaster (2009) postulate that building efficacy via mastery experiences is a cyclical process in which teachers’ instructional successes lead to higher efficacy, which affects their willingness to attempt other challenging approaches. Notably, mastery experiences lead to higher efficacy, as do professional learning opportunities that offer teachers the ability to make changes in their instruction. Ernest et al. (2011) and Tomlinson (1995) suggest that getting teachers to continue using differentiated instruction requires those teachers to experience quick success (i.e., mastery experiences).


HYPOTHESIS


In summary, based on our review of the individual and collective literature on collaboration, differentiated instruction, and teacher efficacy, we hypothesize that teachers’ reports of their collaborative practices will be related to their teaching efficacy when mediated by their reported use of differentiated instruction. Specifically, we propose that when teachers collaborate with a focus on instructional improvement and input into their professional development experiences, they are more likely to attempt challenging instructional approaches (e.g., differentiated instruction) that require risk taking and perseverance. In turn, when teachers report that they participate in such transformative enactive experiences, their efficacy beliefs are likely to be strengthened.


METHODS


In this section, we describe the study participants who completed our surveys. Following that, we provide details about the measures we used. Finally, we describe our analytic procedures.


PARTICIPANTS


We employed data from the first year of the School Leadership Improvement Study (SLIS).1 As co-Principal Investigator, the first author was involved in all aspects of data collection for this study. We note that the current study is not an experimental study to examine the effects of McREL’s professional development training; instead, our study makes use of baseline data to test the hypothesis stated above. The sample for this study was 95 elementary schools serving students in rural high-poverty areas located in the northern regions of a Midwestern state. A total of 1,623 elementary teachers (an average of 17 teachers per school) who responded to our first round of surveys for SLIS during the 2008–2009 school year were included in the data analyses for this study. Survey data were collected from October 2008–January 2009. We drew demographic and achievement data for fourth grade students (n = 4,167), the 1,623 elementary teachers, and 95 schools from a state accountability data system for the 2008–2009 school year. Because student data were not directly linked to teacher data, we used aggregated average scores for student data at the between-school level.


MEASURES


To examine our research question, we controlled for the differential effects of school contextual variables by including three school-level measures (percent free and/or reduced lunch, percent minority students, and enrollment size) for data analysis. Also, aggregated student achievement scores for fourth grade math and reading were used as covariates. The sources for math and reading scores were state-mandated assessments required as partial fulfillment of No Child Left Behind standards. Information on the school-level variables was drawn from a public-use state accountability information system.


Three teacher-level measures—teachers’ reports of their collaborative practices focused on instruction, curriculum, and professional development; reported use of differentiated instruction; and teaching efficacy—in addition to teacher demographic information (gender, education level, years of experience, and ethnicity) were obtained from the surveys. Participating schools were rostered and those teachers with at least 50% time in each school were asked to complete surveys. Teacher surveys were coded to ensure confidentiality and to allow follow-up with nonresponders. Surveys were mailed to schools and teachers were asked to complete them during regularly scheduled faculty meetings. Follow-up for nonresponders was conducted in two stages. First, reminder postcards were sent to those teachers from whom surveys were not received. Next, a second set of surveys was hand-delivered to schools with the request that teachers complete and return them. Of 1,873 teachers recruited to participate, 1,623 returned completed surveys, for a response rate of 87%.


Teacher collaboration for instructional improvement was measured by 13 items with three subconstructs representing 1) the extent to which teachers work collectively to plan school improvement, select and evaluate curriculum and instructional materials and methods, and determine and plan professional development activities (5 items); 2) the presence of formal structures supporting teacher collaboration (4 items); and 3) the extent to which collaboration occurs informally among staff (4 items). These items, their factor loadings, and Cronbach’s alpha are presented in Table 1.


Table 1. Teachers’ Reported Collaboration Measurement Properties


Teachers Collaborate on Instructional Policy

Cronbach’s alpha =.89 (5 items)

Factor

loading

Teachers in this school work collectively to plan school improvement.

