Predicting homework motivation and homework effort in six school subjects: The role of person and family characteristics, classroom factors, and school track

Learning and Instruction 19 (2009) 243e258 www.elsevier.com/locate/learninstruc

Predicting homework motivation and homework effort in six school subjects: The role of person and family characteristics, classroom factors, and school track Ulrich Trautwein*, Oliver Lu¨dtke Center for Educational Research, Max Planck Institute for Human Development, Lentzeallee 94, Berlin 14195, Germany Received 24 November 2007; revised 1 March 2008; accepted 5 May 2008

Abstract This study examines the determinants of homework motivation and homework effort in six school subjects at three levels: student level, classroom level, and school level. We hypothesized that several factorsdincluding stable personality characteristics such as gender and conscientiousness, students’ domain-specific homework motivation, and characteristics of homework assignmentsdhave concomitant effects on student homework effort. The sample consisted of 511 students in Grades 8 and 9. Across all six school subjects, multilevel modelling showed that students’ homework motivation and homework effort varied primarily as a function of their shared perceptions of homework quality and control (classroom level) and of their conscientiousness, individual perception of homework quality, and expectancy and value beliefs (student level). Domain-specific patterns were found for student gender in line with gender stereotypes. Cognitive ability, family background, and parental homework help or control were only loosely associated with homework motivation and homework effort. Ó 2008 Elsevier Ltd. All rights reserved. Keywords: Gender differences; Conscientiousness; Motivation; Effort; Homework

1. Introduction The majority of teachers, parents, and students regard homework as a valuable educational tool (Cooper, 1989; Cooper, Lindsay, Nye, & Greathouse, 1998). Empirical findings support this view (Cooper, Robinson, & Patall, 2006; Trautwein, 2007). Indeed, studies have shown that the way students approach their homework assignments has profound effects on their school grades, with greater effort investment in homework being associated with higher achievement (Schnyder, Niggli, Cathomas, Trautwein, & Lu¨dtke, 2006; Trautwein, 2007; Zimmerman & Kitsantas, 2005). Insights into the mechanisms that influence students’ homework behaviour may therefore help to enhance student achievement. When asked why some students put more effort into their homework than others, teachers and students typically offer different explanations. Teachers tend to attribute differences in homework effort to what they perceive to be students’ stable personality traitsdcarefulness, conscientiousness, and lazinessdor to unfavourable family conditions. Students, on the other hand, often identify differences in homework characteristics (e.g., in homework quality or control) as major determinants of how much effort they put into their assignments in different school subjects. The present article builds on a recently proposed homework model (Trautwein, Lu¨dtke, Schnyder, & Niggli, 2006), which predicts that several factorsdincluding characteristics of homework assignments, students’ stable personality characteristics, and

* Corresponding author. E-mail address: [email protected] (U. Trautwein). 0959-4752/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.learninstruc.2008.05.001

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students’ domain-specific homework motivationdhave concomitant effects on student homework effort. In the present article, we test the predictions of this model in six school subjects. 1.1. Predictors of homework motivation and homework effort Somewhat surprisingly, given the importance of homework in students’ lives, few studies have focused explicitly on why students do or do not complete their assignments (cf. Cooper, 1989; Trautwein & Ko¨ller, 2003; Wagner, Schober, & Spiel, 2008; Wagner & Spiel, 2002; Warton, 2001). Our study builds on the homework model recently proposed by Trautwein, Lu¨dtke, Schnyder, et al. (2006), which draws on stable personality characteristics, characteristics of homework assignments, parental homework behaviour, as well as homework motivation, to explain homework effort. Empirical findings have provided support for central assumptions of this model (see Trautwein, 2007; Trautwein & Lu¨dtke, 2007; Trautwein, Lu¨dtke, Kastens, & Ko¨ller, 2006; Trautwein, Lu¨dtke, Schnyder, et al., 2006). Fig. 1 presents core aspects of the model covered in the present article. The homework model predicts homework effort to be positively related to achievement, and influenced by homework motivation. In accordance with expectancy-value theory (Eccles & Wigfield, 2002), homework motivation is conceptualized to comprise an expectancy and a value component. Expectancies of success are defined as individuals’ beliefs about how well they will perform on a future task (‘‘Can I succeed on this task or activity?’’; Wigfield & Wagner, 2005, p. 224). Task value reflects their reasons for engaging in activities (‘‘Why do I want to do this activity?’’; Wigfield & Wagner, 2005, p. 224), and comprises four dimensions: intrinsic value, attainment value, utility value, and cost (Eccles, Wigfield, & Schiefele, 1998). The value component has been operationalized in various ways in empirical studies. Whereas some researchers have focused on one specific dimension or treated the dimensions separately, it is also quite common to use a combined measure that integrates, for instance, the attainment and utility dimensions (see Jacobs, Lanza, Osgood, Eccles, & Wigfield, 2002; Nagy, Trautwein, Baumert, Ko¨ller, & Garrett, 2006; Watt, 2004). The homework model further predicts that homework characteristics affect homework motivation and effort. Building on previous research (Brophy & Good, 1986; Walberg, 1991; Weinert & Helmke, 1995; see also Kunter, Baumert, & Ko¨ller, 2007), the model identifies homework quality and homework control as potentially critical variables. High-quality homework requires careful selection and preparation of appropriate and interesting tasks. It means using homework assignments to reinforce classroom learning and to diagnose individual students’ learning progress and difficulties.

Homework Assignments Homework Behavior

- Homework quality

- Homework control

Homework Expectancy

Homework Compliance

Student Characteristics Achievement

- Gender - Cognitive ability - Conscientiousness

Homework Value Role of Parents

Percentage of Tasks Attempted

- School-related communication

- Homework help - Homework control

Fig. 1. Adapted version of the homework model (see Trautwein, Lu¨dtke, Schnyder, et al., 2006).

