Teachers and differentiated instruction: exploring differentiation practices to address student diversity

Given the increasing diversity of the student body, teachers are called to appropriately address students ’ various learning needs by means of differentiated instruction (DI). However, empirical research has yielded mixed evidence on teachers ’ reported use of DI. Using nationally representative data from the National Educational Panel Study in Germany, this article aimed to explore German (as native language) and Mathematics teachers ’ use of DI practices. In addition, this study took into con-sideration contextual factors, such as school track, and investigated the impact of teachers ’ constructivist beliefs on their DI implementation. Results from a mixed analysis of covariance indicated that teachers occasionally implement DI practices. Fur-thermore, between-subject effects reported differences across school tracks. It appears that advanced secondary school teachers implement less often DI practices. The covariate of teachers ’ constructivist beliefs was also positively linked to overall teachers ’ implementation of DI. Implications of the results, as well as further lines of research are discussed.


Introduction
Even though school systems worldwide have responded to student diversity by establishing classrooms with different levels of student ability (tracking or streaming) (Dupriez, Dumay, and Vause, 2008), large-scale data (e.g. PISA) clearly indicate that the diversity of the student population is substantial and continuously increasing (Dixon, Yssel, McConnel, et al., 2014). Students differ greatly in terms of performance, cultural background, language competence, gender-based learning preferences, learning styles, motivation, interest, self-regulatory competencies and other features (Dijkstra, Walraven, Mooij, et al., 2016;Tomlinson, Brighton, Hertberg, et al., 2003;Wenning, 2007). As used herein, dealing with student diversity encompasses the requirements associated with inclusive education. In this line, in order to address students' various learning needs, teachers must be able to adequately differentiate their instruction.
Differentiated instruction (DI) is a well-known and practice-proven approach that responds effectively to the diverse students' needs (Coffey, 2011;Coubergs, Struyven, Vanthournout, et al., 2017;Hall, 2002;Landrum and McDuffie, 2010;Lawrence-Brown, 2004;Santangelo and Tomlinson, 2009;Smit and Humpert, 2012;Tomlinson, 2014;Wischer and Trautmann, 2012). Within DI research, there is evidence that supports this claim. Valiandes (2015), for example found that students in classrooms where teachers implemented DI performed better compared to those students who did not receive DI. Similarly, Reis, McCoach, Little, et al. (2011), as well as Baumgartner, Lipowski and Rush (2003) reported positive effects of DI on students' achievement, specifically on their reading fluency and comprehension.
As the successful and effective implementation of DI relies mainly on teachers, research has focused on examining how and how frequently teachers differentiate their day-to-day instruction. Empirical research has yielded, however, mixed evidence on teachers' reported use of DI. For instance, Moon, Callahan, Tomlinson, et al. (2002) reported that teachers rarely use DI practices in their everyday teaching. Similarly, Smit and Humpert (2012) indicated that teachers occasionally make use of DI practices. Moreover, their findings also indicate that teachers show rather low variance in their use of DI practices as they substantially differentiate by tiering activities or implementing flexible grouping. In contrast, Roy, Guay and Valois (2013) reported a moderate usage of DI practices, whereas Prast, van de Weijer-Bergsma, Kroesbergen, et al. (2015) indicated a higher implementation rate.
Given the mixed state of evidence, there is still a clear need to explore in detail how teachers differentiate their instruction, particularly from large-scale studies on DI (Graham, Morphy, Harris, et al., 2008;Prast, van de Weijer-Bergsma, Kroesbergen, et al., 2018;Ritzema, Deunk, and Bosker, 2016). In addition, research must take into account the potential effects of context factors (e.g. school subject) on teachers' DI application (see Prast, van de Weijer-Bergsma, Kroesbergen, et al., 2015;Ritzema, Deunk, and Bosker, 2016). Therefore, this study aims to explore secondary school teachers' implementation of DI practices using large-scale data from the National Educational Panel Study (NEPS). The NEPS is a longitudinal study on education conducted nationally in Germany that follows a multi-cohort sequence design with the aim to examine educational processes and outcomes in different developmental stages of life (Blossfeld, Roßbach, and von Maurice, 2011). Specifically, this study examines secondary teachers' use of distinct DI practices in German (as native language) and Mathematics lessons across school tracks, and further explores whether the implementation of these practices are influenced by teachers' constructivist beliefs.
For the purpose of this study, DI is conceptualised as a toolbox of instructional practices, which enables teachers to appropriately cater to students' specific learning requirements and ensure successful learning for all students within a diverse and inclusive classroom. The following section will briefly discuss the current state of literature on DI in order to clarify the conceptualisation chosen for this study. Afterwards, it will elaborate on the taxonomy of DI practices (Pozas and Schneider, 2019) that guides this paper.
