Keyword

1 Introduction

Education systems are frequently designed to provide instructional opportunities for a heterogeneous group of learners. Especially since the ratification of the UN Convention on the Rights of Persons with Disabilities (CRPD) in 2009 (United Nations, 2006), there is an obligation to provide good and effective education for all children in Germany. Since this ratification, school inclusion is now a mandate for all educational institutions (KMK, 2011). The goal is therefore to produce the best possible academic and social development for all students. Previous studies have shown that the school system has not been well adapted to children at risk (e.g., children from poorer families, children with parents/legal guardians with low educational achievement, children from migration backgrounds, and children with special education needs: SEN). Such inclusive classrooms may contain students with differing backgrounds. For example, children may differ in terms of socio-economic status (SES), or their first language might differ from the one used in class. The same classroom may also contain students with differing prior ability levels, SEN, and academic self-perceptions. Moreover, instructors may also employ a varied set of instructional techniques (e.g., group work and classroom discussions) that are not always optimally suited to their diverse classrooms. These individual, environmental, and classroom factors are only a small part of the complex classroom environment. This chapter will examine these factors via two studies that draw on the German National Education Panel Study (NEPS; Blossfeld et al., 2011).

2 The Multilevel-Supply-Use Model

The multilevel-supply-use model (German; Angebots-Nutzungs-Model; Brühwiler & Blatchford, 2011; Helmke, 2009; Seidel, 2014) encompasses both individual and environmental learning factors. Within this model, instructional supply may be used by individual learners to reach educational outcomes. Instructional supply is defined as an interaction of classroom variables such as teaching methods, teacher characteristics, and classroom environment along with school-level variables. However, the use of the supply by the learner depends on an interaction with individual learning processes (e.g., instructional activities), individual preconditions (e.g., cognitive processes, self-perceptions, SENs), and their learning environments (e.g., family background, SES, migrant status). Subsequent sections will focus mostly on these three use aspects (for a more comprehensive review, see Brühwiler & Blatchford, 2011).

Within this context, risk factors may be individual or environmental. Individual risk factors may include the presence of SEN or low pre-existing ability levels, whereas environmental factors may include being a second-language learner or coming from a lower SES background. In addition, individual self-perceptions such as self-esteem and self-concept interact with both these risk factors and the instructional activities to produce learning outcomes. For instance, a child with a higher self-concept in math who comes from a poorer economic background may be at a lower risk of poor performance.

2.1 Environmental Learning Factors

Having a low SES has been frequently linked to worse educational outcomes. The link to lower SES is found in many countries and has been shown to contribute to a diverse set of learning outcomes (Bjorklund & Salvanes, 2011; Currie, 2009; DeVries et al., 2018a; Rambo-Hernandez & McCoach, 2014; White, 1982; White et al., 1993). Moreover, these findings generally hold regardless of SES or the other variables employed (e.g. Sirin, 2016). Being a second-language learner is also tied to a multitude of worse academic outcomes (Crosnoe & Fuligni, 2012; Duong et al., 2016; Solari et al., 2014). Within the multi-level supply-use model, these environmental risk factors are themselves associated with individual learning factors through which they interact with instructional activities. For example, a child who is a second-language learner may have trouble understanding longer, language-heavy instructions (e.g., lectures) due to increased cognitive demand.

2.2 Individual Learning Factors

Individual factors themselves may also present a risk for poorer educational outcomes. For instance, learners with SEN often attain worse academic outcomes (Gebhardt et al., 2015; Korhonen et al., 2014). This is complicated by additional factors such as higher levels of social exclusion (DeVries et al., 2018b; Schwab et al., 2014) and a lower academic self-concept and self-esteem (Gurney, 2018; Novita, 2016). These risks also may relate to subject-specific effects and differing instructional methods (Savolainen et al., 2018), and both risks and subject-specific effects vary greatly from individual learner to learner (Cambra & Silvestre, 2003; Möller et al., 2009).