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With respect to student characteristics, the homework model incorporates gender, cognitive ability, and conscientiousness. Gender has been shown to be weakly associated with homework motivation and homework behaviour (Wagner et al., 2008; Xu, 2006). Wagner et al. used a diary assessment instrument to measure the overall homework time reported by boys and girls in secondary schools, and found girls to report more time on homework than boys. Likewise, in a questionnaire study with students in Grades 9e12, Xu (2006) found girls to report more total time on homework than boys. Moreover, girls were less likely to report to come to class without homework than boys. Based on the literature on domain-specific gender differences in motivation and behaviour (Watt & Eccles, 2008), Trautwein, Lu¨dtke, Schnyder, et al. (2006) argued that the strength of gender differences in homework may vary depending on the school subject. Their empirical analyses provided preliminary support for this hypothesis, with girls reporting statistically significantly higher homework compliance in English and French, but not in mathematics. The gender effects on homework behaviour were partly mediated by homework motivation. The model predicts a positive effect of cognitive ability on the expectancy componentdstudents with high cognitive ability will be confident of being able to complete assignments; however, no a priori predictions are made regarding direct effects on homework behaviour. Somewhat surprisingly, the Big Five personality trait of conscientiousness (see McCrae & Costa, 1999) has received little attention in previous research on school achievement (De Raad & Schouwenburg, 1996) and, more specifically, in homework research despite its intuitive relevance. Conscientious persons are characterized as being industrious, systematic, dutiful, high on achievement striving, and hard-working. In one of the few studies to have examined the effects of conscientiousness in the school setting, Trautwein, Lu¨dtke, Kastens, et al. (2006) found the association between conscientiousness and effort to be particularly pronounced in the homework context. Finally, with respect to parental homework involvement, the homework model draws on self-determination theory (Deci & Ryan, 2002), which stresses students’ needs for autonomy, relatedness, and competence. Clearly, certain forms of parental homework support are more likely to be congruent with these needs than others (Grolnick & Slowiaczek, 1994). Generally speaking, more distal variables, such as high parental education, parental interest in school-related matters, and trustful parentchild communication about school, have been found to be positively related to better adjustment, whereas findings on more proximal variables, such as parental homework support and control, have been mixed (Chiu & Xihua, 2008; Grolnick & Slowiaczek, 1994), particularly in studies focusing on the quantity of homework help and homework control. Although many students benefit from direct parental involvement in their homework, the homework motivation and behaviour of others may be impaired by their parents’ involvement (Knollmann & Wild, 2007; Pomerantz, Wang, & Ng, 2005). Accordingly, the homework model predicts that parent-child communication is positively related to homework motivation and effort, but does not predict a clear positive association between direct parental involvement in the homework process and these variables. 1.2. Differentiating analytical levels in homework research To date, homework research has almost completely neglected the critical differentiation between student-level effects and classroom-level effects (Trautwein, 2007; Trautwein & Ko¨ller, 2003). A classroom-level effect implies differences between classes; a student-level effect describes differences between students in the same classes (for a recent example, see Frenzel, Pekrun, & Goetz, 2007). A multilevel perspective is thus required whenever the effects of characteristics of homework assignments on students’ homework motivation and behaviour are examined. Because homework research has largely failed to distinguish between student and classroom level, however, little is known about the extent to which classes differ with respect to homework variables. Are there reliable differences in mean homework effort across classes? Or do most classes have a similar mix of students with high and low homework morale? What are the predictors of any differences that emerge across classes? In one of the very few published articles taking a multilevel approach to homework, Trautwein, Lu¨dtke, Schnyder, et al. (2006; Study 2) examined the predictive power of perceived homework quality for homework motivation and behaviour in French as a foreign language. The authors used students’ individual perceptions of homework quality as a student-level variable, but also aggregated the students’ perceptions to form a classroom-level indicator of homework quality. Two main research questions were addressed using data obtained from 93 Grade-8 classrooms in Switzerland. First, do students in different classes differ in their homework behaviour and motivation as a result of their teachers’ levels of homework quality and control (classroom-level perspective)? Second, within each class, how different are the students’ perceptions of their homework and what are the consequences of varying perceptions (student-level perspective)? Trautwein, Lu¨dtke, Schnyder, et al. (2006) found statistically significant and meaningful effects (regression coefficients of 0.19) at both the individual and the classroom level. Self-reported homework effort was higher among students who had a more favourable perception of homework quality than among their classmates, and higher in classes in which the mean student perception of homework quality was comparatively high. Furthermore, as predicted by the authors, the effects of perceived homework quality were largely mediated by the homework motivation variables. Another important characteristic of homework assignments is the degree and intensity of homework control. According to Walberg, Paschal, and Weinstein (1985) «.homework benefits achievement and attitudes, especially if it is commented upon or graded» (p. 76). Findings from an intervention study by Elawar and Corno (1985) seem to support that claim. Elawar and Corno

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(1985) trained teachers in their experimental group to give a specific form of written feedback. The authors found improved achievement and attitudes in the experimental group relative to the control group at all ability levels. Because the Elawar and Corno (1985) study was based on an intervention program, however, it remains unclear whether teachers’ typical homework control practices also have positive effects on homework effort and motivation. In fact, some theoretical accounts imply that grading and strict control of homework completion might be at odds with the aim of increasing student motivation. According to self-determination theory (Deci & Ryan, 2002), extensive control and external rewards are likely to undermine students’ intrinsic motivation. Students’ homework motivation and effort might thus be weakened by teachers’ overcontrolling behaviours.

1.3. The present study The present study builds on and extends the studies by Trautwein, Lu¨dtke, Schnyder, et al. (2006) and Trautwein and Lu¨dtke (2007). We examined homework effort and potential predictors of homework effort in six school subjects, using a multilevel framework as both a conceptual scaffold and an instrument for data analysis. Five main research questions were addressed. First, to what extent do students in different classes vary in their homework effort, homework motivation, and their perceptions of homework quality and control? Based on the homework model, we expected to find meaningful variation across classrooms (Hypothesis 1). Second, to what extent do homework motivation and conscientiousness predict homework effort? Based on the homework model and prior empirical findings for some school subjects, we expected conscientiousness, expectancy beliefs, and value beliefs to significantly predict homework effort in all six school subjects (Hypothesis 2). Third, to what extent do homework quality and homework control predict homework motivation and homework effort? In line with the predictions of the homework model and first empirical findings (Trautwein, Lu¨dtke, Schnyder, et al., 2006), we expected student-reported homework quality to be positively associated with homework motivation and homework effort, and homework motivation to partly mediate the predictive effects of homework quality on homework effort (Hypothesis 3). Given the conflicting theoretical predictions and mixed empirical results, no predictions were made for homework control. Fourth, are there gender differences in homework motivation and homework effort? Previous research that did not differentiate between school subjects suggests that girls exhibit higher homework effort. However, based on the homework model and preliminary evidence from our prior study (Trautwein, Lu¨dtke, Schnyder, et al., 2006), we expected the pattern of results to be somewhat domain specific, with boys reporting higher homework motivation and homework effort in stereotypically ‘‘male’’ school subjects, such as mathematics and physics (Hypothesis 4). Fifth, to what extent is family background associated with homework motivation and homework effort? Parental interest in students’ academic progress is generally believed to be positively associated with positive outcomes. Direct parental involvement in homework can, however, be a mixed blessing. Accordingly, we did not expect to find a positive association between parental homework support/control and the outcome variables (Hypothesis 5).

2. Method 2.1. Sample A total of 511 students (53.0% female) from Grades 8 (51.5%) and 9 (48.5%) participated in the study.1 Their mean age was M ¼ 14.7 years (SD ¼ 0.76) and the vast majority of participants were Caucasians (>95%). A notable proportion of students (22.7%) reported that at least one of their parents was not born in Germany, but most reported speaking German at home with at least one (93.3%) or both of their parents (87.9%) most of the time. Turkish was the primary home language of 47%, and Polish the primary home language of 32.3% of the students who did not usually speak German at home. Student participation was voluntary, and written consent was obtained from parents. The participation rate was above 90% in all classes. Students were sampled from 42 classes in 9 state schools in or around a large German city. As is typical of German schools, the student groups remained intact across the school subjects under investigation, most of which were taught by different teachers. All students were enrolled in one of the three major secondary school tracks: 47% in the academic-track Gymnasium, 36.8% in the intermediate-track Realschule, and 16.2% in the lower-track Hauptschule. In most German states, students are assigned to secondary tracks at the end of Grade 4, primarily on the basis of their achievement in elementary school. This early ability tracking leads to major differences in average achievement in schools of different tracks and to more similar achievement levels in schools of the same track (Trautwein, Lu¨dtke, Marsh, Ko¨ller, & Baumert, 2006). The clearly articulated purpose of tracking in the 1 The same data set was used by Trautwein and Lu¨dtke (2007); in that study, however, a within-person design was used to predict homework time and homework effort.

