Differentiated instruction in small schools

Teaching and Teacher Education 28 (2012) 1152e1162

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Differentiated instruction in small schools Robbert Smit*, Winfried Humpert University of Teacher Education St. Gallen, Müller-Friedbergstr. 34, 9400 Rorschach, Switzerland

h i g h l i g h t s < We examine the practice of differentiated instruction (DI) in small rural schools. < Teachers differ in their practice, but only few uses DI on a daily basis. < Two groups of teachers using DI can be distinguished. < A high pedagogical team culture has a positive influence on a teacher’s individual practice of DI. < Students’ achievement is not affected by DI.

a r t i c l e i n f o

a b s t r a c t

Article history: Received 12 December 2011 Received in revised form 7 July 2012 Accepted 11 July 2012

Rural areas in the alpine regions suffer from dwindling student numbers. Differentiated instruction (DI) could help improve the teaching culture by allowing instructors to better adapt to heterogeneous student groups. At the beginning of a combined research and school improvement project, a survey of 162 teachers and 1180 students was conducted to obtain an overview of the types of DI that are currently practiced. In addition, we examined the school conditions that supported the implementation of DI. This cross-sectional study demonstrates a difference in practices between teachers with more- and lessdeveloped DI cultures, and it was determined that team collaboration that includes pedagogical topics enhances teachers’ use of DI. Ó 2012 Elsevier Ltd. All rights reserved.

Keywords: Differentiated instruction Rural schools Diversity

1. Introduction Alpine and subalpine regions have faced demographic declines that are threatening the survival of the regions’ rather small schools (Meusburger, 2005). This phenomenon, however, is not unique to alpine regions as outcries about school closures can be heard throughout the rural regions. The dwindling population in these rural regions is a key problem for schools in the United States and Canada (Arnold, Newman, Gaddy, & Dean, 2005; Barley & Beesley, 2007; Wallin & Reimer, 2008), Europe (Hargreaves, 2009; Kalaoja & Pietarinen, 2009; Leroy-Audouin & Suchaut, 2007), Australasia (Kearns, Lewis, McCreanor, & Witten, 2009; White & Reid, 2008) and in developing countries (Little, 2006). A research team from 4 educational universities located in the alpine regions has been investigating the situations of small schools in Switzerland and Austria. The aim of the “Schools in Alpine Regions” project (www.schulealpin.org) was to provide substantive information that local and district authorities can use as a basis for

* Corresponding author. E-mail address: [email protected] (R. Smit). 0742-051X/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.tate.2012.07.003

their decisions regarding the educational future in these areas. In addition, school leaders, teachers and parents should begin to engage in informed discussions regarding favourable conditions for teaching and learning in heterogeneous or diverse student groups. If small villages concerned about the decreasing population decide to maintain local school service, they may be forced to combine classes of different grade levels. This combination would produce increasing heterogeneity and require multi-grade teaching. Teachers are generally accustomed to working with a diverse population of students as children with immigrant backgrounds, learning difficulties or special needs often contribute to the heterogeneity of a class. However, many of the skills that are important for heterogeneous single-grade classes require a heightened emphasis in the context of the preparation of teachers for multi-grade teaching (Mulryan-Kyne, 2007). One well-known teaching concept for addressing heterogeneity that has, to date, not been deeply researched is differentiated instruction (DI) (Tomlinson, 1999; Tomlinson et al., 2003). Our portion of the “Schools in Alpine Regions” project focused on teachers’ actual instruction habits with regard to differentiation in the Eastern alpine regions of Switzerland. We also examined the way in which DI is embedded within the teaching culture of the

R. Smit, W. Humpert / Teaching and Teacher Education 28 (2012) 1152e1162

school and its actors. Goddard, Neumerski, Goddard, Salloum, and Berebitsky (2010) demonstrated that leadership is vital to teachers’ use of differentiated instruction; however, in this study, we not only consider leadership but also the role of a professional team culture in the implementation of DI. The results from this research have influenced the school improvement processes and have been instrumental in evaluating developments in the instructional practices of schools and teachers (see Smit, Humpert, Obertüfer-Gahler, Engeli, & Breuer-Brodmüller, 2011). 2. Differentiated instruction 2.1. Theory and concept To cope with diversity, teachers must adapt their teaching. “Adaptive teaching is teaching that arranges environmental conditions to fit learners’ individual differences” (Corno & Snow, 1986, p. 621). A concept that is closely related to adaptive teaching, but is newer and more detailed, is differentiated instruction, an approach that enables teachers to plan strategically to meet the needs of every student. This concept is rooted in the belief that because there is variability among any group of learners, teachers should expect student diversity and adjust their instruction accordingly (Tomlinson, 1999, 2001; Tomlinson et al., 2003). The initial practical applications of DI involved gifted students, but the DI concept has also been well received in inclusive classrooms (Lawrence-Brown, 2004). Practitioners working with struggling students and students with special needs differentiated their instruction long before teachers with regular classes began to employ DI. In addition, research in the field of inclusion has searched for ways to manage mixed-ability classrooms. For example, Schumm, Vaughn, and Leavell (1994) developed a 3-level planning pyramid that permits individualised goals for students with severe intellectual disabilities. Recently, DI has become an interesting option for use in regular classrooms as well, classrooms where learning has become studentoriented and collaborative and where all students are successfully and meaningfully challenged (George, 2005; Subban, 2006). The theory from the field of DI incorporates the following main characteristics of a differentiated classroom (Hall, 2002; Randi & Corno, 2005; Subban, 2006; Tomlinson, 1999): the teacher attends to students’ differences, a formative assessment assists in identifying the next learning sequence, the teacher modifies content, process and products in accordance with the learners’ needs, the teacher and students collaborate in learning process. From Vygotskij (1978), we know that individuals learn best when they are in a context that provides a moderate challenge; Vygotskij refers to this environment as the “zone of proximal development”. Learning tasks must be adjusted to each student’s appropriate learning zone. Brimijoin, Marquissee, and Tomlinson (2003) suggest using (formative) assessment data to differentiate instruction when preparing students for state standardised testing. An assessment should be used as a teaching tool to extend rather than to merely measure instruction (Smit, 2009; Hall, 2002); therefore, teachers require high diagnostic competence. Diagnostic teaching lies at the centre of adaptive teaching, according to Houtveen, Booij, de Jong, and van de Grift (1999). Miller (1989) posits that the teacher’s roles in a collaborative classroom include acting as a facilitator who creates a rich learning environment and functioning as a model for students. In this context, modelling serves to share with students not only what the teacher thinks