2.3 Instructional Activities

Different teaching activities such as group work and individualized assignments have been shown to reduce the effects of not only disadvantaged backgrounds but also personal factors (Bešić et al., 2016; Tomlinson & Imbeau, 2011; Torres, 2018). Individualized instruction involves providing tailored tasks adapted to varying individual learners’ needs and ability levels. Moreover, group learning may mitigate risks of social exclusion and boost engagement (Cohen et al., 2014; Miller et al., 2017; Roseth et al., 2008). In particular, groups involving learners of differing ability levels have shown better learning outcomes than more homogeneous groups (Igel & Urquhart, 2015; Marzano et al., 2003). Conversely, classroom discussions may foster learning in some (e.g., Jocz et al., 2014) but not in other students (e.g., Kang & Keinonen, 2018).

However, classroom size may also interact with instructional activities. Within the multilevel-supply-use model, classroom size may affect teacher activities and, as a result, learning. For instance, in a larger classroom, a teacher may be less able to monitor multiple diverse group activities or each individual learner’s reactions during a classroom discussion. When considered alone, larger class sizes are often shown to have a small, but significant negative effect on a diverse set of learning outcomes (Brühwiler & Blatchford, 2011; Krassel & Heinesen, 2014; Watson et al., 2016). However, other evidence has shown that reduced class size does not relate directly to better outcomes (e.g., Hattie, 2002, 2005; Phelps, 2011). Instead, it may have an indirect effect through classroom management and differing instructional activities (Blatchford et al., 2011; Blatchford & Russell, 2018; Harfitt & Tsui, 2015; Wright et al., 2017).

2.4 Mediating Factors

As described above, individual learning factors strengthen environmental risk factors. For instance, there is a higher rate of SEN diagnoses in individuals from minority backgrounds (de Valenzuela et al., 2006). However, other individual learning factors such as self-concept and self-esteem may also mediate risks. In classical self-concept theory (Shavelson et al., 1976), the self-concept represents numerous aspects of self-perception in multiple contexts (Marsh, 1986, 1990). One of these aspects—academic self-concept—is of particular interest in the educational context (Marsh, 2014; Marsh & Martin, 2011). Academic self-concept relates to self-perceptions regarding academic and scholastic activities, and it may be further differentiated by academic subject (e.g., math or reading; Gogol et al., 2016). Subject-specific self-concept relates to current and future subject-specific achievement (Susperreguy et al., 2018).

Another relevant self-perception in the academic context is self-esteem. Generalized measures of self-esteem have been shown to also relate to academic achievement (Di Giunta et al., 2013; Diseth, 2011; Ferla et al., 2009), For instance, Valentine et al. (2004) found in a meta-analysis that significant effects of self-esteem measures remained after accounting for subject-specific measures such as self-concept. Valentine and DuBois (2005) have developed this further in a combined model to account for the roles of both subject-specific self-concept and generalized self-esteem.

The relationship of these self-perception measures to academic outcomes is correlated most commonly in self-perception theories (Marsh & Craven, 2006) as well as the multilevel-supply-use model (Brühwiler & Blatchford, 2011). For example, a child’s ability level may influence self-concept, which, in turn, influences later achievement. A recent large-scale assessment demonstrated that variables of self-efficacy and self-concept both relate similarly to subsequent achievement, but that both self-perception variables were also separate constructs (Arens et al., 2020). However, instead of merely covarying with background and achievement, self-perceptions may mediate the effect priors (e.g., prior achievement, SEN, SES) on academic outcomes (e.g., Diseth, 2011).

2.5 Present Studies and Research Questions

This chapter presents two studies investigating the role of individual, environmental, and classroom-level factors in learning outcomes. Each study was conducted with data from NEPS (Blossfeld et al., 2011). NEPS provides the opportunity to conduct large-scale, longitudinal analyses that incorporate a diverse and comprehensive set of variables. Both studies utilized data from the third cohort (SC3; starting in the fifth school year). The first study examined the effects of SES and second-language learning on the development of math and reading skills in secondary students between Grades 7 and 9 (DeVries et al., 2020). It simultaneously investigated the effects of teaching techniques (i.e., individualized assignments, group work, and discussions) and their interactions with other variables; and it also evaluated the relationship between class size and teaching techniques. This study focused on the first three of the following research questions:

  1. 1.