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German school system is to form homogeneous learning groups, which are believed to increase the learning rates of all students (but see Organization for Economic Cooperation and Development [OECD], 2001). 2.2. Procedure Within each class, students were randomly assigned to participate in either the present study or a second, unrelated study. The mean number of students per class who participated in the present study was M ¼ 12.17. The study took place during the second semester of the 2003/2004 school year. Measures were administered to intact classes during regular school hours by a trained research assistant. The 45-min study was administered in school subjects selected by the head teachers of the participating schools based on availability of testing time. In most classes, teachers were not present during the study administration. On the occasions that they were present, teachers were given written information about the study; they did not communicate with their students during the session and did not assist in the data collection. Two versions of the questionnaire were used, differing only in the sequence of sections. Preliminary analyses indicated that the sequencing of the sections had no effects on the results reported. All participating students were entered in a prize draw, with one cinema voucher worth 10 euros (about 14 US$) being awarded in each class. 2.3. Instruments The test booklet consisted of a 7-min standardized test of cognitive ability (administered at the beginning of the session) and a questionnaire section. Questionnaire items were adapted from previous studies (see Appendix in Trautwein, Lu¨dtke, Schnyder, et al., 2006). Strictly parallel wording was used for all domain-specific items, that is, the items for German, English, history, biology, mathematics, and physics were exactly the same except for the name of the school subject. A 4-point Likert-type scale ranging from 1 (completely disagree) to 4 (completely agree) was used for all multi-item constructs. Factor analyses conducted before data analysis supported the hypothesized factor structure and the domain-specificity of the scales. 2.3.1. Homework effort Homework effort was measured in terms of two overlapping constructs: homework compliance and percentage of tasks attempted. Homework compliance was measured by five items; example items were ‘‘I often copy mathematics [physics/biology/German/ English/history] homework from others’’ (reverse scoring) and ‘‘I do my best in my mathematics [physics/biology/German/ English/history] homework’’. Students scoring high on this scale do their homework assignments carefully and to the best of their ability; they typically do not copy from others. Internal consistency (Cronbach’s a) for all school subjects ranged from 0.78 to 0.82. A single-item indicator measured the percentage of homework tasks attempted per week: ‘‘On average, what percentage of your mathematics homework do you make a serious effort to do?’’ 2.3.2. Homework motivation Four items were used to assess the expectancy component of homework motivation (e.g., ‘‘If I make an effort, I can do all of my mathematics [physics/biology/German/English/history] homework’’). Internal consistency (Cronbach’s a) for all school subjects ranged from 0.63 to 0.73. Students scoring high on homework expectancy are optimistic about their capability to work successfully on the tasks assigned, even if those tasks are complicated. The value component of homework motivation also comprised four items (e.g., ‘‘Our mathematics [physics/biology/German/ English/history] homework takes a lot of time and is of little use to me’’ (reverse scoring)). Internal consistency (Cronbach’s a) for all school subjects ranged from 0.69 to 0.75. In terms of the Eccles and Wigfield (2002) expectancy-value conceptualization of motivation, the homework value items focused on the facets of utility and cost. 2.3.3. Characteristics of homework assignments Two scales were used to describe perceived characteristics of homework assignments. Perceived homework quality. Four items assessed how well prepared and interesting the homework assignments was perceived to be. The items tapped students’ overall impression of the quality of homework; they did not probe for specific aspects of homework assignments such as percentage of cognitively activating tasks. An example item was ‘‘Our mathematics [physics/ biology/German/English/history] teacher knows what homework to give us so that we understand the material covered in the lesson’’. Internal consistency (Cronbach’s a) for all school subjects ranged from 0.76 to 0.83. Perceived homework control. Two items described the teacher’s active control of homework completion and his or her knowledge of students’ failure to comply with assignments. An example item was ‘‘Our mathematics [physics/biology/German/ English/history] teacher always knows who hasn’t done their homework’’. Internal consistency (Cronbach’s a) for all school subjects ranged from 0.60 to 0.74.

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For both homework quality and homework control, we aggregated the ratings of all students in each classroom to produce class-average quality and control ratings. Both the individual score and the class-average score were included in the subsequent analyses (see below). 2.3.4. Parental variables Three items were used to tap students’ perceptions of family communication on school matters. An example item was ‘‘My parents and I often talk about things that have happened at school’’. Internal consistency was satisfactory, Cronbach’s a ¼ 0.74. Four items assessed parental homework help. An example item was ‘‘My parents ask how they can help me with my homework’’. Internal consistency was satisfactory, Cronbach’s a ¼ 0.76. A single-item indicator was used to assess the frequency of parental homework control: ‘‘How often do your parents check that you’ve done your homework per 10 homework assignments?’’ The response scale ranged from 0 (never) through 1 (once), 2 (twice), 3 (three times),.to 10 (always). Additionally, we assessed the cultural capital of the family by asking how many books there were in the family home. A high number of books is seen as an indicator of cultural capital or learning opportunities (see Buchmann, 2002) and thought to be associated with academic outcomes. 2.3.5. Cognitive ability The Figure Analogies subscale from the Cognitive Ability Test 4-12þR (Heller & Perleth, 2000), a German version of the CogAT by Thorndike and Hagen (1993), was used to tap cognitive ability. The scale consists of 25 figural items in multiple-choice format and is considered to be a test of reasoning that is relatively free of environmental effects. The internal consistency (KuderRichardson formula 20) of the cognitive ability test was 0.92. Because the figural analogies scale taps highly g-loaded ability components, it is frequently used as a parsimonious test of cognitive ability. 2.3.6. Conscientiousness Conscientiousness was measured with a German version of the NEO Five Factor Inventory (Borkenau & Ostendorf, 1993; original version by Costa & McCrae, 1992). One of the 12 items was discarded due to its low discrimination. The internal consistency of the remaining 11 items was good, Cronbach’s a ¼ 0.80. 2.3.7. Additional control variables As additional predictor variables, we included the students’ immigration status, 0 (none) and 1 (immigration background) as well as the school track attended (reference category: intermediate-track Realschule). 2.4. Statistical analyses 2.4.1. Analyzing hierarchical data The students in the present study were nested within 42 classes and 9 schools. Hierarchical linear modelling (HLM) is ideally suited to analyze such hierarchically structured data. At the first level (student level), regression equations were modelled for student-level variables. At the second level (classroom level), regression equations were modelled for variables that differ between classes. In addition to grade level, we included class-aggregated student reports of homework quality and control as classroomlevel variables. At the third level (school level), we used school type (academic track and lower track) as a dummy-coded predictor variable. A detailed presentation of multilevel analysis can be found in Raudenbush and Bryk (2002). All analyses were conducted with HLM 6 (Raudenbush, Bryk, Cheong, & Congdon, 2004). All models reported are random-intercept models estimated by full information maximum likelihood (FIML). For all variables, standardized scores were used in HLM. The resulting regression coefficients at the student level can thus be interpreted in the same way as the standardized coefficients emerging from ordinary regression analysis. Classroom-level homework quality and homework control were the classroom averages of the corresponding student-level variables and were not re-standardized. The centring of Level-1 (student-level) predictor variables is a crucial issue in multilevel analysis (see Enders & Tofighi, 2007; Kreft, de Leeuw, & Aiken, 1995). There are essentially two centring options: the level-1 predictor variables can be adjusted to the mean of the cluster to which the student belongs (centring at the group mean) or to the mean of the whole sample (centring at the grand mean). The decision to centre Level-1 predictors at their group or grand mean can affect the interpretation of the parameters estimated (Enders & Tofighi, 2007). Lu¨dtke, Robitzsch, Trautwein, and Kunter (submitted for publication) argued that students’ ratings of the learning environment should typically be centred at the group mean because constructs assessing aspects of the environment are generic group-level constructs. Using grand mean centring to control for interindividual differences among classes in these ratings would eliminate an essential component of the aggregated ratings (see also Karabenick, 2004). Students’ perceptions of homework quality and control were thus centred at their classroom mean in the present study. However, the other Level-1 predictor variables, which are constructs that are primarily defined at the individual level, were centred at their grand mean. Applying grand-mean centring to these variables allows between-classroom differences in homework behaviour to be