A taxonomy of DI practices Worldwide, literature and research has acknowledged DI as a set of effective instructional practice (Chamberlin and Powers, 2010;Lawrence-Brown, 2004;Tomlinson, Brighton, Hertberg, et al., 2003). Given the importance of DI, a number of well-established models have been proposed (e.g. Hall, 2002;Lawrence-Brown, 2004;Tomlinson, 2014) varying in terms of their structure, elements and preconditions for differentiation (for a comprehensive discussion of these models please refer to Pozas and Schneider (2019). In spite of the extensive literature and models on the topic, however, there is still no theoretical agreement on the conceptualisation of DI (Jennek, Gronostaj, and Vock, 2019;Roy, Guay and Valosi, 2013). In return, the term DI has been used as a one-dimensional construct of single practices such as learning centres, small-group interaction and tiered activities (e.g. Coffey, 2011;Latz and Adams, 2011;Levy, 2008;McTighe and Brown, 2005;Santangelo and Tomlinson, 2009). Consequently, this one-dimensional approach hinders the possibility of testing the effectiveness of unique DI practices for addressing in-classroom student heterogeneity (Valiandes and Koutselini, 2009).
Additionally, within the literature on DI, there is a large variety of instructional practices that teachers can make use of in order to address diversity within a classroom. However, teachers' implementation of DI in their daily teaching practice remains critical (Suprayogi, Valcke, and Godwin, 2017). It seems that many teachers either feel overwhelmed by the vast amount of possible practices at hand (Reis, McCoach, Little, et al., 2011), report feeling unprepared by their teacher training to effectively use DI (Idol, 2006), or simply have a lack of understanding of DI (Whipple, 2012). As a result, it is likely that teachers end up selecting single practices on an arbitrary basis without critical reflection of its practical implications and, thus, with suboptimal outcomes.
These barriers inherently limit the effective implementation of DI and call for a systematisation of the DI construct and a categorisation of the possible instructional practices applied to address the broad array of student differences. To this aim, and in order to facilitate secondary school education teachers' instructional decisions, Pozas and Schneider (2019) propose a taxonomy of DI practices attempting to bridge the gap between educational theory and everyday instructional practice. The taxonomy is framed within the current DI literature and research and builds on existing literature by providing teachers with practical and concrete advice on how to design and differentiate their instruction to successfully address classroom diversity. The taxonomy of DI practices is divided into six categories: 1. Tiered assignments: qualitative and/or quantitative variation of materials and tasks according to challenge level, complexity, outcome, process, product, and/or resources. 2. Intentional composition of student working groups: establishing decidedly homogeneous or heterogeneous subgroups based on performance, readiness, interests, etc. 3. Tutoring systems within the learning group: high ability students take up the role of teacher assistants and tutor low ability students. These roles may persist for a long term. 4. Staggered non-verbal learning aids: carefully and purposely designed series of learning aids that range in complexity level. The learning aids must only contain the minimal information necessary for a student to overcome an obstacle in the learning process. If they still are unable to deal with the task, a second aid with additional information and guidance is provided, and so on. 5. Mastery learning: all instructional practices which ensure that all students achieve at least minimum standards (in combination with higher standards for the more advanced students). This involves close monitoring of students´learning progress. 6. Open education/granting autonomy to students: students are responsible for their own learning process and may autonomously decide on materials to work upon. Examples of such practices include: student choice of tasks, station work, project-based learning, portfolios, etc.
Despite being distinct instructional methods, the different practices categorised within the taxonomy are not necessarily conceptualised to be implemented uniquely. Some practices may only be effective when used in a meaningful combination. For instance homogeneous within-class grouping demands implementing adapted assignments or materials (Lou, Abrami, and Spence, 2000), and heterogeneous within-class grouping suggests setting up peer tutoring systems (Slavin, 1987). In other situations, however, the different DI practices might limit each other's practical use: mastery learning implies teachers' thorough monitoring of students' learning progress, whereas open education/granting autonomy suggests quite the opposite.
Therefore, none of these practices can be identified as 'the most appropriate', given the fact that each practice may have its advantages and disadvantages. In addition, as empirically proven, their effective implementation will depend on learner's characteristics, such as student's age and specific learning prerequisites, or teacher's characteristics, such as growth mindset and constructivist beliefs (Coubergs, Struyven, Vanthournout, et al., 2017;Dijkstra, Walraven, Mooij, et al., 2016;Dweck, 2010). Likewise, context factors such as school subject (Prast, van de Weijer-Bergsma, Kroesbergen, et al. 2015;Ritzema, Deunk, and Bosker, 2016) and school track (Jennek, Gronostaj, and Vock, 2019) can also influence teachers' implementation of DI practices.