    How do low SES and second-language learning affect the development of reading and math competence in secondary school? Both of these factors were expected to impact negatively on competence gains in reading and math (DeVries et al., 2018a; Gebhardt et al., 2015; Solari et al., 2014).

  2. 2.

    How does the use of individualized assignments, group work, and discussions affect the development of reading and math competence in secondary schools? In particular, individualized assignments and group work were expected to produce better outcomes overall and more benefits for learners with SEN, of lower SES, or who were second-language learners (Miller et al., 2017; Roseth et al., 2008; Tomlinson & Imbeau, 2011; Tomlinson & Moon, 2013).

  3. 3.

    How does class size affect the development of reading and math competence in secondary school, and does it interact with specific group work, classroom discussions, and individualized assignments? Class size was expected to relate negatively to learning gains, (Glass & Smith, 1979; Phelps, 2011), and to interact negatively with teaching techniques that require more teacher–student interactions (i.e., group work and individualized assignments; Blatchford et al., 2011; Harfitt & Tsui, 2015; Wright et al., 2017).

The second study used a latent growth model to examine changes in achievement from 5th to 9th grade (DeVries et al., 2021). Within this framework, SES, the presence of SEN, gender, non-verbal reasoning, and school track (Gymnasium or academic track vs other tracks) were related to the overall level (intercept) and rate of change (slope). Further, generalized self-esteem and subject-specific self-concept were introduced as partial mediators between predictors and outcomes. This modelling structure was designed to address the final two research questions:

  1. 4.

    How do SES, SEN, gender, reasoning ability, and school track relate to starting level and rate of change in reading and math competence in secondary school? SES and non-verbal reasoning were expected to relate positively to both starting competence and rate of competence growth in the model (intercept and slope), whereas children with SEN were expected to have a lower starting level (intercept), but not necessarily slower growth (slope). A gender effect in which girls had higher starting levels in reading and boys had higher starting levels of achievement in math was also expected.

  2. 5.

    Do generalized self-esteem and subject-specific self-concept mediate the relationship? Both generalized measures of self-esteem and subject-specific self-concept were expected to be significant mediators.

3 Study 1

3.1 Methods

Complete data from parents, teachers, and student self-reports were available for 724 students for reading competence (47.7% male) and 1072 students for math competence (48.5% male) in Starting Cohort 3 (SC3; starting in the fifth school year). Separate math and reading models were created with corresponding Grade-9 competence levels as dependent variables.

3.1.1 Models

Each model included Grade-7 competence, low parental education level (both parents lacking a university degree), second-language learner status, school track (academic track vs others) as predictors. Also included were the Grade-7 teacher’s self-reported use of group work, discussions, and individualized assignments together with class size. Cases in which the child’s competence data, the teacher’s self-reports, or the parents’ data were missing were excluded entirely. Other missing values were omitted via pairwise deletion. Furthermore, all two-way interactions between the instructional techniques (i.e., group work, discussions, and individualized assignments) and all other variables were also considered. Finally, a random intercept was incorporated on the classroom level to account for the hierarchical structure of the data.

3.1.2 Notes on Variables Used

Reading and math competence were treated as separate variables and used only in their corresponding models (i.e., math competence in the math model). Values were taken from Warm’s Likelihood Estimates (WLEs) calculated from NEPS competence testing (Pohl & Carstensen, 2012). Grade-7 competence was included as a predictor to control for starting level competence when predicting Grade-9 competence. Low parental education was converted into a binary variable indicating whether both parents lacked a university degree. These data came from parental responses. Second-language learner status was also converted into a binary variable indicating whether German was the second-language of the learner (i.e., L2). These data were based on self-reports of the learners. School track was divided into academic tracks and compared to all others. Only students attending a Gymnasium school were defined as being in the academic track. The use of group work was based on teacher responses to how often they ‘work with small student groups’ and use ‘partner work’. Discussions were based on teacher responses to how often they use ‘discussion rounds’ and how often ‘the class and I have discussions’. Individualized assignments came from five questions about how they vary their instruction, teaching techniques, and assignments based on the ability of their students (e.g., ‘I give students homework ranging in complexity based on their capability’, and ‘If students have difficulties in understanding, I give them additional assignments’).