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adjusted for differences among these student-level predictor variables. Hence, we control for differences in the student composition of a classroom when estimating the effects of aggregated student perceptions of homework quality and control. 2.4.2. Missing values Missing data represent a potentially serious methodological problem in many empirical studies. For the items and scales considered here, the average percentage of missing data was 6% ranging from 0% to 15%. Questions toward the end of either of the two versions of the questionnaire tended to have a somewhat higher percentage of missing values, indicating that some students were unable to complete the whole questionnaire within the given time frame. In the methodological literature on missing data (Schafer & Graham, 2002), there is growing consensus that multiple imputation of missing data is superior to traditional pairwise and listwise deletion methods. Hence, we opted for the multiple imputation procedure (Lu¨dtke, Robitzsch, Trautwein, & Ko¨ller, 2007; Peugh & Enders, 2004). The NORM software (version 2.03, see Schafer & Graham, 2002) was used to generate five data sets in which all missing data were replaced by estimated values. The overall estimates and standard errors from the analysis of the five imputed data sets take into account the uncertainty of missing data. 3. Results 3.1. Descriptive results With means ranging from 2.51 to 2.90, students reported only moderate levels of homework compliance, and there was considerable variation across the six school subjects examined. The difference between the school subject with the highest reported effort (mathematics) and that with the lowest reported effort (physics) was more than half a standard deviation. Significance tests performed using HLM showed that the subject-by-subject comparisons were significant in several instances. The highest percentage of homework tasks attempted was reported for mathematics (about 75% of tasks assigned). The percentage was somewhat lower for German (69.9%) and English (68.8%) and considerably lower for history (63.2%), biology (51.7%), and physics (50.7%). There was also considerable and statistically significant variation in the motivational predictor variables (expectancy and value beliefs). Students’ expectancy beliefs regarding their homework assignments differed across the six school subjects, with the highest expectancy beliefs being reported for history (M ¼ 3.21, SD ¼ 0.63) and the lowest for physics (M ¼ 2.85, SD ¼ 0.76). Perceived homework value was highest in mathematics (M ¼ 3.06, SD ¼ 0.71) and lowest in physics (M ¼ 2.71, SD ¼ 0.76). In the case of the characteristics of the homework assignments, students rated the quality of history homework (M ¼ 2.73, SD ¼ 0.73) most favourably and reported the highest amount of homework control for German (M ¼ 3.07, SD ¼ 0.79). To examine the degree of domain-specificity of the homework variables, we calculated correlations between each of the six school subjects for each homework indicator. The correlations for the percentage of homework tasks attempted ranged between r ¼ 0.25 (German and physics) and r ¼ 0.51 (German and English); those for homework compliance ranged between r ¼ 0.32 (German and physics) and r ¼ 0.56 (German and history). For expectancy beliefs, the lowest correlation was found between English and physics (r ¼ 0.17) and the highest between German and history (r ¼ 0.54); for value beliefs, the lowest correlation was found between English and physics (r ¼ 0.25) and the highest between English and German (r ¼ 0.47). Correlations for homework quality ratings ranged from r ¼ 0.22 (German and physics) to r ¼ 0.49 (German and history). Finally, correlations for perceptions of homework control ranged from r ¼ 0.03 (German and physics) to r ¼ 0.42 (German and history). Taken together, although there were statistically significant associations between corresponding homework variables across the school subjects, these relationships were by no means perfect, indicating that the constructs included in our study were domain specific, and that separate models should be specified for each of the six school subjects. 3.2. Classroom-level differences Our first research question concerned variation in central homework variables within and across classrooms. How strongly do homework motivation, homework effort, and perceptions of homework quality and control covary across students in the same classroom? Consensus (or, more correctly, reliability of student responses) can easily be calculated by means of the intra-class correlation coefficients ICC1 and ICC2 (see Bliese, 2000; Lu¨dtke, Trautwein, Kunter, & Baumert, 2006; Snijders & Bosker, 1999). The ICC1 indicates the proportion of the total variance that is located between school classes; given the same total variance, the higher the ICC1, the more similar the homework ratings of students in the same classes and the more different the homework ratings of students in different classes. Theoretically, the intra-class correlation coefficient ranges between zero and 1.0. When student perceptions of the classroom environment are used, however, ICC1 values typically do not exceed 0.30 (Frenzel et al., 2007; Kunter et al., 2007; Trautwein, Lu¨dtke, Schnyder, et al., 2006), and school effects on psychological outcomes are typically much smaller, with ICC1 values of around 0.05e0.10 signifying substantial between-classroom variation (Anderman, 2002). Although there is no direct test of statistical significance for ICC1 values, it is possible to report the statistical significance of the between-class variance components that form the basis of the ICC1 values. In the present study, of the 36 between-class variance

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components calculated (see variables in Table 1), only two (English and mathematics compliance) were not statistically significant. The ICC2 can be used to evaluate the reliability of the aggregated student ratings at the classroom level. In general, values of ICC2 of 0.60 are considered as a lower bound for acceptable reliability of aggregated scores. We report the ICC2 only for those variables used as classroom variables (i.e., homework quality and homework control). As shown in Table 1, there were meaningful between-classroom differences in students’ homework effort. The ICC1 was somewhat higher for the percentage of homework assignments attempted (ranging from 0.06 in English to 0.17 in biology and German) than for homework compliance (ranging from 0.00 in mathematics to 0.11 in physics and German). Meaningful between-classroom differences were also found for the motivational predictors; the ICC1 for homework expectancy beliefs ranged from 0.05 in mathematics to 0.09 in physics and biology; the ICC1 for homework value beliefs ranged from 0.05 (mathematics and English) to 0.13 (biology and German). Again, these results point to meaningful between-classroom differences. We also calculated the ICC1 for the two homework assignment variables. The ICC1 for homework quality ranged from 0.12 in German to 0.21 in biology; the ICC1 for homework control ranged from 0.15 in English to 0.30 in biology. These figures indicate that there were considerable between-classroom differences in students’ perceptions of homework assignments. For the two homework assignment variablesdwhich were used as classroom-level predictors in later analysesdwe also calculated the ICC2. The ICC2 for homework quality ranged from 0.63 in German to 0.76 in biology, indicating that the aggregated homework quality scores are a reliable indicator of homework quality across classrooms. Likewise, the ICC2 for homework control ranged from 0.69 to 0.84, indicating good reliability at the classroom level. 3.3. Predicting homework motivation Our next four research questions concerned the prediction of homework motivation and homework effort. We therefore specified a series of prediction models, starting with homework expectancy and value beliefs as dependent variables. At the student level, student perceptions of homework quality and control (both class-mean centred), their reports of family background (immigration status, cultural capital) and of parental school-related behaviour, conscientiousness, and cognitive ability (all grandmean centred) were entered; at the classroom level, class-average ratings of homework quality and control as well as grade level were included. At the school level, school type was used as a predictor variable. The results for homework expectancy beliefs are reported in Table 2. Based on the homework model, perceived homework quality was expected to positively predict expectancy and value beliefs at both the classroom and the student level; the results confirmed this prediction. At the student level, homework quality statistically significantly predicted homework expectancy beliefs in all six school subjects: those students within a classroom who perceived their homework assignments to be of high quality typically also reported high expectancy beliefs. At the classroom level, homework quality was statistically significantly related to expectancy beliefs in mathematics, physics, German, and history. Homework control was statistically significantly related to expectancy beliefs in only one school subject (biology) and only at the classroom level. With respect to gender effects, we predicted that boys would report higher homework motivation and homework effort in stereotypically ‘‘male’’ school subjects. In support of this prediction, we found boys to have higher expectancy beliefs for mathematics and physics homework. Unexpectedly, they also reported higher expectancy beliefs for history homework. Of the parental variables, cultural capital was the most consistent predictor. Students from families with high cultural capital reported higher expectancy beliefs in five of the six school subjects. Students with an immigration background reported lower expectancy beliefs in German, but not in the other school subjects. Parental school-related behaviour was only loosely associated with expectancy beliefs (all regression coefficients 0.10). Conscientiousness was statistically significantly associated with expectancy beliefs in four school subjects, and cognitive ability was statistically significantly related to expectancy beliefs in mathematics, biology, and English. Moreover, students in academic-track schools reported higher expectancy beliefs than students in the intermediate track in two of the six school subjects, and 9th graders reported higher expectancy beliefs in German and English than 8th graders. The results for homework value beliefs are reported in Table 3. In line with our predictions, perceived homework quality statistically significantly and consistently predicted value beliefs at both the classroom and the student level. Boys reported higher Table 1 Intra-class correlation coefficients. Predictor variables