Context factors
School subject A context factor that may essentially influence teachers' use of DI practices is the school subject. Wiley, Good and McCaslin (2008) found that Mathematics lessons have the tendency to be more structured than reading lessons. The nature of a subject-domain may inherently guide how teachers implement DI practices (Prast, van de Weijer-Bergsma, Kroesbergen, et al., 2015). A study by Nurmi, Viljaranta, Tolvanen, et al. (2012) examined how Finnish teachers adapted their instruction according to their students' performance level in the subjects of Reading and Mathematics. Even though teachers tailored instruction according to students' achievement level, the teaching practices varied considerably across domains. In contrast to Wiley et al.'s research (2008), in this study, Finnish reading lessons tend to be far more structured and teacher-directed in comparison to (Finnish) Mathematics, where lessons are far less structured and teachers have more freedom to vary their instructional practices.
In a recent study by Ritzema, Deunk, and Bosker (2016) where Dutch second-and third-grade teachers' DI practices in Reading and Mathematics were explored, important variations among the subject-domains were also observed. More specifically, results show that teachers included more content in their reading lessons, as well as implemented more whole-class instruction, whereas Mathematics teachers relied on more organisational discourse, extended instruction and seatwork. Overall, Ritzema, Deunk, and Bosker (2016) reported that Mathematics teachers implement DI practices more often.
In order to investigate the use of DI practices in Germany, Westphal, Gronostaj, Vock, et al. (2016) compared teachers' use of DI in the subjects of Mathematics and German. Their findings indicated significant variations between the subjects, it appears that Mathematics teachers differentiate their instruction more often than German teachers. In detail, the study revealed that tiered assignments ranging in difficulty levels are far more implemented by Mathematics teachers than German teachers.