3.2 Results

3.2.1 Student Background Variables

Table 6.1 gives an overview of the results of both reading and math models. In both models, competence at Grade 7 was a significant predictor of competence at Grade 9, but parental education level and second-language status were not significant predictors. Thus, the rate of change between Grades 7 and 9 was not related to parental education or second-language status. However, attending the academic track did predict greater increases in both models.

Table 6.1 Mixed-effects regression coefficients for math and reading competencies in Grade 9
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3.2.2 Teaching Techniques

Table 6.1 also gives the main effects of teaching techniques on 9th-grade competence. In neither model were any teaching techniques by themselves related to greater competence gains. However, there were also several significant interactions between teaching techniques and other variables in both models. Group work in math classes related to larger gains for second-language learners, but also to smaller gains for academic track students. Meanwhile, discussions in math classes related to smaller gains for second-language learners, and discussions did not relate to improvements for other learners. In German classes, learners with higher reading ability in Grade 7 demonstrated smaller gains from group work in reading classes.

3.2.3 Class Size

In Table 6.1, it is important to note that class size is centred on the median classroom size. These results showed a small but significant interaction (β = .03) with class size and the use of discussions in math classrooms. Thus, as class sizes increase above the median, a small, but significant gain in Grade-9 competence can be expected when more classroom discussions are used. In the same sense, as class sizes decrease below the median, discussions relate to smaller gains in math competence.

3.3 Brief Discussion

Study one showed a number of lasting effects of Grade-7 instructional techniques that resulted in identifiable changes in Grade-9 competence levels, particularly in math classrooms. Furthermore, in some cases, these effects interacted with second-language status and school track. These are summarized in Figs. 6.1 and 6.2, which show the predicted gains for using group work in 7th grade. The crossover effects demonstrate the value of group work for second-language learners in math classrooms. Notably, whereas group work leads to significantly greater gains in math competence for second-language learners, there are significantly smaller gains in math competence for academic-track students. Although discussions relate to worse math competence gain for second-language learners overall, in larger classrooms, they relate to slightly greater increases in math competence.

Fig. 6.1
A set of four graphs. In high school track, a, Graph of group work versus high parental education. b, Graph of frequency versus low education. In other school tracts, c, Graph of frequency versus high education. d, Graph of group work versus low education.

The effect of group work in 7th-grade math classes on 9th-grade math competence. (Note: Figure originally published in DeVries et al., 2020; CC-BY license. Plotted are the predicted values based upon our regression models for a classroom of typical size and ability level. Lines are not interpolated past the values extant in the data, which results in a shorter line in some cases)

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Fig. 6.2
A set of 4 graphs. In the highest school track, a, Frequency of discussions versus high education. b, Graph of discussions versus low education. In other school tracks, a, Discussions versus high education. b, Graph of discussions versus low education.

The effect of discussions in 7th-grade math classes on 9th-grade math competence. (Note: Figure originally published in DeVries et al., 2020; CC-BY license. Plotted are the predicted values based upon our regression models for a classroom of typical size and ability level. Lines are not interpolated past the values extant in the data, which results in a shorter line in some cases)

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4 Study 2

4.1 Methods

Study 2 used self-report responses from 5923 students in its math model and 5919 students in its reading model. Responses were taken from SC3 with data collected longitudinally in Grades 5, 7, and 9. Data came from student self-reports, competence tests, and parent responses. These included both reading and math competence, end-year grades, the presence of SEN, SES-related factors, migration background, gender, generalized self-esteem, and both math and German academic self-concepts.

Among other NEPS measures, reading competence (Gehrer et al., 2013) and mathematics competence (Schnittjer & Duchhardt, 2015) were assessed. Additionally, student reports of grades, socio-economic factors, migration background, gender, year of birth, self-efficacy, and self-concept were recorded. Caregivers answered—among others—questions regarding migration background and school track attended by the respective child (Gymnasium or academic track vs other tracks).

