The role of domain-specific ability self-concepts in the value students attach to school

The role of domain-speci

fic ability self-concepts in the value students

attach to school

Kerstin Schütte

⁎

, Friederike Zimmermann

, Olaf Köller

a

Department of Educational Research, Leibniz Institute for Science and Mathematics Education (IPN), D-24098 Kiel, Germany

b_{Department of Educational Psychology, Kiel University, Olshausenstr. 75, D-24118 Kiel, Germany}

a b s t r a c t

a r t i c l e i n f o

Article history:

Received 20 October 2015

Received in revised form 14 August 2016 Accepted 12 October 2016

Available online xxxx

Expanding the prevalent within-domain perspective, the present study investigated how students' domain-spe-cific ability self-concepts relate to the value they attach to school. With a longitudinal design and a sample of N = 1592 lower secondary school students from n = 82 classes in different educational tracks, we tested the hypothesis that mathematics and verbal self-concept interact in predicting how students value school. In addi-tion to statistically significant main effects, structural equaaddi-tion modeling revealed the expected latent interacaddi-tion effect. Response surface methodology demonstrated that students valued school more highly when their ability self-concepts were high in both domains rather than just one; a single low self-concept predisposed students to attach less value to school just as much as low self-concepts in both domains did. Helping all students frame at-tainable goals, thereby providing them with opportunities to experience success across domains, might increase the value they attach to school.

© 2016 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Keywords:

Motivation Academic self-concept Devaluation

In an ideal world, students would enjoy going to school, studying, and learning, and they would all live up to their potential. But they may not reach their full potential if they entertain negative beliefs about their academic abilities. If they think that they are weak in math-ematics, for example, their motivation to learn that subject declines. In addition, however, domain-specific ability self-concepts probably play a role in the value students attach to school in general.

We seek to contribute to a better understanding of the psychological processes underlying devaluation of school, using structural equation modeling and response surface methodology to investigate the effects that domain-specific measures of mathematics and verbal ability self-concept have on the value students attach to school while controlling for actual achievement in the respective domains. Students who attach little value to school tend to disengage from it. Disengagement from school is not only negatively related to students' academic motivation (Loose, Régner, Morin, & Dumas, 2012); it is also associated with a greater likelihood of dropping out of school as well as an increase in de-linquency, substance use, and depression (Li & Lerner, 2011; Wang & Fredricks, 2014).

1. Theoretical framework

Devaluing school is negatively related to academic motivation (Loose et al., 2012) and impairs learning behavior as well as

performance (Green et al., 2012). At the same time, students' cognitive representations of their academic abilities—their academic self-concepts—positively predict educational outcomes such as their level of educational attainment (Guay, Larose, & Boivin, 2004) and attitude towards school (Green et al., 2012; Spinath & Steinmayr, 2008). More generally, ability-related beliefs are predictors of academic outcomes (e.g.,Valentine, DuBois, & Cooper, 2004; Zuffianò et al., 2013). 1.1. Academic self-concepts

In contrast to the aforementioned studies on domain-general effects, most research has focused on the effects of self-concept within domains. Domain-specific ability self-concepts are reciprocally related to aca-demic achievement in the respective domain; that is, achievement pre-dicts self-concept and self-concept in turn prepre-dicts subsequent achievement (e.g., Chen, Yeh, Hwang, & Lin, 2013; Huang, 2011; Marsh, Trautwein, Lüdtke, Köller, & Baumert, 2005). Besides, students base the formation of their academic self-concepts on social compari-sons with relevant peers (e.g.,Marsh et al., 2008; Seaton, Marsh, & Craven, 2009). A relatively low academic standing in a class in a partic-ular school subject will thus produce a comparatively low domain-spe-cific self-concept. Dimensional (Möller & Marsh, 2013) and temporal comparisons (Zell & Alicke, 2009) are also sources of ability self-con-cepts. Dimensional comparisons involve an individual's achievement in different domains. Students' mathematics self-concepts are thus a function not only of their perceived mathematics achievement, but also of their perceived achievement in the verbal domain. Temporal Learning and Individual Differences xxx (2016) xxx–xxx

⁎ Corresponding author.

E-mail address:[email protected](K. Schütte). LEAIND-01399; No of Pages 7

http://dx.doi.org/10.1016/j.lindif.2016.10.003

1041-6080/© 2016 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Contents lists available atScienceDirect

Learning and Individual Differences

comparisons assess an individual's current achievement within a given domain relative to prior achievement in that domain.