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regarding the content to be learnt but also to engage the teacher in the process of communication and collaborative learning. The third role that Miller envisions for teachers is that of a coach. Coaching or scaffolding involves supplying hints to students, providing feedback to those students, redirecting their efforts, and helping them to use a strategy to learn the content (Collins, Brown, & Newman, 1989). Wang (1980) stresses the importance of teaching students to become self-directed learners in adaptive instruction settings by teaching students self-management skills. She also proposes the use of grouping to easily adapt school instruction to meet the individual differences of students. Both self-regulated student learning and explicit, direct and extended instruction to groups are crucial components of DI, especially for struggling learners (Tobin & McInnes, 2008). In schools in German-speaking countries, there is a wellestablished tradition of teaching with differentiated and studentoriented learning forms, such as “jena-plan work” or “project work”; these forms are based on reform pedagogy, also known as progressive education (Trautmann & Wischer, 2009). Teachers in these countries distinguish between DI strategies that employ open, student-centred teaching methods and strategies that involve more structured forms that incorporate tiered learning tasks for different levels of competence. If a teacher’s student’s work (freely) in groups during differentiated learning sequences, then these groups are not fixed and, as a consequence, they may look quite different in the very next lesson. Although teachers often accept the necessity of addressing learner variance in the regular classroom, they seldom plan or realise elements of DI to achieve that aim (Hootstein, 1998; Moon, Callahan, Tomlinson, & Miller, 2002; Tomlinson et al., 2003). If teachers do adapt their teaching, they typically are merely offering support for struggling readers (Baumann, Hoffman, Duffy-Hester, & Jennifer Moon, 2000). In other words, rather than viewing differences as a challenge to expand their teaching competencies, they judge differences to be problematic and view integrating these differences into lesson planning as a time-consuming task. Therefore, teachers’ motivations to implement DI must also be considered. This line of reasoning leads to the following research model of effective DI (Fig. 1), the main components of which are shared with a model described by Hall (2002). These components, or elements (Tomlinson, 1999), of DI can be viewed as part of a learning cycle. In practice, teachers should use each element flexibly, e.g., they may start with formative assessment prior to planning instruction. Our model illustrates two main tasks for teachers: planning differentiated lessons and assisting (groups of) students as they are working on individual or group tasks. Both components rely on formative assessment strategies, which provide teachers with the necessary information to modify their instruction as they guide their students to attain mastery, as defined by Bloom (Guskey, 2007). Description of the components: Attitude: The teacher has a more constructivist view of learning; i.e., each learner has unique needs, and the learner shares the responsibility for learning with the teacher. It is important for the teacher to pre-assess each student’s knowledge and the plan for each student’s individual needs and way of learning. Content: The proximal educational goals must be aligned with the prior knowledge and learning profiles of the individual students or groups of students being taught. The teacher needs to clarify the final goals with examples of successful work from other students to illustrate these goals. Process/products: Tasks must be aligned with these individual goals and student interests, and they must be structured to allow students to work at their own pace. The tasks should offer different ways to explore the educational content and allow varied products

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Fig. 1. A research model of differentiated (diff.) instruction (adapted from Hall, 2002).

from the students; moreover, they should enable students to work alone, in pairs or in groups. Communication/collaboration/coaching: The teacher supports the students’ learning processes by monitoring the students and providing descriptive feedback. The students are encouraged to self-assess their own learning processes, while the teacher diagnoses learning difficulties. In providing feedback, the teacher coaches the students, suggesting learning strategies and reflecting on the students’ perceptions of their learning processes. Formative assessment: DI is intertwined with formative assessment. Formative assessment is crucial for identifying each student’s next steps of learning and for adapting instruction accordingly. 2.2. Research evidence of differentiated instruction There is some support from previously published research regarding the establishment of DI. According to Scheerens’ (2000) review of important “aspects of structured teaching”, there is an average effect of .22 from differentiation/adaptive teaching on student achievement. In a review of the research of 13 experimental studies on multi-age classes (differentiated by intent and necessity), Miller (1990, 1991) found achievement test results favouring multi-grade classrooms versus single-grade classrooms in 81 per cent of the 21 separate measures used, whereas Gutiérrez and Slavin (1992) specified that non-graded organisation can have a positive effect on student achievement if more direct instruction is provided. However, Gutiérrez and Slavin (1992) found no effect from individualised instruction. In Veenman’s (1995) best-evidence synthesis about multi-grade classes, there were no differences between single-grade and multi-graded classrooms, which, according to Veenman, demonstrates that there are no cognitive or non-cognitive negative effects in multi-grade classrooms. One reason, according to Veenman, for the lack of positive effects may be the lack of preparation teachers have in teaching in multi-grade classrooms. As a result of this lack of training, these teachers often continue to use the same practices in multi-grade classrooms that they employed in single-grade classrooms, rather than incorporating strategies such as DI. Thus, the critical variable that affects student learning is the teacher, not the classroom structure (Hattie, 2002; Wilkinson & Hamilton, 2003).