.77

Teachers in this school work collectively to select instructional methods and activities.

.82

Teachers in this school work collectively to evaluate curriculum and programs.

.89

Teachers in this school work collectively to determine professional development needs and goals.

.90

Teachers in this school work collectively to plan professional development activities.

.81

  

Formal Collaboration

Cronbach’s alpha =.74 (4 items)

Factor

loading

The principal, teachers, and staff collaborate to make this school run effectively.

.66

Collaboration in this school occurs formally (e.g., common planning times, team meetings).

.80

When teachers in this school collaborate, our collaboration time is typically structured; we stick to an agenda and/or we systematically work on a particular goal.

.83

The principal at this school participates in instructional planning with teams of teachers.

.64

  

Informal Collaboration

Cronbach’s alpha =.85 (4 items)

Factor

loading

Teachers in this school work collectively to communicate with parents.

.56

Collaboration in this school occurs informally (e.g., in the halls/lunchrooms, at randomly available times).

.64

Teachers talk about instruction in the teachers’ lounge, faculty meetings, etc.

.83

Teachers in this school share and discuss student work with other teachers.

.79

Note. The rating scale is 1–6: strongly disagree to strongly agree.


Teachers’ reports of their differentiated instruction practices consisted of seven items (see Table 2). Importantly, the words “differentiated instruction” were not used in the survey items, because the construct is widely misunderstood (Tomlinson et al., 2003). Differentiated instruction is a compilation of many theories and practices; therefore, it was beyond the scope of this study to measure comprehensively all imaginable forms of differentiated instruction. Instead, items were worded to tap the construct by asking teachers to report various instructional activities that, when “packaged” (Hall, 2002), would examine specific teachers’ approaches toward differentiation. Our focus was on teachers’ reports that they considered students’ needs, interests, and skill levels; provided choices; used flexible grouping and assessment; and attended to students’ individual progress. We purposefully avoided constructs such as multiple intelligences and learning styles, given the lack of evidence supporting such constructs. Thus, we believe that our measure of teachers’ reported differentiated instruction use is a valid proxy for examining instructional practices.


Table 2. Teachers’ Reported Differentiated Instruction Measurement Properties


Differentiated instruction

Cronbach’s alpha =.84 (7 items)

Factor

loading

I use a wide range of assignments, materials, or activities matched to student’s needs and skill level.

.78

I provide several activities in class so that students can choose from among them.

.75

I regularly offer students opportunities to choose learning activities or individuals with whom to work.

.74

I make efforts to recognize all students' individual progress.

.71

I use flexible grouping in my classroom.

.71

I frequently use assessments to decide what my students need next.

.67

I use a wide range of assignments, materials, or activities matched to students' interests.

.71

Note. The rating scale is 1–6: strongly disagree to strongly agree.


We measured teacher efficacy beliefs using four items adapted from Hoy and Woolfolk Hoy (1993) and employed previously by R. D. Goddard and Goddard (2001) to tap teachers’ perceptions of their ability to teach all students successfully. Table 3 provides details about the items, their factor loadings, and Cronbach’s alpha.


Table 3. Teacher Efficacy Measurement Properties


Teacher efficacy

Cronbach’s alpha =.74 (4 items)

Factor

loading

If a student did not learn content from a previous lesson, I am confident I would be able to increase his/her learning in the next lesson.

.68

If a student in my class becomes disruptive or noisy, I feel confident that I can redirect him/her quickly.

.79

If one of my students couldn't do a class assignment, I would be able to assess accurately whether the assignment was at the correct level of difficulty.

.80

If I try really hard, I can get through to even the most difficult students.

.77

Note. The rating scale is 1–6: strongly disagree to strongly agree.


For each measure described above, a 6-point Likert-type scale was adopted for teacher responses, ranging between 1=strongly disagree to 6=strongly agree.