High ability self-concepts are regarded as desirable educational out-comes. Their significance stems in part from their impact on other psy-chological variables associated with learning behavior (Wigfield & Eccles, 2000). Students' domain-speci_{fic ability self-concepts predict} the interest they will have in that domain (Marsh et al., 2005) and the value they attach to it (e.g.,Jacobs, Lanza, Osgood, Eccles, & Wigfield, 2002). A study of elementary school students provided only weak evi-dence for the effects of self-concept on the value subsequently attached to a particular domain (Spinath & Steinmayr, 2008), butDenissen, Zarrett, and Eccles (2007)demonstrated that the strength of the associ-ation between domain-specific ability self-concept and interest in the domain increased with students' age. Moreover, a cross-cultural study showed that students in a diverse set of countries attached greater value to science_{—to the domain in general as well as for themselves} personally—the higher their science self-concepts were (Schütte, 2015). Expanding this perspective, the current research investigated psychological consequences of the interplay between verbal and math-ematics self-concepts on a domain-general level, specifically, on the value attached to school.

1.2. Devaluing academic domains

Students who attach little value to school tend to disengage from it. Psychological disengagement from a domain might be employed by members of groups that are stigmatized as performing poorly in the re-spective domain, as a means to protect the self (Aronson et al., 1999; Major & Schmader, 1998; Major, Spencer, Schmader, Wolfe, & Crocker, 1998; Schmader, Major, & Gramzow, 2001; Steele, 1997). Persons dis-engage from a domain when they redefine their self-concepts in such a way that evaluations in the (threatened) domain are no longer used as a basis for self-esteem. Devaluing a domain is one psychological pro-cess used to disengage one's self-esteem from outcomes in that domain (Major & Schmader, 1998). Although this line of research relates to stig-matized groups, it converges with developmental theories that posit that disengagement is adaptive with regard to unattainable goals (Heckhausen, Wrosch, & Schulz, 2010; see alsoOyserman, Bybee, & Terry, 2006; Wrosch, Scheier, Carver, & Schulz, 2003). In that sense, devaluing school is a self-regulative strategy to reduce one's commit-ment to achievecommit-ment in school (i.e., identification with school achieve-ment;Steele, 1997).1_{The belief that their abilities arefixed as opposed} to malleable further predisposes these students to devalue school (Aronson, Fried, & Good, 2002; Burkley, Parker, Stermer, & Burkley, 2010). Devaluing school is associated with deteriorating learning be-havior (Loose et al., 2012); all things considered it does more harm than good. Some researchers have even found that devaluing does not have the expected protective effect on self-esteem (Lesko & Henderlong Corpus, 2006; Loose et al., 2012).

In educational psychology research, the expectancy–value model has most prominently featured subjective values as important determi-nants of achievement-related variables (Eccles et al., 1983;Wigfield & Eccles, 2000). The expectancy–value model encompasses not only at-tainment value, which is defined as the importance of doing well on a task and is thus conceptually highly similar to commitment to or iden-tification with the task, but also interest (i.e., intrinsic value) and utility

value as two further dimensions of the value component. Students' in-trinsic motivation to learn usually decreases over the course of their school careers (e.g.,Gottfried, Fleming, & Gottfried, 2001; Lepper, Corpus, & Iyengar, 2005; Musu-Gillette, Wigfield, Harring, & Eccles, 2015; Spinath & Steinmayr, 2008). As they attach less and less value to school, students increasingly disengage from school (Martin, 2007). This trend might be exacerbated in students with low academic self-concepts. These students would be particularly unlikely to maintain high intrinsic motivation, because attaching a high value to school is in-consistent with the belief that one has little academic ability, and should therefore generate psychological discomfort (Gawronski, 2012).

Loss of interest in a domain in which students do not consider them-selves competent (e.g.,Marsh et al., 2005) may be the result of a moti-vated process—a motivated devaluation of the domain. Devaluation might thus contribute to the process through which academic self-con-cepts affect subsequent achievement. The notion of motivated devalua-tion is supported by the positive associadevalua-tions between two domain-specific self-concepts and the value attached to school observed in a cross-sectional study of upper secondary school students (Kessels & Steinmayr, 2013). Estimating linear effects of academic self-concept on the value attached to school, however, provides only limited insight into the potentially complex interplay of both predictors. A low mathematics self-concept, for example, might exert a disproportionate-ly negative effect on one's attitude towards school on a more general level (Baumeister, Bratslavsky, Finkenauer, & Vohs, 2001); in addition, its effect on the value attached to school might vary as a function of the verbal self-concept.

2. The present research

We hypothesized that ability self-concepts in important academic domains (i.e., mathematics and German as the verbal domain) are pos-itively associated with the value students attach to school; this relation-ship is assumed to hold after controlling for achievement in the respective domains. We were specifically interested in whether the do-main-specific self-concepts interacted in predicting students' later valu-ing of school. We employed response surface methodology, which is not yet common in educational research, to gain comprehensive insights into the interplay between domain-specific ability self-concepts and their effect on the value attached to school that go beyond insights achieved through other methods.