Baumgartner, Lipowski and Rush (2003) used DI to improve the reading achievement of primary and middle school students. The specific differentiated strategies implemented in their study included flexible grouping, student choice regarding a variety of tasks, increased self-selected reading time, and access to a variety of reading materials. Based on an analysis of student achievement data and attitudes towards reading, Baumgartner et al. concluded that the implementation of DI strategies was an effective approach that successfully increased reading achievement. Tieso (2005) examined the effects of curricular differentiation with betweenand within-class groupings on student achievement using a curriculum-based assessment as a pre- and post-test measure to evaluate student performance. Students with diverse abilities who received the DI intervention experienced significantly greater mathematics achievement than students who did not receive DI. Similarly, Chamberlin and Powers (2010) reported positive effects using DI to address the diverse needs of college students, particularly in mathematics, and they recommend the use of DI in guiding the student’s learning process regarding logarithms. In addition, they note that not every lesson must be differentiated. Tomlinson et al. (2003) offer a review of further research evidence connected with DI. Research indicates that humans learn best when presented with moderate challenges (Tomlinson, 1999). What is moderately challenging and motivational for one learner, however, may be far too difficult for another student. Self-determination theory asserts that optimal challenges, informational feedback, and interesting and stimulating material promote intrinsic motivation and achievement (Deci & Ryan, 1985). According to Urdan and Turner (2007), this finding indicates that teachers should allow the students to make choices about classroom experiences and about the work in which the students are to engage. However, it is difficult for researchers to trace the causal flow of motivational influences in classrooms, as teachers also respond to student preferences. Grimes and Stevens (2009) conducted action research in a 4th grade classroom experimenting with a selfassessment system that enables teachers to differentiate the teaching of elementary mathematics. DI appears to have improved test scores for both low- and high-achieving students. In addition, all of the students exhibited an increased desire to


perform and to improve in math as they gained confidence in their mathematical abilities. 2.3. Implementing differentiated instruction The aim of our project was to prepare small schools for upcoming changes, such as the combination of classes. This section addresses favourable context variables that enhance the use of DI strategies, such as a professional team culture and a supportive leadership. Many teachers experience difficulty including the principles of DI within their repertoire of instructional strategies because, in addition to insufficient teacher preparation courses, the implementation of DI is also often hindered by a lack of administrative support and a failure by school leaders to encourage and promote DI (Holloway, 2000). Pettig (2000), who guided a five-year project centred around improving the DI classroom culture in one district, identified strategies for implementing DI. One of the most important of these strategies is peer collaboration, which begins when teams of professional educators are formed, time is provided, beliefs about DI are examined, and expectations are made clear (Fogarty & Pete, 2011). Sharing and discussing ideas with a colleague are the beginnings of the implementation process. Pettig recommends starting small with DI by choosing, for example, just one topic within one’s subject area. From their own experience of leading a school change project focused on DI, Tomlinson, Brimijoin, and Narvaez (2008) stress the importance that school leaders must be more than mere administrators; rather, appropriate DI leaders must have a vision and know how to plan and evaluate with the end goal in mind. While good leadership is crucial for successful improvement efforts (Hopkins, 2001; Reezigt & Creemers, 2005), leadership that is effective for student outcomes should not be limited to good leaderestaff relationships but should also focus on specific pedagogical work

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(Robinson, Hohepa, & Lloyd, 2009). In Switzerland, school leadership is in a transformation process, transitioning from leaders who are primus inter pares, principals who serve as teachers with additional administrative duties, to leaders with a more functional, transactional role (Vogt, 2004). Leadership in Austria and Germany is also changing, but these changes are hindered by a bureaucratic governance structure (Schratz & Petzold, 2007). Transformational leadership, however, is still rarely found in schools in Germanspeaking countries. Reezigt and Creemers (2005) discuss schools with a favourable culture for improvement, positing that these schools will start and continue improvement efforts more easily than schools that constantly try to avoid change and are fearful of improvements. For this reason, we included school leadership, school climate and team collaboration (culture) as variables in our research and examined how these variables interact with DI. According to Opdenakker and Van Damme (2007), important interrelated variables at the school level that impact learning includes the composition of the schools (students, teams, leadership), and the contextual characteristics of the schools (e.g., school size, climate). In many of the recent literature, school leadership is no longer proposed to have a direct influence on learning outcomes, though it does have an indirect influence through its impact on school organisation and school culture (Hallinger & Heck, 1998; Opdenakker & Van Damme, 2007). There is fairly wide consensus within school effectiveness research regarding the main categories of variables that can be distinguished as effectiveness-enhancing conditions (Hulpia & Valcke, 2004; Scheerens, 2000). Our supply-use research model (Fig. 2) adapted from Brühwiler and Blatchford (2010) attempts to address many of these factors and could be viewed as a variation of the more well-known inputeoutput models of school effectiveness (Scheerens, 2000). According to Fend (2008), the following 4 levels can be identified: the system level (IV), the school level (III), the

Fig. 2. A multilevel supply-use model of student learning. The variables observed in the present study are printed in italics (adapted from Brühwiler & Blatchford, 2010).