School track
School track is another important contextual factor that seems to play a crucial role when implementing DI. According to Gamoran (1992), it appears that tracked schools with a certain degree of flexibility (i.e. having tracked courses, such as specialised advanced courses) implement more DI practices in comparison to highly selective school systems or forms of organisation which inherently build on ability tracking. Germany 1 implements a formalised tracking system in which students are assigned to a secondary school based on academic ability (Grade 5) at an early age. As the German federal states (L€ ander) are primarily responsible for the education system, tracking systems slightly vary across the country. However, the Standing Conference of the Ministers of Education and Culture (Kultusministerkonferenz, KMK) that is in charge of the coordination and development of education in the country, establishes the following main secondary school tracks (KMK, 2017): Since in Germany ability tracking is the standard in secondary education, variations of teachers' use of DI practices within tracks have been reported. Evidence from PISA 2009 (Hertel, Hochweber, Steinert, et al., 2010) for the subject of German reveals that comprehensive school teachers implement the most DI practices and are followed by general secondary school and school with different courses of education teachers. In contrast, teachers in advanced secondary schools (the most highly selective school track in Germany) reported a rare implementation of DI practices (Hertel, Hochweber, Steinert, et al., 2010;Letzel and Otto, in press).
A recent study by Jennek, Gronostaj, and Vock (2019) indicated that, on average, the overall use of DI does not differ significantly between school tracks. Even when looking deeper into the specific single implemented DI practices, such as tiered assignments or learning aids, the authors found no clear differences among the school tracks.
In sum, the implementation of DI could be influenced by the subject-domain and school track. Therefore, such contextual factors must not be neglected when examining teachers' use of DI.
Teacher characteristics: teacher beliefs Scientific literature and theoretical models have stated that teachers' beliefs are important variables influencing teachers' response to their learners' needs (e.g. Mansour, 2009;Smit and Humpert, 2012;Tomlinson, 2003). Even though there is no universal definition, it is commonly known that beliefs are non-scientific notions referring to psychological understandings, premises or propositions that are felt to be true (Richardson, 1996). Pajares (1992) stated the need to differentiate knowledge from beliefs: 'Belief is based on evaluation and judgement; knowledge is based on objective fact' (p. 313). Teacher beliefs can be linked to, for example their view on the way students learn, as well as on which teaching practices are effective or the role of learners' activity, and are therefore highly connected to teachers' activities in the classroom (Hancock and Gallard, 2004;Oser and Bl€ omeke, 2012). Moreover, they are seen as one of the most important determinants of professional behaviour (Schneider, Pakzad and Schl€ uter, 2013) and can be understood as the convictions, philosophy, tenets, or opinions about teaching and learning (Milner, Sondergeld, Demir, et al., 2012). Therefore teachers' beliefs refer to views on specific teaching practices, teaching approaches such as direct-transmissive or constructivist, and views concerning student diversity, learning and ability (Fives and Buehl, 2012). Literature distinguishes two types of beliefs: direct-transmissive and constructivist beliefs (e.g. Baumert and Kunter, 2006;Peterson, Fennema, Carpenter, et al., 1989;Staub and Stern, 2002). Teachers holding direct-transmissive beliefs rather tend to structure their contents and to see the learning process as the transfer of knowledge from teacher to student (Sfard, 1998). In contrast, teachers understanding learning as an active process rooting in the students themselves and focusing on their previous knowledge as well as their interests rather hold constructivist beliefs (e.g. Bereiter, 1994).
Both literature and research have continuously suggested the positive influence of teachers' constructivist beliefs on their use of DI (Dijkstra, Walraven, Mooij, et al., 2016;Tomlinson, Brighton, Hertberg, et al., 2003). Smit and Humpert (2012), for example indicated that teachers holding constructivist beliefs tend to make a frequent use of a greater variety of DI. The same was found by Tomlinson (2003): DI was linked to constructivist instructional approaches, student collaboration, individual differences, personal meaning development, etc. This study recognises the theoretical and empirical significance of teachers' constructivist beliefs, and therefore, they are considered within this investigation.

Purpose and research questions
Despite the importance of DI for successful learning, research into how teachers implement DI is still scarce (Graham, Morphy, Harris, et al., 2008;Prast, van de Weijer-Bergsma, Kroesbergen, et al., 2018) and the small amount of research available has yielded heterogeneous results. Therefore, the aim of this study was to use nationally representative large-scale data from the NEPS in Germany in order to explore how distinct DI practices are applied in classroom teaching taking into account contextual factors such as school subject and school track. Additionally, teachers' constructivist beliefs were included as covariates. The research question guiding this study was: Which DI practices do teachers apply in their classroom teaching and how often?
To explore this research question, two sub-questions were formulated: Does the implementation of DI practices vary across school tracks and school subjects? To which extent is the implementation of DI practices related to teachers' constructivist beliefs?
Based on existing DI research, it was hypothesised that tiered assignments and intentional composition of student working groups would be the most frequently implemented DI practices (Smit and Humpert, 2012). Furthermore, it is assumed that significant differences among the use of DI practices between the subjects of German and Mathematics, as well as variations amongst school tracks are to be found: specifically, it was expected that less selective school types (such as general secondary school or comprehensive schools) encourage the most frequent use of single DI practices. Finally, it is hypothesised that teachers' constructivist beliefs are positively associated to teachers' implementation of DI practices.