DATA ANALYSIS


To examine our research hypothesis, we employed multilevel structural equation modeling (MSEM), which allowed us to take into account the nested structure of the data (i.e., teachers’ responses nested within schools). Previous research shows that ignoring the multilevel structure leads to underestimated standard errors of the parameter estimates (Hox, 2010; Raudenbush & Bryk, 2002; Snidjers & Bosker, 1999). MSEM accounts for data dependency within a cluster by modeling both within- and between-level models and avoids having biased standard errors. Intraclass correlation coefficient (ICC; McGraw & Wong, 1996) is the measure of correlation among units within the same clusters and is calculated by the proportion of cluster-level variance over the total variance. Multilevel analyses should be employed when intraclass correlation exists (Hox, 2010; Raudenbush & Bryk, 2002), as it does in our study.


To assess whether our theoretical model fit our data, we examined various fit indices associated with SEM techniques: the χ2 goodness-of-fit test, the comparative fit index (CFI), the root mean square error of approximation (RMSEA), and the standardized root mean square residual (SRMR). In general, cutoff values of the fit indices indicating acceptable fit are CFI ≥ .90, RMSEA<.08, and SRMR ≤ .08 (Bentler, 1990; Bentler & Bonett, 1980; Browne & Cudeck, 1993). We employed Mplus6.1 (Muthén & Muthén, 1998–2011) for conducting MSEM. The Mplus program MODEL INDIRECT was used to test the statistical significance of the indirect path from teacher collaboration through differentiated instruction to teacher efficacy beliefs. The estimation method used for multilevel analysis was maximum likelihood with robust standard errors (MLR). Descriptive statistics including correlation analysis were conducted using SPSS19.0 (IBM Corp., 2010).


RESULTS


Given that the normality assumption is required for employing SEM analysis, we first conducted basic descriptive analyses for the variables included in the model. Skewness and kurtosis showed that all variables were normally distributed. This dataset had no missing data at the school level and low missing data rate at the teacher level. Teacher survey responses including demographic information had less than 1% of missing data for all variables. Because we found no systematic missing pattern, missing at random (MAR) was assumed. Under the assumption of MAR, all cases with even missing at some variables were included in the primary data analysis using Mplus6.1 (Muthén & Muthén, 1998–2011).


We then proceeded with our data analyses by confirming the factor structure and internal consistency for our measures of collaboration, differentiated instruction, and teacher efficacy. First, we developed a measurement model for collaboration, which consists of three subscales (i.e., teachers’ collaboration on instructional policy, formal collaboration, and informal collaboration). In addition to examining the structure (formal and informal) in which collaborative practices occur, we asked teachers to report the extent to which they and their colleagues worked together around important issues such as school improvement, instruction and curriculum, and professional development. We conducted confirmatory factor analysis (CFA) for each subscale and showed adequate fit to support the factor structure. Table 1 presents the factor loadings of the collaboration items on each subscale. Then, the average score across the items for the subscale was computed and used as an observed variable to construct the latent variable for collaboration. Because latent variable modeling increases power by taking into account measurement error (Heck & Thomas, 2009), we adopted this approach rather than using the average score of the three subscales. We also conducted CFA for differentiated instruction and teacher efficacy to confirm the single factor structure. Tables 2 and 3 show factor loadings for differentiated instruction and teacher efficacy, respectively. As shown in Table 4, the model fits were adequate to support that the measures were valid for further analyses. To reduce the model complexity, we employed the average score of subscales for differentiated instruction and teacher efficacy, rather than including the measurement model. Cronbach’s alpha ranged from 0.74 to 0.89 for the collaboration, differentiated instruction, and teacher efficacy measures. Descriptive statistics for all variables used in the multilevel SEM are reported in Table 5; correlations among these variables appear in Table 6.