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teacher or class level (II) and the individual student level (I). Levels II through IV describe the supply of learning opportunities, whereas level I describes the use of these opportunities. Furthermore, the levels and factors influence each other in both directions and across different levels. While our research questions are embedded within this supply-use model, we did not test the conceptual framework as a whole. In addition, we did not consider all possible interconnections but, rather, focused on certain theoretically or empirically interesting relationships connected to the practice of DI. 2.4. Research questions The aim of the present study was to obtain an overview of DI in the rural and alpine schools participating in our school improvement and research project. Moreover, we were interested in analysing factors that may support the use and the quality of DI. In their research on DI, McQuarrie and McRae (2010) referred to these two foci (use and quality) as “effective pedagogies and learning supports” and “effective project supports”, respectively. In addition, we addressed the concerns of parents and policy makers that new learning procedures may affect results on standardised achievement tests. This aim produced the following research questions: 1. How do teachers incorporate DI in their teaching? 2. How are school team collaboration and school leader support associated with the practice of DI? 3. Does DI affect student achievement? 3. Method 3.1. Sample Participating in the survey of this sub-study of the project “Schools in Alpine Regions” were 8 primary schools (grades 1e6) and 14 secondary schools (grades 7e9) from the rural alpine region, which is situated mainly in the eastern part of Switzerland. These 22 schools volunteered either to participate in a school improvement project (10) or to take part in the research study without the school improvement project (12). Several schools entered after the project had started. The sizes of the primary schools were between 11 and 61 students, with a mean of 22, whereas the number of students in the participating secondary schools ranged from 14 to 132 with a mean of 60 students. A total of 162 teachers (29 primary school and 133 secondary school teachers) and 1180 students (154 primary and 929 secondary school students) responded to the questionnaires described herein. The teachers’ mean duration of service was 17.3 years (standard deviation (SD) ¼ 11.5, with a range of 1e43 years). The sample is representative of the project population. For a portion of the sample, we included the data from a district-approved standardised achievement test (the “Klassencockpit”) in the survey data. The missing values are due to non-identification or to schools that withdrew from the study. The test results for mathematics and German from 440 pupils (351 secondary school students and 89 primary school students) were included in the study. 3.2. Measurements The cross-sectional data are derived from a pre-test of a panel study in the summer of 2009. Teachers, pupils, school leaders and members of the school administration responded to a questionnaire. Several studies have shown that anonymous teachers’ selfreports on their teaching are highly correlated with classroom observations and that one-time surveys asking teachers questions

about the content and strategies they emphasise are quite valid and reliable in measuring their instructional characteristics (Desimone, Smith, & Frisvold, 2010). In addition, surveys are cost-efficient for handling large populations. Nevertheless, additional interviews were employed to gain deeper insights as well, and the results of the interview analysis are presented in the final report, as is the evaluation of the school improvement project (see Smit et al., 2011). 3.2.1. Teacher questionnaire A questionnaire for teachers with a total of 21 scales and 104 items (plus 39 single items and a few open-ended questions), most of which employed a 4-step Likert scale (4 absolutely agree; 3 rather agree; 2 rather disagree; 1 absolutely disagree), was developed for teachers. For all scales, a reliability index (Cronbach’s alpha) was computed. Scales with Cronbach’s alpha values below .7 were eliminated. The scales covered topics related to school leadership (SL), pedagogical team culture (TC; e.g., team climate, readiness for innovations, a shared pedagogical vision, the availability of time for discussing pedagogical topics), DI and learning climate (LC). Table 1 presents the scales for DI, which are consistent with the theoretical model in Fig. 1. 3.2.2. Achievement tests In many Swiss cantons (states), teachers are officially allowed to use an electronic achievement test (the “Klassencockpit”) as a benchmark for class performance in their mother tongue of German and in mathematics. The schools that participated in our project were asked to perform these tests in their classes even if they had not previously intended to do so. Three tests are administered each year, and these examinations must be conducted within certain time frames as they are aligned to the official curriculum. We used data from the first test in the new school year. Several of the students who completed the questionnaire finished school before they took the tests, and several new students took the tests after the first survey had been administered. These issues led to a certain number of students dropping out of the study. 3.3. Data analysis The questionnaires contained open and closed items. The answers to the open questions were categorised in accordance with qualitative content analysis (Mayring, 2000). To test for group structures, we performed a latent class analysis based on the categorised data using Mplus, version 6. The closed items were

Table 1 A description of the scales that measured DI. Factor:

Scale:

Description/example item

DI

Motivation for differentiated instruction Diagnostic competence

e.g., the consideration of individual competence levels while planning lessons e.g., I can easily explain the origin of learning difficulties to pupils The importance of training in self-assessment

DI

DI

Student selfassessment

DI

Differentiated feedback

DI

Differentiated learning goals

DI

Differentiated tasks

The provision of individual oral and written feedback to pupils Pupils receive individual learning goals e.g., I regularly use open tasks with different ways to solve a problem