Sampling and sample
The analysis of this study was conducted using the nationally representative data from the NEPS in Germany.
The NEPS provides Scientific Use Files (SUF) for registered users that include separate data files corresponding to student, teacher and parent questionnaires. For the purpose of this study, the starting cohort three which assesses students entering Grade 5, was selected. The first wave of data collection began in 2010 (fifth grade), and up to now there are data obtained from seven measurement points (sample entering the tenth grade).
The analyses were conducted with data from the measurement points in sixth and ninth grade taken place during 2011 and 2014. The total sample consisted of 1164 sixth (N 6 = 475) and ninth grade (N 9 = 689) teachers (65% female). NEPS provides five age categories in their SUF, see Table 1 for details. The sample is divided correspondingly into the school subjects of German and Mathematics and was stratified according to school track within the . Teachers from special education schools 2 were excluded from this study, as well as teachers with missing data.

Instruments
NEPS uses three different types of self-report questionnaires for teachers: (1) the general questionnaire for all teachers, (2) the class teacher questionnaire and (3) the subject-specific (Math and German) teacher questionnaire. The subject-specific teacher questionnaire includes items that collect information on the quality of teaching as well as how they organise their instruction and learning.
DI practices. For the purpose of our study, the subjectspecific (Math and German) teacher questionnaire that contains items that correspond as to how (and with which frequency) teachers conduct, plan and organise their lessons were selected (see Table 2 for descriptive statistics    (2010). The scale consists of four items based on a 4-point scale (1 = completely disagree to 4 = completely agree) (i.e. 'My role as a teacher is to make it easier for the students to investigate and explore things'.) (a = 0.61).

Analyses
In order to answer the research question and sub-questions, a mixed analysis of covariance was used. In line with the DI taxonomy guiding this study (Pozas and Schneider, 2019), all items pertaining to DI practices were submitted to a mixed ANCOVA as dependent variables, while school track and school subject were included as independent variables. Teachers' constructivist beliefs were used as a covariate.
To reduce complexity and provide comparability, items pertaining to Category I. tiered assignments (slow/fast students, additional assignments and extra assignments) were combined into a mean score. This mean score served as a within-subject factor. Additionally, the DI items of tutoring and project-based learning were originally measured with a 6-point Likert-scale. Consequently, it was necessary to adjust them to a 5-point Likert-scale range in order to include them in the analysis.
With regard to assumption considerations, it is important to note that the sphericity assumption was violated and the Greenhouse-Geiser e exceeded 0.75, thus, the Huyhn-Feldt corrected test statistic is reported for the within-subjects factor and the interaction.