3. Method 3.1. Participants

Data from two subsamples of the multicohort–multioccasion study Development and Implementation of a School-to-Work Transition Concept for Schools Serving Disadvantaged Communities conducted in two urban school districts in Germany were used to answer our re-search questions. All schools involved in that study served disadvantaged communities (high percentages of families of low socio-economic status and with an immigrant background). Recognition of social and ethnic disparities in Germany led to the implementation of school-improvement measures to mitigate the effects of student back-ground on achievement. The study Development and Implementation of a School-to-Work Transition Concept for Schools Serving Disadvantaged Communities assessed students' mathematics and ver-bal achievement as well as their interpersonal behavior over the course of 4 years while such measures were being implemented.

Students were excluded from analyses if they had not taken any of the achievement tests, nor completed the questionnaire associated with the assessment that served as ourfirst measurement point. In ad-dition, all cases were dropped for which no student data were available for the second measurement point (total N = 2114 prior to exclusions). The n = 714 (50.6% female), and n = 878 students (50.0% female) from

1

Steele (1997)used the term disidentification to denote disengagement, but other re-searchers use the term differently.Voelkl (1996), for example, operationalized identifica-tion with school as encompassing valuing of school as well as belongingness in school. As one's self-esteem can be disengaged from evaluations in a particular domain by means other than devaluation (e.g.,Major & Schmader, 1998), it seems in order to draw a clear distinction between devaluation and disengagement. It is important to note that discounting the validity of feedback makes disengagement possible while identification with the domain may be maintained.

Grades 5 und 7, respectively, attended n = 82 classes in different educa-tional tracks of the public school system. They were M = 10.87 (SD = 0.57) and M = 12.96 (SD = 0.59) years old. On average, students' socio-economic status was comparatively low, as reflected in a mean of 39 for the overall sample on the Highest International Socio-Economic Index of Occupational Status (Ganzeboom & Treiman, 1996); the mean of the national population of 15-year-old students assessed in 2000 was 48.9 (Organisation for Economic Co-operation and Development, & UNESCO Institute for Statistics, 2003). Moreover, 41.3% of the students reported primarily speaking a language other than German at home; these students are likely to have an immigrant background.

3.2. Procedure and measures 3.2.1. Academic achievement

Students took standardized mathematics and reading comprehen-sion tests on two consecutive days at the beginning of the 2006/2007 school year. Trained teachers administered the tests according to stan-dardized procedures. The tests_{—compiled using established} measures—had been constructed to ensure curricular validity for the re-spective grades (i.e., Grade 5 and Grade 7;Lehmann, Gänsfuß, & Peek, 1999; Lehmann & Peek, 1997). The mathematics tests covered typical topics in lower secondary school, such as algebra, arithmetic, and geom-etry. The reading comprehension tests required students to retrieve in-formation from different types of texts and understand how aspects of the text relate to one another, as well as to interpret and draw conclu-sions from the text. The majority of items in both tests were multiple-choice, a few were short constructed-response questions. Anchor-item designs allowed us to generate achievement scores that share a com-mon metric for students in both grades. Weighted likelihood estimates (WLEs;Warm, 1989) were obtained from scaling models based on item response theory as individual scores of mathematics and reading achievement. These WLEs were standardized to have a mean of zero and a variance of one across the entire sample.

3.2.2. Motivational constructs

At the end of the second day, student questionnaires were adminis-tered that contained 4-point rating scales (fully applies– does not apply at all) measuring students' self-concepts relating to the two subjects of mathematics and German (cf.Marsh et al., 2005). Wording of thefive items was identical except for the name of the subject (e.g.,“Although I make a real effort, mathematics [German] seems to be harder for me than for many of my fellow students.”). The reliability of both measures for the overall sample was satisfactory (ω = .85 and ω = .86 for math-ematics and verbal self-concept, respectively).

Two years later, student questionnaires assessed how highly stu-dents valued school, usingfive items. In line with the most prevalent operationalization (e.g.,Loose et al., 2012; Martin, Anderson, Bobis, Way, & Vellar, 2012; Schmader et al., 2001), the value attached to school tapped the attainment value as conceptualized by theEccles et al. (1983)model (three items; e.g.,“School is important to me.”). In addi-tion, valuing of school tapped the intrinsic value component (two items; e.g.,“I enjoy school lessons.”). The scale's reliability was satisfac-tory (ω = .84). Again, the response format was a 4-point rating scale (not true at all– absolutely true). Items were coded so that higher values reflect higher domain-specific self-concepts and a high value attached to school, respectively.