Scale, 6 items, teacher questionnaire Scale, 5 items, teacher questionnaire Scale, 4 items, teacher questionnaire Scale, 6 items, teacher questionnaire Scale, 8 items, teacher questionnaire Scale, 5 items, teacher questionnaire


summarised in scales and tested for reliability by classical item analysis and subsequent confirmatory factor analysis. To test the relationships of the latent variables on the teacher level (question 2), structural equation models (SEMs) using the software Amos 6.0 were constructed. As a combination of factor analysis and path analysis, the SEM is appropriate for testing proposed theoretical models with latent variables. Because the units of analysis for question 3 included teachers and students nested within classrooms and schools, a multilevel analysis was also applied (Mplus Version 6 and MLwiN 2.19). This procedure considers that students are influenced by teachers, and the properties of the class are, in turn, influenced by the individual students. As a consequence, variables may be defined at each level: student, class/teacher and school levels. We considered context factors on teacher level (e.g., school type, gender, age) and individual preconditions of students (e.g., gender, age, language spoken at home) that impact teaching and learning. Student context variables could exhibit variance within class and between classes. As predictors for student achievement, we used DI and TC at the class level. 4. Results 4.1. The practice of differentiated instruction 4.1.1. What teachers sayean inductive approach Teachers were asked in the first part of the questionnaire to freely note (in their own words) a maximum of three elements of DI that they commonly practice. These elements were analysed and clustered into 13 categories (see Table 2). In the data collection process, 278 answers were derived from a total of 143 teachers. If teachers differentiate instruction, they typically provide individual tasks (tiered assignments), adapt the number of tasks or provide more time for certain students to work on tasks. Only a few teachers mentioned the complementary strategies related to assessments, such as diagnosing prior knowledge or conducting a formative assessment. Compared with our research model (Fig. 1), many teachers in our study focused on differentiating while planning instruction and less upon assisting or coaching students’ individual learning (in the sense of cognitive apprenticeship). Thus, these teachers likely still retain a whole-class orientation rather than a perspective centred on working continuously with flexible groups. Although the terminology used in the research of McQuarrie and McRae (2010) differs from the terms used in this study, a comparison of their DI strategy results for schools in Alberta with our results for schools in East Switzerland indicates

Table 2 Forms of DI: a categorisation of teachers’ answers. How do you realise/practice DI (max. 3 possibilities)? Categories

n answers

%

Differentiation of tasks or goals (difta) Adapt time or number of tasks (adtim) Individualised learning (indle) Peer work (peerw) Student-oriented, progressive teaching methods (stmet) Dividing class into groups (divcl) More coaching than instruction (coach) Other Variation of instructional methods (varin) Additional teaching staff (adtes) Formative assessment (formas) Rich, open-ended learning tasks (oplet) Diagnose prior knowledge (diagn) Total

56 41 34 31 28 28 13 12 10 9 8 7 1 278

20.1 14.7 12.2 11.2 10.1 10.1 4.7 4.3 3.6 3.2 2.9 2.5 .4 100

N ¼ 143.

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that flexible grouping is less common in our schools and that alternative assessments are very rare in East Switzerland, whereas peer tutoring occurs equally frequently and tiered assignments are very common in project schools in both Alberta and East Switzerland. It should be added that unlike the schools in Alberta, our schools are still in the beginning stages of the school improvement process. Several of our teachers mentioned that they often practice the stated strategies of DI. In most cases, the teachers apply these strategies once a week, while those who noted coaching and additional teaching staff use these strategies every day. A more indepth analysis further indicates that certain teachers have a broader view of DI than others. 4.1.2. Two groups of teachers practising DI As a next step, we were interested in the clustering practices of DI to obtain a clearer picture of the strategies that teachers may use in combination. Latent class analysis, a concept similar to cluster analysis, identifies latent variables that determine the membership of an individual teacher in a certain group based upon the practices that he or she mentions (Vermunt & Magidson, 2002). We compared a two- and a three-group model that were based on the categorised data shown in Table 2. The two-group model evinced slightly better fit indices with a BIC of 1389.22, an AIC of 1315.15 and an aBIC of 1310.12 than the three-group model, which had a BIC of 1436.55, an AIC of 1323.96, and an aBIC of 1316.31. In Fig. 3, the values that are shown indicate the conditional probability that a teacher of one of the groups would mention a certain category. Interpretation of this data must be undertaken cautiously as each teacher had to limit himself or herself to three practices, and several teachers indicated even fewer than three. Group 2 (n ¼ 80) is distinguished by the strategies differentiating the number of tasks, adapting time to work on tasks and peer work. It may be supposed that teachers in this group have a limited view of DI as a reactive strategy to address advanced or slow learners. At times, these teachers offer additional exercises to prepare the student for tests or to foster special interests. According to Tomlinson et al. (2003), these teachers seldom make pre-planned or proactive lesson modifications; moreover, they do not plan lessons for individuals or change assessment procedures. Group 1 (n ¼ 64), by contrast, embraces progressive teaching methods, such as plan or project work, in addition to ordinary whole-class instruction. Often, this group includes cooperative learning as well. Teachers in this group more frequently provide individual learning activities, and they may differ in other aspects as well, such as the use of formative assessment, but because these strategies were seldom reported by all teachers surveyed, no statistical basis for making this claim currently exists. In general, when examining the curve of group 1, it appears that these teachers hold a more holistic attitude towards DI than do those in group 2 and that they employ a greater variety of strategies. As progressive teaching methods require a significant amount of preparation time, it is likely that teachers in group 1 consider differentiation more often while lesson planning; thus, they employ DI proactively, which is a key aspect of successful DI (Chamberlin & Powers, 2010; Tobin & McInnes, 2008). There are no significant differences between the two groups with regard to contextual factors, such as length of service, gender or school type, though the last of these contextual variables evinced the greatest differences between the two groups. 4.1.3. Inductive and deductive approach combined As can be observed in Table 2 and Fig. 4, we measured DI, as deduced from theory, using a second-order scale (factor) based on 6 subscales, which was in accordance with our theoretical model (Fig. 1). It may be interesting to test whether the two groups