Results
The mixed ANCOVA indicates that the contextual factors have an influencing role on teachers' use of DI practices. Specifically, the tests of between-subject effects of the mixed ANCOVA results reported a significant main effect of school track, F(4, 828) = 5.99, P < 0.001, partial g 2 = 0.03. Overall it appears that advanced secondary school German and Mathematics teachers implement DI practices less often in comparison to their counterparts in other school tracks, thus, they show to have a smaller repertoire of DI practices. In addition, the covariate of teachers' constructivist beliefs were significantly positive related to teachers' implementation of DI practices, F(1, 828) = 26.87, P < 0.001, partial g 2 = 0.03.
The tests of within-subject effects showed significant variations within the single use of DI practices, F(3.61, 2991.80) = 6.12, P < 0.001, partial g 2 = 0.01. In detail, teachers tend to differentiate their instruction predominately using tiered assignments and building heterogeneous (ability-level) groups, while they seldom differentiate by carrying out project-based learning and building homogeneous groups (Figure 1). The implementation of tutoring systems, in contrast, appears as well to be seemingly practiced, yet far less than tiered assignments or heterogeneous groups. Furthermore, a significant interaction effect between the DI practices and school subject (F(3.61, 2991.80) = 23.59, P < 0.001, partial g 2 = 0.03) (Figure 2), as well as a significant interaction effect between the DI practices and school track (F (14.45, 2991.80) = 4.37, P < 0.001, partial g 2 = 0.02) ( Figure 3) were found, indicating that these pattern of effects concerning the differences within the use of DI practices appear to be consistent across both subjects and school tracks. Finally, a significant interaction effect among DI practices, school subject and school track was revealed (F(14.45, 2991.80) = 1.70, P < 0.05, partial g 2 = 0.01). These findings indicate important significant differences, particularly, for the use of tutoring and project-based learning. It appears that Mathematics teachers across all school tracks tend to implement tutoring systems far more often than project-based learning. In contrast, German teachers tend to rather implement projectbased learning than tutoring systems across all school tracks (Figure 4a and b).
Overall, the results clearly indicate that, (1) in general, teachers indeed apply DI practices in their in-class instruction, however, the frequency in which they implement such practices is less than recommended for successfully dealing with heterogeneity (Moon, Callahan, Tomlinson, et al., 2002) and (2) when they actually do implement DI, they mostly adhere to tiered assignments and heterogeneous ability groups which clearly indicates that teachers hold a rather low variance of DI practices.

Discussion
While it is widely acknowledged that teachers must differentiate their instruction to address the diverse students' needs, little research has been conducted across largescale data to empirically explore how teachers implement specific DI practices. This study tackles the current gaps in DI empirical research and seeks to further contribute by taking into account contextual factors and teacher characteristics that may influence teachers' use of DI practices. The aim of this study was to explore in detail how and with which frequency sixth-and ninth-grade German and Mathematics teachers across different school tracks in Germany apply DI practices in their in-classroom teaching.
Concerning the general research question, teachers do in fact make use of DI practices, nonetheless, in a very low frequency. This result is in line with previous international research that has also found that teachers have, without a doubt, a considerable room for improvement (Moon, Callahan, Tomlinson, et al., 2002). Additionally, the findings indicate visible differences within the distinct DI practices. First, tiered assignments are, by far, the most applied DI practice. This result is not surprising, as previous research has shown that teachers commonly address student needs by tiered assignments (Smit and Humpert, 2012). Second, consistent with previous research, intentional composition of student groups was also reported as a frequently used DI practice (Tieso, 2005). It appears that the implementation of intentional composition of student groups is commonly regarded by teachers, as a simpler practice to prepare and carry out (Chiner and Cardona, 2013). In detail, results indicate that both German and Mathematics teachers across school tracks tend to build heterogeneous ability groups in order to support low, medium and high achievers (Lou, Abrami, Spence, et al., 1996). However, no concrete information on whether teachers have built such heterogeneous groups intentionally or rather spontaneously, as well as whether these groups are formed for a short or long amount of time. Moreover, NEPS does not provide information on whether teachers form groups based on alternative grouping formats, such as grouping according to students' academic self-concept, interest, motivation and other characteristics (Nielsen and Yezierski, 2016;Tomlinson, 2001).
Third, the least frequently reported DI practices were tutoring systems and project-based learning. In the case of tutoring systems, this result is quite unfortunate. According to Hattie (2009), peer tutoring has a large significant positive effect on student achievement (d = 0.55), and furthermore, fosters positive interactions between students (Wentzel, 2000). Likewise, project-based learning appears to be rarely used by teachers. This DI practice is a variant of open education, yet, this item alone is not broad enough to comprise the complete category of open education. It could possibly be that other variants such as portfolios, station work, interest-based centres (Tomlinson, 2001(Tomlinson, , 2017 are more commonly employed. Taken all together, the significant differences within DI practices seem to follow findings from previous DI research (Graham, Morphy, Harris, et al., 2008;Jennek, Gronostaj, and Vock, 2019;Schumm and Vaughn, 1991): teachers appear to implement more frequently those single