Due to the large-scale nature of NEPS, many cases include missing values on one or more variables of interest. Ignoring missing cases can introduces bias due to sample selection (Schafer & Graham, 2002). Therefore, multiple imputation was used to deal with missing data. Specifically, multiple imputation with chained equations was used to repeatedly sample missing values according to the predictions of an imputation model (van Buuren & Groothuis-Oudshoorn, 2011; see DeVries et al., 2021, for a full description of the imputation model).

Separate latent growth models were calculated for reading and math competence changes over Grades 5, 7, and 9. In each case, both a partial mediation and a direct effects model was calculated for a total of four models. In each model, the intercept (i.e., starting competence level) and slope (i.e., rate of change) were then regressed on the presence of SEN, gender, reasoning ability, school track, and a latent variable for SES. In the partial mediation models, the intercept and slope were also regressed on ratings of general self-esteem and of the participant’s subject-specific self-concept, which were then also regressed on all predictor variables. Finally, each model also introduced a cluster variable to account for classroom-specific effects. An overview of the partial mediation models can be seen in Figs. 6.3 and 6.4.

Fig. 6.3
A flow diagram of variables affecting math competence growth mediated by self-esteem and self-concept. Solid lines indicate significant paths, and dashed lines indicate non-significant paths.

Background variables affecting math competence growth mediated by self-esteem and self-concept. (Note: Figure originally published in DeVries et al., 2021; CC-BY license. This figure describes all pathways used in the mediation model. The no mediation model was calculated by zeroing out regressions from and onto the mediators. Solid lines indicate significant paths, and dashed lines indicate non-significant paths. WLE is based on achievement on the NEPS math competence test. I intercept, S slope, M. Self-Concept math self-concept, SES socioeconomic status, SEN special education needs, Reason non-verbal reasoning scores)

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Fig. 6.4
A flow diagram of variables affecting reading competence growth mediated by self-esteem and self-concept. The self-concept and self-esteem include S E S, S E N, sex, reason, and school track.

Background variables affecting reading competence growth mediated by self-esteem and self-concept. (Note: Figure originally published in DeVries et al., 2021; CC-BY license. This figure describes all pathways used in the mediation model. The no mediation model was calculated by zeroing out regressions from and onto the mediators. Solid lines indicate significant paths and dashed lines indicate non-significant paths. WLE is based on achievement on the NEPS math competency test. I intercept, S slope, M. Self-Concept math self-concept, SES socioeconomic status, SEN special education needs, Reason non-verbal reasoning scores)

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The ratio of direct effects between both models and the ratio of indirect effects between both models were calculated to investigate the presence of mediation (MacKinnon et al., 2007; Wen & Fan, 2015). The direct ratio (DR) was given by the formula

$$ DR=\frac{c^{\prime }}{c}\kern0.5em , $$

where c is the standardized path coefficient for the non-mediation model of the predictor onto the outcome (intercept or slope) and c′ is the same standardized coefficient in the mediation model. The indirect ratio (IR) was given by the formula

$$ IR=\frac{ab}{c}\kern0.5em , $$

where c is the same as above, a is the path onto either mediator (self-esteem or subject specific self-concept), and b is the path from that mediator onto either outcome (intercept or slope). 

4.1.1 Notes on Variables Used in the Final Models

Similar to Study 1, competence was determined separately for German and math and was based on WLEs of ability from NEPS. However, in this study, competence from Grades 5, 7, and 9 was used to create a growth model across early secondary school. Differing from Study 1, we used student statements about what resources they had in the home (e.g., own desk, own computer, a private study area) to assess SES. We chose this method because it provided a direct assessment of available academic resources in the home (see Sirin, 2016, for more on differing measures of SES in academic research).

4.2 Results

Figures 6.3 and 6.4 show the significant and non-significant paths in the math and reading partial mediation models. In both the direct-effects and the partial mediation models, the presence of SEN related to lower 5th-grade competence values, whereas higher non-verbal reasoning and attending the academic track related to higher values. In the reading model, girls had a higher starting competence; and in the math model, boys had a higher starting competence. The only effect on rate of change (slope) showed that children with higher non-verbal reasoning ability had a slightly slower rate of growth.