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Fig. 3. A conditional item plot for the two-class model of reported differentiated instruction strategies (please see Table 2 for abbreviation definitions).

identified differ not merely based on the teachers’ reported strategies but also on a theoretically underpinned survey scale. Predicted group 1 (M ¼ 3.00, SD ¼ .34) has a close-to-significant, t (140) ¼ 1.90 (p ¼ .059), higher value than group 2 (M ¼ 2.89, SD ¼ .36). This observation confirms the appropriateness of the groupings regarding the teachers’ reported DI strategies. 4.2. The influence of school team collaboration and school leader support on the practice of differentiated instruction Because our study provides information for an accompanying school improvement project, we were interested in the

relationships and linkages between school leadership, team collaboration, learning climate and teacher quality regarding the practice of DI. To study the relationship of these 4 unobserved, latent variables, we used manifest indicators that is, the scales as grouped in 4 topics (see chapter “measurements”). Our model (Fig. 4) consists of a measurement part for each of the 4 latent variables and a structural equation model. For the measurement part, each latent variable is based on a set of scales (the measures) similar to factor analysis. In the structural model, the theoretical causal relationships among the latent variables are described by means of a set of general linear equations. Dependencies are represented in diagrams by one-headed arrows (paths) representing

Fig. 4. A SEM of DI at the teacher level, N ¼ 162. All of the paths are significant, p < .01, and all of the effects are standardised. Dotted paths were tested in earlier model versions but found to not be significant.


regression relationships. We expected that our teacher model, in accordance with the literature (e.g., Hopkins, 2001), would produce a hierarchical path from school leadership (SL) to team culture (TC) and learning climate (LC). LC should have an effect on TC and DI. Therefore, the fewer problems a teacher has with discipline, the higher the realisation of DI should be. This first model has the following fit indices: c2 ¼ 109.09, df ¼ 85, p ¼ .04, CFI ¼ .97, TLI ¼ .95, and RMSEA ¼ .05. As this first model showed, for some paths, insufficient regression coefficients, we explored further models with fewer and/or different paths. The final model (Fig. 4) only shows an effect of SL on TC (b ¼ .49), not the effect of SL on LC. Pedagogical TC appears to be the most effective variable as it influences both LC (b ¼ .39) and the practice of DI (b ¼ .68). Teachers who use DI strategies to a greater extent more frequently report that their team possesses a high pedagogical TC. This relationship is even stronger for LC. In addition, there is no direct path from LC to the practice of DI. This finding implies that a good climate in the school and classroom is not a precondition for the implementation of DI, although teachers often cite a difficult climate as a reason for not practising DI (Tomlinson, 2001; Tomlinson et al., 1997). The final model has the following fit indices: c2 ¼ 79.37, df ¼ 74, p ¼ .31, CFI ¼ .99, TLI ¼ .99, and RMSEA ¼ .02. Additional multilevel path analysis was applied to check for separate effects at the school and the teacher levels. There is a small degree of variance (14% of the total) between schools with respect to DI. This value corresponds to the results from Goddard et al. (2010), although the Goddard study used a much larger sample (77 schools). Teacher gender and school type do have effects on DI, but only at the teacher level. Female and primary teachers practice more DI than male and secondary teachers. Contrary to the study of Goddard et al. (2010), there is no effect of school leader or team on DI at the school level. This discrepancy may be due to the small sample size. The support of a school team for a teacher practising DI is perceived differently within each school but not differently between schools. Teachers demonstrating a rather high inclination to employ DI feel that they are supported by their school team, whereas teachers in teams that use DI less frequently consider their teams to be less collaborative with respect to pedagogical issues.

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large-scale assessments (Hargreaves, 2001), satisfying results from such tests based on core topics of the curriculum do support acceptance of changes in teaching practices. For approximately half of the sample, data from a standardised mathematics test and a German test were available to assess the effects of DI on student achievement. As the total points for each grade were different, the individual points for each test were normalised as the difference from the cantonal reference group’s mean. All of the continuous predictors were z-standardised to facilitate the interpretation of different variables within one sample (Hox, 2002). The test results for mathematics (M ¼ 1.51, SD ¼ 6.63) and German (M ¼ 2.35, SD ¼ 9.51) were both higher in the sample examined than in the reference group. We calculated first the intraclass correlation (ICC) for both achievement test scores to determine the proportion of variance for the school, class and student level. As the schools barely differ in their achievement test scores, only 1.3% for mathematics and 0% for German at the school level, we continued a further analysis at only two levels. In a first multilevel model, DI was used as a predictor for achievement (Table 3). This answers the question whether the quality of a teacher’s practice of DI has an impact on student test outcomes. However, DI showed no significant effect on either mathematics or German test results. Because DI is influenced by team culture (TC), a second model controls for TC’s influence on achievement. Whereas TC shows a close-to-significant effect for mathematics (p ¼ .058), the effect for German more clearly lacks significance. Stronger effects result from student context variables as both gender and language demonstrated significant effects on achievement, males had better results in mathematics and females scored higher in German. Those students who speak Swiss German at home exhibited generally superior results to those who use a foreign mother tongue. For each model, the total variance explained (R2) at each level is presented in Table 3. As an example, for model 1 (M1), gender and language explain 7% of the variance in mathematics achievement within classes, and together with DI, they explain 1% of the variance between classes. 5. Discussion