Mathematics

Compliance Percentage attempted Expectancy beliefs Value beliefs Homework quality Homework control

0.00 0.10 0.05 0.05 0.18 0.24

ICC1

Physics

ICC2

ICC1

0.72 0.79

0.11 0.09 0.09 0.11 0.20 0.24

Biology ICC2

ICC1

0.75 0.80

0.04 0.17 0.09 0.13 0.21 0.30

German ICC2

ICC1

0.76 0.84

0.11 0.17 0.06 0.13 0.12 0.16

English ICC2

ICC1

0.63 0.69

0.01 0.06 0.06 0.05 0.18 0.15

History ICC2

ICC1

ICC2

0.72 0.68

0.07 0.10 0.07 0.06 0.14 0.18

0.67 0.72

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Table 2 Predicting homework expectancy beliefs: results from HLM analysis. Mathematics

Physics

Biology

German

B

SE

B

SE

B

SE

School level School type: Academic track School type: Lower track

0.07 0.12

0.10 0.11

0.13 0.09

0.09 0.06

0.32 0.03

0.11 0.07

Classroom level Homework quality Homework control Grade level

0.23* 0.01 0.22

0.10 0.08 0.11

0.60*** 0.08 0.09

0.10 0.07 0.15

0.16 0.24*** 0.12

0.10 0.05 0.08

Student level Gender: Male Migration background Cultural capital Homework quality Homework control Family communication Parental homework help Parental homework control Conscientiousness Cognitive ability

0.49*** 0.02 0.12** 0.30*** 0.07 0.05 0.05 0.08** 0.14*** 0.16***

0.06 0.11 0.04 0.04 0.05 0.04 0.03 0.02 0.03 0.03

0.52*** 0.03 0.13** 0.28*** 0.01 0.05 0.01 0.04 0.10** 0.07

0.06 0.12 0.04 0.04 0.05 0.04 0.03 0.03 0.04 0.03

0.15 0.09 0.10 0.24*** 0.05 0.07 0.09* 0.07* 0.11* 0.08*

0.12 0.11 0.06 0.04 0.05 0.04 0.04 0.03 0.04 0.03

B

English SE

0.15 0.00

B

History SE

B

SE

0.09 0.08

0.38*** 0.18

0.07 0.09

0.17 0.32*

0.09 0.11

0.28*** 0.08 0.28**

0.06 0.10 0.10

0.10 0.03 0.25***

0.07 0.05 0.06

0.19* 0.14 0.12

0.09 0.09 0.09

0.07 0.18* 0.13 0.27*** 0.01 0.10* 0.00 0.01 0.14** 0.08

0.07 0.08 0.05 0.04 0.05 0.04 0.06 0.05 0.05 0.05

0.09 0.04 0.13* 0.23*** 0.07 0.01 0.03 0.06 0.15*** 0.08*

0.09 0.05 0.06 0.06 0.06 0.05 0.07 0.05 0.03 0.03

0.34*** 0.04 0.11* 0.27*** 0.06 0.04 0.09 0.03 0.08 0.08

0.09 0.09 0.05 0.05 0.04 0.05 0.06 0.05 0.04 0.05

Residual variance School level Classroom level Student level

0.00 0.02 0.74

0.00 0.04 0.71

0.00 0.00 0.79

0.00 0.03 0.79

0.00 0.00 0.84

0.00 0.01 0.77

Explained variance School level Classroom level Student level

0.17 0.65 0.22

0.30 0.60 0.21

0.99 1.00 0.13

0.99 0.49 0.15

1.00 0.97 0.11

0.97 0.76 0.17

***p < 0.001, **p < 0.01, *p < 0.05.

homework value in physics and lower homework value in English. A total of eight statistically significant predictive effects were found for family variables (immigration background, cultural capital, family communication, parental homework help/control) across the six school subjects, but only one of them was greater than 0.10. In contrast, conscientiousness was statistically significantly associated with homework value beliefs in all six school subjects. Students in lower-track schools reported lower homework value beliefs than students in the intermediate track for two school subjects (physics and history); students in academic-track schools reported higher homework value in two school subjects and lower homework value in one school subject. 3.4. Predicting homework compliance We next specified similar HLM models for homework compliance as the dependent variable. To test our assumption that homework motivation mediates some of the predictive power of homework quality on homework compliance, we specified two models for each school subject. In the first, we used the same variables as in the prediction of homework motivation; in the second, we additionally included homework expectancy and value beliefs. We expected the regression weights of perceived homework quality to decrease when homework expectancy and value beliefs were included, pointing to possible mediator effects. Table 4 reports the results for mathematics, physics, and biology; Table 5 the results for German, English, and history. The results were surprisingly similar across the six school subjects. Importantly, in model M1, perceived homework quality statistically significantly predicted homework compliance at both the student and the classroom level in all six school subjects. In model M2, which included homework expectancy and value beliefs, the regression coefficients for homework quality wered although mostly statistically significantdconsistently smaller than in model M1. Interestingly, homework control was a statistically significant predictor of homework compliance in three school subjects (mathematics, German, and history), but only at the classroom level. Expectancy and value beliefs statistically significantly predicted homework compliance in all school subjects; moreover, as shown in Tables 4 and 5, there was a meaningful increase in the variance explained when the homework motivation predictors were included. We also found a significant regression coefficient for conscientiousness in all models tested; all

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Table 3 Predicting homework value beliefs: results from HLM analysis. Mathematics

School level School type: Academic track School type: Lower track Classroom level Homework quality Homework control Grade level Student level Gender: Male Migration background Cultural capital Homework quality Homework control Family communication Parental homework help Parental homework control Conscientiousness Cognitive ability