DI Practices
Project-based learning Tutoring systems Heterogeneous ability grouping DI practices that require less preparation. A first possible explanation could be related to the high workload that teachers face worldwide (OECD, 2014), and therefore, lack the time to plan and prepare for DI, as well as design the appropriate differentiated materials and tasks (Chiner and Cardona, 2013). On the other hand, previous research has reported that teachers express feeling unprepared to differentiate classroom instruction as a mean to appropriately address student diversity (Avramidis, Bayliss, and Burden, 2000;Dee, 2011;Gaitas and Martins, 2016;Hamre and Oyler, 2004;Tomlinson, Moon, and Callahan, 1998). Without the proper training, teachers are inherently unable to provide meaningful and successful instruction for all students, as they do not count with the knowledge on DI, and in the case of beginning teachers, the experience to teach diverse learners. It is then necessary and urgent that DI receives sufficient attention in pre-service education and further in-service teacher trainings.
Regarding the first sub-question, findings indicate a very similar overall response pattern for both, German and Mathematics teachers across school tracks. Evidently, teachers predominantly implement tiered assignments and heterogeneous ability groups as their main choice for differentiating instruction. Additionally, results also show that teachers in advanced secondary schools implement less often of DI practices. Gamoran (1992) discussed that teachers in high-track schools and classes tend to make use of less differentiation mechanisms as there is the belief that in more selective and 'top' tracks, DI is not necessary, given that the student body is mostly composed of high ability students.
Moreover, when examining in detail the interaction effect between DI practices, school track and school subject, clear differences arise within the DI practices of tutoring systems and project-based learning. Mathematics teachers indicated a higher use of tutoring systems compared to German teachers, whereas German teachers reported a slightly higher implementation of project-based learning. In particular, this difference across school tracks is mainly observed among German advanced secondary school. These differences could be attributable to the particular setup of the subject-domain that guides teachers' planning and preparing for DI (Prast, van de Weijer-Bergsma, Kroesbergen, et al. 2015).
Finally, concerning the second sub-question, results show that teachers' constructivist beliefs are indeed positively influencing teachers' use of DI practices. This result is

School subject
Mathematics German  with findings from, for example Smit and Humpert (2012) and Tomlinson (2003), and therefore, it is recommended that teachers' constructivist beliefs should be integrated in further DI research.

Limitations and further research
This study was focused on German and Mathematics teachers' implementation of DI practices across different school tracks, where their responses indicated how frequently they make use of DI practices. Consequently, such data does not provide information concerning the purposes or goals teachers intended to pursue using such practices (i.e. focusing on achievement or promoting social competences), as well as information on whether such practices were actually effective and successful. Further research should focus on exploring teachers' intentions behind the specific DI practices, and take a longitudinal approach that could shed light into the effects such practices have on student variables, such as achievement, motivation, self-concept, attitudes towards school, and social competencies. Moreover, research should examine the potential aptitude-treatment-interactions each DI practice may have on, for example high-, middle-or low-achievers, in order to ensure that DI is actually beneficial for all students.
A second limitation is that the study uses teachers' selfreports of DI; such responses can inherently be sensitive to overestimation, underestimation, or socially desired answers. Desimone, Smith and Frisvold (2010), however, found out that teachers' self-reports regarding their teaching practices are highly correlated to classroom observations. Future research should not only make use of selfreports but integrate classroom observations as well.
Furthermore, when examining teachers' constructivist beliefs, further research should consider exploring the influence beliefs have on each of the single DI practices applied in order to identify specifically which DI practices are strongly related to constructivist beliefs and which are not. This analysis would support pre-service and in-service teachers to adapt their beliefs to optimal differentiation practices.
Finally, it should be noted that the DI practices of staggered non-verbal learning aids and mastery learning are not included within NEPS teacher questionnaires, and, therefore, could not be entered in the analysis. Further research should incorporate such DI practices into their analyses, as according to Hattie (2009), mastery learning, for example has strong and positive effects on students' achievement.