4.3. The effects of differentiated instruction on student achievement 5.1. How do teachers practice differentiated instruction? It is important to demonstrate that policy makers and parents do not have to fear negative effects of DI. Therefore, we examined student outcomes that were dependent on the teachers’ use of DI. Although individual student learning is difficult to measure with

According to the international literature, certain countries with small schools report a high level of DI (e.g., the Scandinavian countries), whereas small schools in other countries, such as

Table 3 The effects of differentiated instruction and pedagogical team culture on achievement tests.

Intercept Fixed effects Student level Gender male Language Swiss-German Class level Differentiated instruction DI Pedagogical team culture TC R2 student R2 class

Mathematics test

Mathematics test

German test

M1

M2

M1

German test M2

Coefficient

(SE)

Coefficient

(SE)

Coefficient

(SE)

Coefficient

(SE)

15.42

(.95)

15.45

(.09)

29.90

(1.37)

29.95

(1.35)

1.48 3.46

(.49)* (.74)*

1.47 3.45

(.49)* (.74)*

.56 3.21

(.71) (1.07)*

.59 3.22

(.71) (1.07)*

.21

(.65)

.12

(.93)

1.24 .07 .11

(.66)*

1.56 .02 .08

(.95)

.07 .01

*p < .05 (SE) ¼ standard error. N ¼ 446 within 38 classes. Random-intercept models were employed. The predictors were z-standardised, except for dummy variables.

.02 .01

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England, do not exhibit a developed culture of DI (Hargreaves, Kvalsund, & Galton, 2009; Kvalsund & Hargreaves, 2009). However, DI is not limited to small schools and is mostly applied when considering student diversity. Most research studies on DI have been conducted in the United States, though DI is not a common practice in that country. The teachers in our study report that they realise DI primarily by differentiating tasks or goals, adapting the time for or number of tasks and individualising student learning. However, these practices are not performed on a daily basis but are implemented on an occasional basis as add-ons to regular instruction. As Hugener, Krammer, and Pauli (2008) demonstrated in their video study, elements of DI in Swiss mathematics lessons in secondary schools are seldom practiced. In our survey study, teachers stated that, on average, 38% (SD ¼ 26%) of their weekly lessons were differentiated. This value is higher than the 10e20% found in Hugener’s et al. study of DI in mathematics lessons. It is unclear, however, what criteria the teachers in our study used to rate themselves. If we consider the elements that they mentioned in Table 2, we may assume that adapting the time or the number of tasks is already viewed as DI, which is accurate, but this approach is just one strategy and it does not require the teacher to give up whole-group teaching. However, certain teachers who incorporate progressive teaching methods apply more DI strategies and appear to have a more integrated perception of education, including elements such as grouping students. They also believe that teachers, in addition to giving direct instruction, should act as learning coaches, offer necessary support for students, and conduct formative assessments/assessments for learning. Overall, our teachers do not exhibit great variance regarding their practices of DI, as the standard deviation for the DI factor is very small. We also found no differences between schools regarding a culture of DI. Krätzschmar (2010), who conducted a longitudinal study within a school improvement project that combined multi-age classes and individualised instruction, could report only a few effects from multi-age classes or individualised teaching strategies with respect to different self-concepts of the students. Accordingly, she concluded that teachers starting with a school improvement project often do not show differences in their (differentiated) instruction design, possibly because they lack sufficient experience. In summary, the teachers in our sample of small schools do not yet possess a very elaborate practice of DI, although some of the surveyed teachers do stand out for their professionally integrated views, thus enabling them to apply more of the elements in our research model. Based on the interviews with teachers and on the teacher portfolios, we learnt further details regarding exactly what the teachers do when they implement DI (Smit et al., 2011), but in general, our conclusions were confirmed. While we visited some of our project schools, a systematic observation approach could help to describe, in greater detail, the differentiated lessons tested by our teachers.