Physics

Biology

German

English

History

B

SE

B

SE

B

SE

B

SE

B

SE

B

SE

0.25*** 0.06

0.04 0.07

0.04 0.31***

0.05 0.05

0.16 0.06

0.07 0.05

0.25** 0.12

0.06 0.08

0.22* 0.01

0.06 0.06

0.11 0.25**

0.05 0.05

0.57*** 0.01 0.07

0.06 0.06 0.06

0.78*** 0.05 0.06

0.09 0.06 0.07

0.62*** 0.08 0.00

0.08 0.07 0.06

0.54*** 0.28*** 0.06

0.10 0.05 0.05

0.56*** 0.00 0.02

0.05 0.07 0.07

0.62*** 0.08 0.01

0.07 0.04 0.06

0.06 0.08 0.07* 0.56*** 0.03 0.05 0.02 0.06* 0.13*** 0.07*

0.06 0.05 0.03 0.04 0.04 0.03 0.03 0.02 0.02 0.03

0.14* 0.01 0.14 0.51*** 0.10 0.03 0.07** 0.06* 0.10** 0.04

0.06 0.08 0.02 0.04 0.04 0.04 0.03 0.03 0.03 0.03

0.09 0.04 0.01 0.54*** 0.06 0.02 0.00 0.09* 0.12*** 0.08*

0.05 0.08 0.02 0.03 0.03 0.03 0.02 0.03 0.02 0.04

0.09 0.03 0.03 0.59*** 0.05 0.12** 0.00 0.07 0.09*** 0.06

0.05 0.06 0.03 0.03 0.03 0.03 0.02 0.03 0.02 0.03

0.26*** 0.02 0.02 0.52*** 0.02 0.08* 0.01 0.03 0.09* 0.01

0.07 0.07 0.04 0.04 0.05 0.03 0.04 0.04 0.04 0.03

0.05 0.23** 0.07** 0.58*** 0.12* 0.04 0.01 0.05 0.08* 0.04

0.07 0.07 0.02 0.02 0.05 0.03 0.03 0.04 0.03 0.05

Residual variance School level Classroom level Student level

0.00 0.00 0.61

0.00 0.00 0.58

0.00 0.02 0.53

0.00 0.00 0.51

0.00 0.01 0.62

0.00 0.00 0.55

Explained variance School level Classroom level Student level

0.86 1.00 0.36

0.91 0.99 0.34

0.70 0.82 0.39

0.99 0.97 0.41

0.99 0.75 0.34

0.90 0.98 0.41

***p < 0.001, **p < 0.01, *p < 0.05.

regression coefficients for this variable were greater than 0.20, indicating a consistent and powerful association between conscientiousness and homework compliance. Gender was statistically significantly associated with homework compliance in three school subjects. Consistent with our prediction of gender-stereotypic effects, girls reported higher compliance in biology, German, and English, but not in mathematics and physics. Of the family variables, immigration background predicted higher homework compliance in English, and family communication was associated with homework compliance in German and history. All other regression coefficients were statistically nonsignificant and/or below 0.10. In four school subjects (physics, biology, German, and English), there was some evidence that 9th graders showed lower homework compliance than 8th graders. Cognitive ability was statistically significantly associated with homework compliance in mathematics and history, but the regression coefficients were below 0.10. 3.5. Predicting the percentage of homework tasks attempted An identical set of models was specified with the percentage of homework tasks attempted as the outcome variable.2 Overall, the pattern of results was quite similar to that reported for homework compliance, but some qualifications apply. First, the variance explained (and the size of the regression coefficients) was generally lower. This may be due to the percentage-of-tasks-attempted measure having lower reliability, or to a lower degree of common method variance between the predictor variables and this outcome measure (see Section 4). Second, whereas homework quality and homework value consistently predicted the percentage of tasks attempted (apart from biology), the regression coefficient for expectancy value reached the level of significance for only two of the six school subjects when homework value was simultaneously controlled. When homework value was not included, expectancy value was a significant predictor in all school subjects except in history and German. Third, with statistically 2

The results tables, which are not presented here due to space restrictions, are available upon request from the first author.

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Table 4 Predicting homework compliance in mathematics, physics, and biology: results from HLM analysis. Mathematics

Physics

Model M1 B School level School type: Academic track School type: Lower track Classroom level Homework quality Homework control Grade level Student level Gender: Male Migration background Cultural capital Homework quality Homework control Family communication Parental homework help Parental homework control Conscientiousness Cognitive ability Expectancy beliefs Value beliefs

Model M2

Biology

Model M1

Model M2

Model M1

Model M2

SE

B

SE

B

SE

B

SE

B

SE

B

SE

0.05 0.08

0.06 0.09

0.04 0.05

0.07 0.03

0.07 0.07

0.05 0.01

0.05 0.07

0.10 0.12

0.06 0.09

0.02 0.10

0.07 0.09

0.21*** 0.11* 0.03

0.06 0.05 0.08

0.01 0.11*** 0.09

0.06 0.03 0.05

0.66*** 0.03 0.13

0.06 0.06 0.09

0.38*** 0.01 0.13

0.05 0.06 0.06

0.38*** 0.07 0.19***

0.09 0.06 0.04

0.19 0.01 0.21***

0.08 0.05 0.04

0.02 0.07 0.05 0.36*** 0.05 0.05 0.04 0.05 0.30*** 0.09*

0.09 0.09 0.04 0.04 0.05 0.03 0.03 0.03 0.03 0.04

0.11 0.09 0.05 0.13* 0.07 0.03 0.03 0.01 0.24*** 0.05 0.16*** 0.32***

0.07 0.07 0.03 0.06 0.05 0.03 0.03 0.03 0.03 0.05 0.03 0.04

0.06 0.13 0.01 0.41*** 0.06 0.06 0.00 0.02 0.26*** 0.00

0.06 0.12 0.03 0.04 0.04 0.04 0.03 0.04 0.04 0.04

0.08 0.12 0.03 0.25*** 0.05 0.05 0.02 0.00 0.22*** 0.00 0.23*** 0.19***

0.06 0.09 0.03 0.03 0.04 0.03 0.03 0.03 0.03 0.04 0.03 0.03

0.12* 0.17 0.03 0.46*** 0.03 0.03 0.02 0.02 0.29** 0.03

0.05 0.12 0.03 0.04 0.04 0.03 0.02 0.03 0.02 0.02

0.13*** 0.17 0.05* 0.27*** 0.03 0.01 0.00 0.06 0.24*** 0.03 0.23*** 0.25***

0.04 0.10 0.02 0.04 0.03 0.03 0.02 0.04 0.02 0.03 0.03 0.04

0.01 0.09

Residual variance School level Classroom level Student level

0.00 0.00 0.69

0.00 0.00 0.59

0.00 0.03 0.57

0.00 0.02 0.50

0.00 0.00 0.59

0.00 0.00 0.48

Explained variance School level Classroom level Student level

0.93 0.87 0.30

0.93 0.94 0.41

0.64 0.76 0.36

0.10 0.85 0.44

0.57 0.97 0.39

0.14 0.98 0.49

***p < 0.001, **p < 0.01, *p < 0.05.

significant regression coefficients in five school subjects, homework control at the classroom level was somewhat more closely associated with the percentage of tasks attempted than with homework compliance. 4. Discussion This study provided support for predictions derived from the homework model by Trautwein, Lu¨dtke, Schnyder, et al. (2006). First, students in different classes showed meaningful variation in their homework effort, homework motivation, and perceptions of homework quality and control (Hypothesis 1). Second, as expected (Hypothesis 2), we found conscientiousness, expectancy beliefs, and value beliefs to significantly predict homework effort in all six school subjects investigated. Third, homework quality predicted homework motivation and homework effort (Hypothesis 3). Fourth, in line with our expectations (Hypothesis 4), the pattern of results was somewhat domain specific, with boys reporting higher homework motivation and homework effort in stereotypically ‘‘male’’ school subjects (mathematics and physics). Fifth, in line with Hypothesis 5, the association between family background/parental homework behaviour and homework motivation and behaviour was not very strong. 4.1. The multilevel perspective and implications for classroom practice Homework is a prime example of a research area in educational psychology that calls for a multilevel approach (Trautwein & Ko¨ller, 2003). Teachers typically assign the same tasks to all the students in a class, and expect them to complete these tasks outside classroom hours. In somedbut not alldfamilies, parents are involved in controlling homework and its completion. It is therefore likely that multiple factors at different levels contribute to how much effort students put into their homework (Trautwein, Lu¨dtke, Schnyder, et al., 2006).