In the mediation models, both generalized self-esteem and subject-specific self-concept related to higher math and reading competence in Grade 5. These values also related to the predictor variables. Students in the academic track had higher subject-specific self-concept and generalized self-esteem. Students with higher non-verbal reasoning had generalized self-esteem and math-specific self-concepts, whereas students with SEN had lower levels of self-esteem and lower reading self-concept. Moreover, girls had a higher reading self-concept and boys had a higher math self-concept.

Furthermore, both generalized self-esteem and subject-specific self-concept mediated the effects of SEN, gender, non-verbal reasoning, and school track on 5th-grade math and reading competence. An overview of the direct ratio and indirect ratio of these mediations can be seen in Table 6.2. Notably, math self-concept mediated nearly one third of the effect of gender on 5th-grade math competence and approximately one sixth of the effect on 5th-grade reading competence. Also, nearly one sixth of the effect of SEN on 5th-grade competence was mediated by the combination of reading self-concept and generalized self-esteem. Smaller, but significant mediations were shown for non-verbal reasoning and school track. Because SES was not a significant predictor in the direct effect models, a significant mediation effect could not be observed. Although not shown in Table 6.2, inconstant mediation effects were shown for both mediators between non-verbal reasoning and learning growth.

Table 6.2 Mediation effect sizes on 5th-grade competencies in Study 2
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4.3 Brief Discussion

Study 2 used multiple imputation and latent growth modelling to examine the role that subject-specific self-concept and generalized self-esteem play as mediators between environmental and personal variables and math and reading competence. The first important finding was a confirmation that the set of background variables played a significant role on 5th-grade math and reading competence; however, they did not relate to the change of competence between Grades 5 and 9. In other words, rates of change were similar across all background variables. The second important finding is the role that both generalized self-esteem and subject-specific self-concept play as mediators. Whereas there was significant mediation for all background variables except SES, mediation was particularly strong for gender and the presence of SEN. This further highlights the important role that individual learning factors play in the educational process.

5 General Discussion

The two studies presented here examined several key factors affecting classroom learning. These included environmental and individual effects as well as the effects of different instructional techniques. Many different, but important environmental factors were investigated in both of these studies, including the role of SES, gender, school track, and second-language learner status. Also, several interrelated individual learning factors were examined such as non-verbal reasoning ability, the presence of SEN, self-concept, and self-esteem. Finally, learning processes were examined through teachers’ use of group work, discussions, and individual assignments. These factors are all key concerns within a typical inclusive classroom (Capp, 2017; Miller et al., 2017). Several of these factors are discussed in more detail below.

5.1 Environmental Factors

5.1.1 Socio-economic Status

In both studies, SES did not have a significant effect on the rate of improvement throughout early secondary education, and in Study 2, it was also not related to math or reading competence levels in 5th grade. Furthermore, Study 1 also did not find any interactions with SES and the use of group work, discussions, or individualized assignments. Additionally, both studies used slightly differing measures of SES. Study 1 used parental education level, whereas Study 2 developed a latent variable based on student responses about what resources they had in their home. The second study definition was intended to identify more specifically the resources available to higher SES learners that may support learning (see Sirin, 2016), but there was still no significant identifiable effect of SES. At first glance, this appears to be a surprising finding. An effect of SES is commonly identified across many diverse studies (e.g., Bjorklund & Salvanes, 2011; Currie, 2009; DeVries et al., 2018a; Kim & Quinn, 2013; Rambo-Hernandez & McCoach, 2014). However, these results do not indicate that there is no effect of SES within these samples, but instead suggest that the effects of other modelled variables sufficiently explain the observed variance. Notably, both studies used attendance in the academic track (German Gymnasium schools). This particular variable has been demonstrated repeatedly to have a large effect in German school systems, and moreover has also been shown to correlate with measures of SES in Germany (e.g., Dumont et al., 2019; Skopek & Passaretta, 2020). In line with this interpretation, it remains important to examine multiple indicators of SES alongside of school track when looking at data from countries with stratified educational systems such as Germany.