reiterate that school leaders’ influence on student learning is mediated by teachers and/or school climate. A meta-analysis by Robinson et al. (2009) presents some positive examples indicating that strong pedagogical leadership can affect student outcomes mediated by staff development. However, from our own project, we learnt that, if such leadership is missing, teacher collaboration could affect the necessary professional development. A professional learning community with teachers learning to advance classroom practice is the centre of school improvement (Bryk, Camburn, & Louis, 1999). According to the recently published MetLife Survey (Metropolitan Life Insurance Company, 2009), collaboration among teachers improves school climate and teacher career satisfaction and results in positive consequences on student achievement. Respondents who say that they are very satisfied with teaching as a career are more likely to strongly agree that the teachers in a school are responsible for the achievement of all students. Younger teachers, in particular, recognise a need to improve teacher collaboration with regard to DI. Our study supports these results concerning the effect of teacher collaboration on school climate and on student achievement. Moreover, a high pedagogical team culture appears to have a positive influence on a teacher’s individual practice of DI. In a rural school improvement case study by Chance and Segura (2009), collaboration was the heart of the success. By shortening one school day a week, teachers had time to become truly involved in decision making for school improvement. Additionally, leadership ensured that planning was student-centred and that teachers were held accountable for specific actions. As our schools vary with respect to team collaboration, it may be interesting for future research to observe whether team-oriented school improvement with a focus on DI leads to greater variation between schools for this variable. Finally, this aspect could lead to more distinct effects of DI on student outcomes. The study by Opdenakker & Van Damme revealed that schools could affect the outcomes of their students independent of their student composition and context by means of school practice. We agree with Mulryan-Kyne (2007) that multi-grade teachers need on-going support rather than a “quick fix”. However, because small schools consist of few teachers, internal team development may be difficult or limited. Therefore, networking between small schools should be fostered so that a variety of successful DI strategies can be shared (Wallin & Reimer, 2008). The schools in our project have started a community of interests to exchange pedagogical, financial and political strategies. Staff development should address the reality that teachers differ in readiness, interests, and learning profiles (see our groups 1 and 2) and thus offer adaptive support. Certain teachers, e.g., those from our group 1, may serve as teacher leaders and assist with professional team development (Tomlinson, 2005).

5.2. Do school team collaboration and school leader support influence the practice of differentiated instruction?

First, classes that implement DI do not experience poorer performance on standardised achievement tests. This fact is important for stakeholders, such as parents and policy makers. However, this study could not confirm the positive results from DI on student achievement as stated by Scheerens (2000), either. One possible reason for this lack of confirmation may be that the standardised tests were not directly related to the actual lessons being taught using DI strategies. Because DI needs to be aligned with appropriate formative assessments to fully develop its relevance for learning, more authentic assessments are likely better suited to show the effects of DI. The best research design to test for the effects of DI is an experimental design with a control group. Baumgartner et al. (2003) and Tieso (2005) both used this design

The influence of a school leader on school improvement is limited without the involvement of the school team. In our model, there is no direct link between school leadership and DI, as was found in the study of Goddard et al. (2010), but there is an indirect link via team culture. This result is consistent with that of Opdenakker and Van Damme (2007). In their study, school leadership did not greatly affect school practice, perhaps because of the lack of strong educational leadership in most of the Flemish secondary schools e a concern that may apply to the leadership in Swiss schools as well. In addition, Hallinger and Heck (1998)

5.3. Does differentiated instruction affect student achievement?


and reported positive effects. It is often difficult for a researcher to control the experimental conditions within school improvement projects. In our project, for example, the participating teachers could choose two out of four in-service training modules. It was up to the teachers to decide the number of differentiated instruction lessons to develop and to select the subjects within which they would incorporate these lessons. There are many other factors that influence achievement, such as studenteteacher relationships and the quality of direct instruction (Hattie, 2008), as well. In addition to DI, we examined the teacher team culture in the school. School teams that are open to innovation, that share a pedagogical vision and that have time to discuss pedagogical topics appear to be more favourable with respect to student achievement. This observation is in accordance with the results of Opdenakker and Van Damme (2007), who demonstrate that the effects of school size on school climate and student outcomes, among other factors, were mediated by the amount of cooperation among the teachers.

5.4. Limitations and implications for future research All of the analyses were conducted within a limited sample of schools that voluntarily participated in our research and school improvement project. Further research should attempt to enlarge the sample to cover complete (alpine) regions, which should lead to higher external validity. A larger sample should also enable one to conduct separate modelling for school type (primary/secondary school), although we controlled for school type in our student model within this study. It should be mentioned that multi-grade secondary classes are not allowed in several Swiss cantons. As a result of our project, however, the government has changed its views and has become more open to discussing local needs. We attempted to consider many aspects of the small schools’ problems with respect to teaching improvements in our study and were able to clarify certain relationships, whereas others remain for further research. One important question that we did not cover is the relationship between DI and class size. Do teachers feel more at ease implementing DI with smaller classes? In our study, teachers from primary classes use DI more often than teachers at the secondary level, who have larger class sizes. Brühwiler and Blatchford (2010), however, suggest independence between class size and teacher quality. Consequently, future research should help to clarify the connection between class size, DI quality and grade level. From the final evaluation of the school improvement project (Smit et al., 2011), we know that changing teachers’ instructional habits requires more than two years. This conclusion is particularly true if school teams and leaders must find common ground before pedagogical issues can be addressed. Fortunately, almost all of our project schools were granted an extension in time to continue work on the projects’ aims before the government finally makes a decision regarding school closures.

Acknowledgements The present study was based on the research project ‘‘Schools in Alpine Regions”, which was funded by the Interreg IV, Regio lake of Constance (Project number 96). We are very grateful to the research team (Dr. Alois Keller, project leader and the coaching team), as well as to the teachers and children who gave their time to take part in this research.

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Robbert Smit is an educational researcher at the University of Education at St. Gallen, Switzerland. He received his PhD (2009) in Educational Science from the University of Zurich. He is also an experienced secondary school teacher. His main areas of interest are school improvement, teacher education and formative assessment.

Winfried Humpert (PhD) is an educational researcher and lecturer at the University of Education of St. Gallen. He has published books on teacher training and statistics.