Table 4. Model Fit Statistics from the CFA Results[39_21945.htm_g/00002.jpg]


Table 5. Descriptive Statistics for the Variables Included in MSEM Analysis


 

N

 

Min

Max

Mean

SD

School-level variables

      

%Minority

 

95

.00

.74

.11

.15

%Free/Reduced Lunch

 

95

.14

.83

.51

.15

Math Achievement

 

95

404.89

447.79

428.47

7.87

Reading Achievement

 

95

394.22

462.67

430.65

9.53

School Size

 

95

36.00

1,063.00

301.82

145.57


Teacher-level variables

Collaboration on Instructional Policy


1,620


1.00


6.00


4.37


1.07

Formal Collaboration

1,622

1.00

6.00

4.15

1.05

Informal Collaboration

1,621

1.50

6.00

4.72

0.79

Differentiated Instruction

1,618

1.43

6.00

4.87

0.71

Teacher Efficacy

1,618

1.25

6.00

4.90

0.68

Female Teacher

1,569

0.00

1.00

0.84

0.37

Master Degree

1,623

0.00

1.00

0.49

0.50

Years of Teaching Experience

1,571

0.00

75.00

16.22

9.69

Non-White Teacher

1,623

0.00

1.00

0.04

0.19


Table 6. Correlation Coefficients Among All the Observed Variables in MSEM Analysis


 

1

2

3

4

5

6

7

8

9

10

11

12

13

1

Collaboration on

1

            
 

Instructional Policy

             

2

Formal Collaboration

.58**

1

           

3

Informal Collaboration

.52**

.46**

1

          

4

Differentiated

.31**

.28**

.33**

1

         
 

Instruction

             

5

Teacher Efficacy

.23**

.22**

.25**

.43**

1

        

6

4th Grade Math

.01

.03

.10**

.02

.08**

1

       


7

Achievement

4th Grade Reading


.03


.08**


.08**


-.01


.08**


.72**


1

      
 

Achievement

             

8

School Size

-.06*

.01

-.04

.02

.01

.01

-.11**

1

     

9

%Minority

.05

.00

-.03

.02

-.02

-.19**

-.22**

-.16**

1

    

10

%Subsidized Lunch

.01

-.05*

-.04

.03

-.10**

-.29**

-.44**

-.37**

.12**

1

   

11

Female Teacher

-.01

-.02

.07**

.16**

.06*

-.01

.02

.05

.00

-.03

1

  

12

Master Degree

-.04

-.00

.04

.01

.00

-.01

-.01

.04

.00

-.02

.03

1

 

13

Years of Teaching

.06*

.07**

.05

-.06*

.02

.06*

.03

-.03

-.04

.05

-.02

.10**

1

 

Experience

             

14

Non-White Teacher

-.05*

-.04

-.06*

.00

.04

-.02

-.02

-.02

.14**

-.01

.00

-.02

-.02

Note. **Correlation is significant at the 0.01 level (2-tailed).

*Correlation is significant at the 0.05 level (2-tailed).


Given that teachers’ responses were clustered in schools, we calculated ICC to measure the degree of dependency of teachers amongst same schools. Regardless of the small ICC (i.e., ICC=.03), we continued to analyze the data using MSEM, rather than ignoring the multilevel structure.


Figure 1 presents our theoretical model examining the relationship between teacher collaboration and teachers’ reported use of differentiated instruction and the path from differentiated instruction use to teachers’ efficacy. Although the overall model chi-square statistic was significant (χ2 (20)=112.30, p<.001), indicating a misfit of our hypothesized model to the data, other model fit indices showed good fit (i.e., CFI=.95, RMSEA=.06, SRMRwithin=.03, and SRMRbetween=.01). Because the chi-square statistic is sensitive to the sample size and more likely to be significant with a large sample size (Brown, 2006), we were confident to proceed with interpreting the results based on the other three fit indices. This approach is supported by Kline (2010). As shown in Figure 1, we controlled for teacher- and school-associated demographic variables and students’ achievement scores for mathematics and reading. At the teacher level, we controlled for teachers’ gender (1=female), level of education (1=master’s or higher), years of teaching experience, and ethnicity (1=non-white). We included percent minority, percent free and/or reduced price lunch (a proxy for SES), school size, and students’ achievement outcomes as school-level covariates.2 Table 6 presents the correlation among all the observed variables in our MSEM model.