5.1.2 Second-Language Learners

Study 1 examined the role of being a non-native speaker on achievement. Although mean-level differences were identifiable when comparing native speakers to second-language learners, there was no significant difference in Grade-9 competencies once prior levels were taken into account. In other words, there was a similar rate of change in both groups. However, an important caveat to this is the multiple interactions found between second-language learner status and instructional techniques in math classes. When 7th-grade math teachers used more group work, their students had higher levels of math achievement, which was detectable 2 years later. The opposite was true for 7th-grade math teachers who used more discussions. This highlights the value of group work as an instructional method for second-language learners in which such learners may receive extra peer support in their learning processes (Miller et al., 2017).

5.2 Individual Learning Factors

5.2.1 Special Education Needs

Study 2 examined the effects of SEN status within regular classrooms. Findings demonstrated nuanced effects in relation to competence and to self-perceptions. Learners with SEN had a lower overall competence level, but their rate of growth in math and reading competence was similar to learners without SEN. Moreover, they demonstrated lower levels of generalized self-esteem as well as reading self-concept. These findings mirror other results relating to risk of exclusion and achievement (DeVries et al., 2018b; Gebhardt et al., 2015; Möller et al., 2009; Schwab et al., 2014). However, as noted below, there was also a significant mediation for self-perceptions and competence.

5.2.2 Self-Perceptions

Study 2 considered both generalized self-esteem and subject-specific self-concept as important mediators relating to other individual and environmental variables and competence. For instance, after accounting for these self-perceptions, the effects of SEN on reading competence were reduced by nearly 15%. Whereas no significant mediation was found for math self-concept, self-esteem also reduced the effects on math competence by a modest, but significant amount. Moreover, the effects of gender on math and reading competence were greatly mediated by subject-specific self-concepts. Modest mediation effects for self-perceptions were also seen with non-verbal reasoning and school track. These findings highlight the key role of individual factors as both risks and mediators of risk in the learning process.

5.3 Classroom Factors

Study 1 examined two important classroom factors: instructional techniques and class size. Results suggested that group work was generally an effective technique for second-language learners in math classrooms, whereas discussions related to lower-than-expected gains. Simultaneously, group work showed worse gains for German learners with higher pre-existing competence. Moreover, discussions related to modestly higher subsequent achievement in larger 7th-grade math classrooms. Unfortunately, these nuanced findings do not provide a single ‘best practice’ for instructors, but instead point to the importance of varied instructional techniques that best match the learning environment and classroom composition.

5.4 Supply and Use

These nuanced findings can be understood best when related back to the multilevel-supply-use model described in the introduction. The studies focused on the three main factors governing the ‘use’ of educational supply (i.e., environmental factors, individual learning factors, and classroom factors). In this sense, learning outcomes are determined by the interactions found within these three areas. An instructor provides a lesson. That lesson may use more group work, discussions, or other instructional techniques. Some of these techniques may be more suited to certain environmental factors or to individual learners. The interpretation of the lesson then depends on environmental factors (e.g., SEN status and language background) that are also filtered through individual learning processes such as self-perceptions (e.g., ‘I am good at math’), non-verbal reasoning, and other factors. Thus, learning outcomes depend not just on any individual factors, but on the complex system of factors at play. Smaller experimental and quasi-experimental studies are well suited to examine such individual factors as well as specific interventions, but they should also be accompanied by large-scale assessments such as these studies that examine these variables in an interconnected system.

6 Conclusions

The studies summarized here highlight the importance of varied learning and instructional processes. Highlighted are certain factors related to worse academic achievement including SEN status, lower SES, and migration background. Similarly, other factors that affect the learning process such as gender, non-verbal reasoning, prior attainment, and gender were also related to academic achievement. However, these relationships depended heavily on both teaching instructional techniques in math classrooms as well as generalized self-esteem and subject-specific self-concept in both math and German classrooms. Group work in math classrooms related more strongly than expected to math achievement levels detectable up to 2 years later. Both self-concept and self-esteem mediated the effects of school track, non-verbal reasoning, SEN status, and gender on both math and reading ability. Taken as a whole, these results highlight the importance of considering a system of variables in the educational process, the role of teaching techniques suited to the learners, and the role of self-perception on educational outcomes.