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Table 5 Predicting homework compliance in German, English, and history: results from HLM analysis. German

English

Model M1

Model M2

History

Model M1

SE

B

SE

School level School type: Academic track School type: Lower track

0.10 0.12

0.07 0.10

0.14 0.09

0.07 0.10

0.22** 0.31**

0.05 0.07

Classroom level Homework quality Homework control Grade level

0.52*** 0.29*** 0.05

0.05 0.07 0.08

0.35*** 0.23** 0.07

0.08 0.07 0.07

0.27** 0.07 0.19**

0.22*** 0.06 0.08* 0.40*** 0.04 0.11*** 0.02 0.00 0.26*** 0.00

0.04 0.09 0.03 0.04 0.04 0.03 0.03 0.03 0.03 0.03

0.20*** 0.05 0.08* 0.22*** 0.03 0.07* 0.02 0.01 0.22*** 0.01 0.10** 0.25***

0.03 0.09 0.03 0.05 0.04 0.03 0.03 0.03 0.03 0.03 0.03 0.05

0.28*** 0.15* 0.01 0.43*** 0.02 0.04 0.01 0.04 0.27*** 0.02

Student level Gender: Male Migration background Cultural capital Homework quality Homework control Family communication Parental homework help Parental homework control Conscientiousness Cognitive ability Expectancy beliefs Value beliefs

B

Model M2

B

B

Model M1

Model M2

SE

B

SE

B

SE

0.08 0.28***

0.05 0.06

0.05 0.09

0.10 0.16

0.02 0.04

0.09 0.13

0.07 0.05 0.05

0.09 0.07 0.24***

0.07 0.04 0.05

0.37*** 0.15* 0.13*

0.05 0.07 0.06

0.15* 0.10 0.16**

0.07 0.06 0.05

0.06 0.07 0.05 0.04 0.04 0.04 0.03 0.04 0.04 0.03

0.22*** 0.15* 0.03 0.24*** 0.04 0.01 0.01 0.02 0.22*** 0.01 0.19*** 0.28***

0.05 0.06 0.04 0.04 0.02 0.03 0.02 0.03 0.04 0.03 0.03 0.04

0.08 0.13 0.04 0.39*** 0.03 0.11*** 0.02 0.02 0.32*** 0.08*

0.09 0.10 0.03 0.05 0.03 0.03 0.03 0.04 0.03 0.04

0.03 0.08 0.05 0.18** 0.07* 0.09** 0.00 0.00 0.29*** 0.07* 0.19*** 0.27***

0.06 0.10 0.03 0.05 0.03 0.02 0.03 0.04 0.03 0.03 0.05 0.05

SE

Residual variance School level Classroom level Student level

0.00 0.03 0.55

0.00 0.03 0.50

0.00 0.00 0.60

0.00 0.00 0.49

0.00 0.00 0.60

0.00 0.01 0.51

Explained variance School level Classroom level Student level

1.00 0.71 0.37

0.99 0.73 0.43

1.00 0.77 0.38

1.00 0.77 0.50

0.99 0.93 0.36

0.99 0.92 0.45

***p < 0.001, **p < 0.01, *p < 0.05.

Homework researchers have long been aware of the need to differentiate between the classroom and student levels (Cooper, 1989; Corno, 1980), but most studies in the field have nevertheless failed to make this distinction (see articles included in the meta-analysis by Cooper et al., 2006; for exceptions, see Elawar & Corno, 1985; De Jong, Westerhof, & Creemers, 2000). Our study was the first to implement the multilevel perspective in a systematic approach to within- and between-classroom differences in homework motivation and effort across six school subjects. Importantly, when we calculated the intra-class correlation coefficients for various homework variables, we found that a meaningful percentage of variance was located between classrooms. For instance, the classes in our sample differed meaningfully in the average effort that students put into their assignments. Interestingly, the differences in homework effort for mathematics and English as a foreign language were comparatively small. These school subjectsdalong with Germandare particularly important in the 8th- and 9th-grade curriculum in Germany. As expected, given that all students within a classroom had the same teacher and rated the same assignments, the intra-class correlation coefficients for homework quality and homework control were particularly high. In other words, students in the same classroom gave similar ratings for the quality of their assignments as well as for their teachers’ homework control. These findings show that the perception of homework quality and control is not entirely idiosyncratic, but that students in the same classroom share a similar perception of their assignments. The ICC2 for homework quality and control confirmed that the aggregation of student responses to the classroom level yielded a reliable classroom measure. Homework quality was statistically significantly and meaningfully related to homework effort at both the classroom level and the student level, underlining the practical importance of this variable. The present study found a mixed pattern of predictive effects of homework control, with statistically significant classroomlevel effects in three of the six school subjects investigated. Although this finding is in line with prior studies, in which evidence for a significant association between homework control and effort was mixed (Trautwein, Lu¨dtke, Kastens, et al., 2006; Trautwein, Lu¨dtke, Schnyder, et al., 2006), it is somewhat unsatisfactory. From a practical point of view, given that the students in the present study reported making a serious effort in only about 50%e75% of their assignments, there is a clear need to enhance