Figure 1. Multilevel structural equation model for testing the relationship between teacher collaboration and efficacy through the use of differentiated instruction

[39_21945.htm_g/00004.jpg]

Note. All path coefficients are standardized; **Statistically significant at two-tailed p<.01, *statistically significant at two-tailed p<.05, †statistically significant at two-tailed p<.10.


The results demonstrate that teachers’ reported collaboration practice was significantly related to their reported use of differentiated instruction (β = .43, p<.001), indicating that teachers were more likely to report employing differentiated instruction when they engaged in more collaboration. Furthermore, teachers’ efficacy was positively affected by their reported use of differentiated instruction (β = .38, p<.001). As shown in Table 6, there were significant direct relationships between teachers’ efficacy and three measures of teachers’ reports of their collaborative practices (ranging from .22 to .25). This direct relationship between teachers’ collaboration and efficacy beliefs was partially mediated by reports of differentiated instruction, indicating smaller indirect effect (β = .16, p<.001) between the collaboration and efficacy measures.


DISCUSSION


The main goal of this study was to investigate the influence of teachers’ reported collaboration on their reported use of differentiated instruction and in turn the influence of differentiated instruction on

 teachers’ sense of efficacy. In so doing, we were able to model the indirect relationship between collaboration and teacher efficacy as mediated by reported differentiated instructional practices, while controlling for other contextual variables. Results of the analysis supported our research hypothesis. When teachers worked together on issues of school improvement, curriculum and instruction, and professional development, they reported teaching in ways that were challenging and thoughtful. Specifically, a 1-standard deviation change in collaboration was associated with a .43-standard deviation change in teachers’ reported use of differentiated instruction. Similarly, a 1-standard deviation change in reported differentiated instruction use was associated with a .38-standard deviation change in teachers’ efficacy. Thus, via postulated successful enactive experiences, teachers’ efficacy for instructing all students successfully was strengthened in positive, significant ways.


Our outcomes are significant in that they demonstrate the importance of teachers’ collaborative work around school improvement, curriculum and instruction, and professional development. They also support the contentions put forth by Tomlinson et al. (2003) that differentiating instruction requires teachers to reflect on their personal and pedagogical approaches, collaborate with others, and plan instruction in novel ways. Further, our work extends what is known about sources of teacher efficacy. Theoretically, via mastery experiences gained through collaboration and reports of using differentiated instruction in their classrooms, teachers’ efficacy beliefs were strengthened. Indeed, the statistically significant linkages between these constructs support (but do not prove) that theory.


Some authors contend that collaboration should be considered important to system reform efforts, especially teacher evaluation systems, because of its effects on teachers’ professional development and student achievement (Darling-Hammond, Amrein-Beardsley, Haertel, & Rothstein, 2012; Y. L. Goddard et al., 2007). Our results are therefore important for educators at all levels, from teacher and administrator preparation providers to district and building personnel. Teachers require time and logistical support to collaborate. Further, we now have evidence that focusing teachers’ collaborative work on issues of school improvement, curriculum and instruction, and professional development was linked to their reported use of differentiated instruction practices, a time-consuming and challenging approach to teaching. Additionally, teachers’ reported use of differentiated instruction was linked positively to teaching efficacy, which is linked to student achievement in other studies (e.g., Ashton & Webb, 1986; Tschannen-Moran et al., 1998). Importantly, these results were obtained from teachers in high-poverty rural schools in a Midwestern state.