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student homework effort. Homework control seems to be a natural way of achieving higher homework compliance and, ultimately, enhancing academic achievement (Walberg, 1991). However, the situation is complex. Even if teachers increase their control behaviours, they cannot be entirely sure that students really do the assignments themselves and do not just copy from their classmates. Moreover, students might experience a teacher who supervises homework completion strictly as ‘‘controlling,’’ which might undermine their intrinsic motivation. From this, it follows that homework control may take many different, and differently effective, forms. In the study by Elawar and Corno (1985) described above, in which homework control was found to positively affect student outcomes, strict and consistent homework control was combined with an explicit focus on motivating students. Hence, it seems likely that it is less the frequency than the quality of homework control that is positively associated with homework motivation and effort. Researchers should bear this point in mind when constructing assessment instruments for future research. 4.2. The role of conscientiousness and homework motivation Despite growing consensus that student behaviour follows domain-specific patterns, at least to some extent, some homework studies have continued to rely on domain-independent measures or on measures aggregated across domains (e.g., OECD, 2001). This approach is sometimes unavoidable because domain-specific data are not available (Keith, Diamond-Hallam, & Fine, 2004); in some cases, moreover, aggregation is theoretically desirable or justifiable (e.g., when overall homework time is related to overall achievement). However, there are two potential limitations to this approach. First, from the intraindividual perspective, students’ attitudes and behaviours may vary across school subjects. Second, to gain a better understanding of what predicts high or low effort investment in homework in different school subjects, it is necessary to determine whether the processes predicting high homework effort are the same across these domains. The present study showed statistically significant and meaningful differences between homework variables across the six school subjects investigated. For instance, homework effort was considerably higher in the core curricular subjects (i.e., mathematics, German, and English) than in the other three school subjects. Moreover, consistent with earlier findings (Trautwein, Lu¨dtke, Schnyder, et al., 2006), homework expectancy beliefs were comparatively low in mathematics, but homework value beliefs were comparatively high in the same school subject. The similarities across school subjects in the predictive models were quite strong. Interestingly, whereas the expectancy component proved to be a particularly strong predictor of homework compliance in mathematics in our earlier study, no such differences emerged across school subjects in the present study. Although we argue for a domain-specific approach to homework research, we include the stable personality trait of conscientiousness (Costa & McCrae, 1992) as an additional predictor in our homework model. In our view, domain-specificity and domain-generality are not contradictory, but complementary, in homework research. If homework behaviour were determined exclusively by expectancy and value components, it would be highly domain specific. We found a moderate level of consistency across the six school subjects, however, and the introduction of a more general personality trait such as conscientiousness might help to explain this moderate (but by no means perfect) relationship. Empirically, conscientiousness consistently predicted homework motivation and behaviour in all school subjects. Despite the evident predictive power of conscientiousness, educational psychologists have devoted very little attention to this variable in past years (for exceptions see De Raad & Schouwenburg, 1996; Lu¨dtke, Trautwein, Nagy, & Ko¨ller, 2004). One reason for this neglect may be the popular conception of personality being stable (Costa & McCrae, 1992) and essentially immune to pedagogical influences. During childhood and adolescence, however, personality traits are still developing and are open to environmental impact (Roberts & Pomerantz, 2004). As such, the instructional environment that students encounter daily may not be irrelevant to their personality development. In this respect, homework assignments and the way students deal with these assignments might impact personality development. Indeed, proponents of homework assignments have always emphasized that homework does not just help students to acquire knowledge, but also shapes their learning styles, self-regulation, and personality (see Cooper, 1989; Warton, 1997). It is therefore important to include conscientiousness in any comprehensive homework model, to test its predictive power, and, in the long term, to examine whether change in conscientiousness is influenced by homework variables. 4.3. Gender effects Interest in gender effects in the homework context has recently increased. Studies by Wagner et al. (2008) and Xu (2006) suggest that gender is associated with homework motivation and homework behaviour, with girls reporting higher homework morale. Given the empirical findings of gender differences in domain-specific measures of motivation and behaviour (Watt & Eccles, 2008), however, a domain-general perspective should perhaps be complemented by a domain-specific one. Indeed, our results support the call for a domain-specific view. It was only in German, English, and biologydthree stereotypically ‘‘female’’ school subjects (see Watt & Eccles, 2008)dthat we found higher homework compliance in girls. Boys reported higher expectancy beliefs for mathematics, physics and, interestingly, history; higher value beliefs for physics homework; and lower value beliefs for English homework.

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Taken together, our study substantively adds to the current debate on gender effects in the homework context by highlighting the domain-specificity of these effects. Future studies should examine to what extent these differences in homework behaviour contribute to the well-known gender differences in achievement levels (OECD, 2001). 4.4. Family background With respect to parental variables, the results of the present study seem to be somewhat more ambiguous. In general, the pattern of results is in line with our hypothesis that distal variables, such as family background and trustful parent-child communication about school are positively related to homework motivation and behaviour, whereas homework help and homework control can be a mixed blessing. However, the size of the regression coefficients was generally quite low, pointing to the rather limited predictive power of the variables included. This pattern of results does not imply, however, that parental homework is irrelevant. In our view, it reflects the fact that parental homework involvement is a rather complex issue in which the effects of the ‘‘same’’ behaviour (e.g., homework help and control) may depend heavily on the quality of the interaction between parent and child (Knollmann & Wild, 2007; Pomerantz et al., 2005). Although many students benefit from direct parental involvement in their homework, the homework motivation and behaviour of others may be impaired by their parents’ involvement, leading to weak overall effects. It appears that our study was not able to describe the various elements of the quality of parental homework involvement (see Knollmann & Wild, 2007) in enough detail. 4.5. Limitations and future research The present study tested hypotheses derived from an empirically validated theoretical framework in a sample of secondary school students, with parallel instruments being used across the six school subjects under investigation. Some issues should be borne in mind when interpreting the results, however. Most importantly, data were collected by means of student questionnaires only. Thus, student reports are our unique source of information, even on aspects such as homework characteristics and parental variables. This approach is justified in the present context because the homework model assigns particular importance to students’ perceptions of their homework assignments and their parents’ homework behaviours. Nevertheless, self-report as a unique source of information introduces potential biases. In a related vein, common method variance (see Podsakoff, MacKenzie, Lee, & Podsakoff, 2003) may bias results when the measurement methods used impact the empirical association between two constructs independent of the ‘‘real’’ association between the constructs the measures represent. In our study, this potential problem may be more pronounced with regard to the compliance outcome measure than the percentage of homework attempted measure. The format of the percentage measure is clearly distinct from that of most predictor variables, which is known to reduce the amount of common method variance. Hence, the fact that a similar pattern of results was found for both the compliance and the percentage measure is somewhat reassuring. Nevertheless, research would benefit from obtaining additional data on homework characteristics and parental attitudes and behaviours from additional sources (e.g., parents, teachers, classroom observations, computer log files; see Trautwein & Ko¨ller, 2003) to cross-validate the findings. Such a cross-validation should, if possible, use different assessment formats for behavioural predictors (e.g., homework motivation) and actual behaviour (e.g., homework compliance) to rule out unwanted construct overlap. The issue of causality also needs to be mentioned. Strictly speaking, the word ‘‘effect’’ denotes only ‘‘predictive effects’’ in the present study. Predictive effects do not necessarily imply causation, especially in studies with just one point of measurement. For instance, homework expectancy can have a positive (predictive) effect on homework effort if homework expectancy has a causal effect on homework effort, but also if homework effort has a causal effect on homework expectancy or if there is a reciprocal relationship. Hence, although the homework model specifies homework effort as being affected by the other variables in the model, and although empirical support was found for the assumed relationships, the present analysis does not establish causality. Given the somewhat restricted number of classrooms in the present study, generalizability is also an issue. Moreover, given that the sample was restricted to nine schools, any predictive effects of track level that were found or not found should be interpreted with caution. It is further unclear to what extent cultural differences might affect the results. Although no previous studies have documented major differences between homework practices in Germany and, for instance, the United States, cross-cultural studies might detect such differences. For example, the association between homework effort and homework control might differ from the one found in the present data set depending on how homework control is typically implemented. Moreover, it is unclear to what extent the results would be similar in samples of younger or older students. Hence, we would like to see future studies test the homework model in diverse samples from various countries and in different age groups. Finally, although we tested a fairly comprehensive model, our study was restricted to a limited number of variables. For the value component, for example, we used a short measure focusing on the utility and cost dimensions to avoid overburdening participants. Although these items showed the highest association with homework effort in an unpublished pilot study, intrinsic value also proved to be strongly associated with homework effort. We suggest that future homework studies implement a broader conceptualization of the value component if possible. For instance, some homework characteristics or aspects of parental help

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might evidence a closer association with intrinsic value than with utility value or cost. High-quality parental involvement might, for example, be associated with positive emotions or intrinsic value when doing homework (Knollmann & Wild, 2007), but not affect the more extrinsic elements of homework motivation. We also suggest that additional measures of homework performance (see Power, Dombrowski, Watkins, Mautone, & Eagle, 2007) and of learning from homework be included. In addition to such specific improvements to the design of future homework research, studies that specifically analyze the processes and mechanisms involved in the assignment and completion of homework are needed. Moreover, domain- and contentspecific pedagogical approaches must be integrated in research describing and analyzing the domain-specificity of homework processes. 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