Although the outcomes of this study are significant and important, particular limitations exist. A key limitation is the use of teacher surveys in the absence of direct observation. Observing the conversations that occur during collaborative teacher time would provide more specific insight into instructional topics and content addressed during these collaborations. In particular, to what extent and how did teachers discuss differentiated instruction, either in component parts (e.g., how to provide interesting activities and allowing student choice) or as a “package?” Further, direct observations and/or teacher logs and/or teacher interviews could provide important insight into how teachers implemented differentiated instruction in their classrooms. Future research on connections between collaboration and teachers’ differentiated instruction practices should examine how teachers talk together about specific topics such as school improvement, curriculum, instructional practices, and professional development and how they then implement what they learned from these discussions in ways that are differentiated to meet students’ varied needs, interests, and abilities.


In sum, district and school leaders, as well as policy makers, should recognize the kinds of supports that teachers need to improve instruction. Creating time and structure for collaboration—especially collaboration that focuses on school improvement, improved instructional materials and practices, and teachers’ input into professional development—is important to supporting teachers as they work to meet the needs of their academically diverse students. Further, our results indicate that the more teachers report that they collaborate, the more likely they are to report differentiating instruction in their classrooms. When teachers experience positive enactive experiences, social cognitive theory postulates that their sense of teaching efficacy will be strengthened. Indeed, our study supports that theory, suggesting that the positive enactive experiences of reported collaboration and implementation of differentiated instruction were associated with improved teaching efficacy beliefs.


Notes


1. The School Leadership Improvement Study (SLIS) is a large-scale, longitudinal, randomized control trial designed to evaluate the implementation and effectiveness of the McREL Balanced Leadership© (BL) program. The research reported here was supported by the Institute of Education Sciences, U.S. Department of Education, through Grant # R305A080696 to Texas A&M University. The opinions expressed are those of the authors and do not represent views of the Institute or the U.S. Department of Education. A thorough description of this study can be found at Jacob, Goddard, Kim, Miller, & Goddard (2015).

2. In this study, teacher data are nested within the school data, however, student data are not nested within the teacher data because there was no linkage between the student and teacher data. Therefore, the aggregated school-level achievement score was used for the data analyses at the school-level.


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Cite This Article as: Teachers College Record Volume 120 Number 1, 2018, p. 1-24
https://www.tcrecord.org ID Number: 21945, Date Accessed: 1/27/2022 10:37:07 PM

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About the Author
  • Yvonne Goddard
    Ohio State University
    E-mail Author
    YVONNE GODDARD is Visiting Associate Professor at The Ohio State University. Her research and teaching interests include teacher collaboration, differentiated instruction, and efficacy as well as effective literacy practices for students who struggle. Recent articles: Goddard, Y. L., Goddard, R. D., & Kim, M. (2015). School instructional climate and student achievement: An examination of group norms for differentiated instruction. American Journal of Education, 122(1), 111–131. Goddard, R. D., Goddard, Y. L., Kim, E. S., & Miller, R. J. (2015). A theoretical and empirical analysis of the roles of instructional leadership, teacher collaboration and collective efficacy beliefs in support of student learning. American Journal of Education, 121(4), 501–530.
  • Minjung Kim
    Ohio State University
    E-mail Author
    MINJUNG KIM is Assistant Professor at Ohio State University. Her research interests are quantitative psychology including longitudinal data analysis using multilevel modeling and structural equation modeling. Recent articles: 1. Kim, M., Vermunt, J., Baak, Z., Jaki, T., & Van Horn. L. (in press). Modeling predictors of latent classes in regression mixture models. Structural Equation Modeling: A Multidisciplinary Journal. (Impact Factor, 2015: 4.176) 2. Kim, M., Lamont, E. A., Van Horn, L. (in press). Structural equation modeling: Applications using Mplus. Structural Equation Modeling: A Multidisciplinary Journal. (Impact Factor, 2015: 4.176)
 
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