3.3. Analyses

First of all, missing values were multiply imputed (Schafer, 1997) with the Mplus 7.2 software (Muthén & Muthén, 1998-2012). The two-level imputation model contained variables indicating students' demographic, socioeconomic, and immigrant background as well as fur-ther motivational and achievement variables in addition to the variables actually being imputed; at the class-level, average achievement scores

as well as educational track were taken into account. All analyses were performed 50 times and results were integrated following the rules pro-posed byRubin (1987).

Subsequently, measurement invariance for valuing of school and for both self-concepts was established to ascertain that it was appropriate to collapse data across grades. It was not possible in the multiple group models to account for the non-independence of observations for students in the same class, because there were too few clusters (i.e., classes) within grades. In afirst step, we estimated a baseline model in which factor loadings and intercepts of the indicator variables were free to vary between grades. The confirmatory factor analysis model incorporated correlations between the residuals of correspond-ing self-concept items (i.e., correlated uniquenesses) because the word-ing of the self-concept scales differed only with respect to the domain they referred to. In addition, residuals of both items assessing the intrin-sic value component of students' valuing of school were allowed to correlate—as they tap an aspect of valuing of school that is conceptually different from the other three items, their residuals are not likely to be independent of each other. The baseline model provided an appropriate fit to the data, χ2_{(162) = 577.452, pb .001, comparative fit index}

(CFI) = .952, root mean square error of approximation (RMSEA) = .057, and standardized root mean square residual (SRMR) = .040 (Hu & Bentler, 1999). For model comparisons we refer to the cutoff values suggested by F. F.Chen (2007)becauseχ2_{difference testing has not}

yet been developed for multiple imputation; a change ofb −.010 for CFI (see alsoCheung & Rensvold, 2002) and a change ofb .015 for RMSEA indicate measurement invariance. Constraining the factor load-ings to be equal across grades did not diminish thefit of the model, ΔCFI = −.001 and ΔRMSEA = −.002. Imposing scalar invariance in the next step (i.e., constraining both the factor loadings and the inter-cepts of the indicator variables to be equal across grades, thereby impos-ing the constraints necessary to conduct the analyses testimpos-ing our hypotheses) resulted in no meaningful reduction of modelfit as com-pared with the previous model,ΔCFI = 0 and ΔRMSEA = −.001.

Structural equation modeling with the Mplus 7.2 software employed the MLR estimator, thus using robust maximum likelihood estimation with robust standard errors. Correct standard errors and chi-square tests of modelfit were obtained by accounting for the hierarchical data structure of students nested within classes. Multiple group analysis demonstrated that the path coefficients did not vary as a function of grade; a Waldχ2_{(W) test of parameter equalities attested to the}

ab-sence of statistically significant differences between both groups, W(9) = 11.06, p = .272. Therefore, one model wasfitted to the whole sample. The variances of the latent factors werefixed at one and factor means werefixed at zero. We thereby established scale equivalence of both self-concept factors.

Finally, we closely examined the interplay betweenfirst- and sec-ond-order effects of mathematics and verbal self-concept on the value attached to school. We employed response surface methodology to con-duct a formal analysis describing the nature of the three-dimensional surface that results from plotting the value attached to school as a func-tion of mathematics and verbal self-concept.

4. Results

Table 1displays descriptive statistics for the two cohorts. Significant differences were observed in both standardized achievement tests. Seventh-grade students achieved higher scores thanfifth-grade stu-dents in the mathematics as well as the reading comprehension test, z = 11.61, pb .001, and z = 14.06, p b .001, respectively. The average mathematics and verbal self-concepts did not differ between cohorts, z =−0.12, p = .90, and z = 0.58, p = .56, respectively. The value students attached to school was, however, significantly lower in Cohort 2 (then in Grade 9) than in Cohort 1 (then in Grade 7), z = 2.26, p = .02.

Table 2displays the correlations between those variables for the overall sample.

Prior to addressing our main research questions, wefitted a model without the latent variable interaction to our data to obtain absolute and incrementalfit indices; this model provided an adequate fit to the data,χ2_{(105) = 566.98, CFI = .950, RMSEA = .053, SRMR = .036. In}

the next step, we also specified the latent variable interaction and esti-mated the model as displayed inFigure 1. As expected, the coefficient for the latent variable interaction was significantly different from zero, z = 3.42, pb .001. Students' valuing of school was a joint function of their self-concept in both school subjects. At the same time, both math-ematics self-concept and verbal self-concept directly predicted valuing of school, z = 2.71, p = .007, and z = 2.27, p = .02. The lower students' domain-specific self-concepts were at the first measurement point, the less they valued school 2 years later. Students' achievement in the standardized mathematics test negatively predicted valuing of school, z =−2.62, p = .009; reading comprehension was not a statistically significant predictor of how much students valued school, z = −1.51, p = .13.

To account for potential nonlinearities in the relationship between domain-specific self-concepts and valuing of school, we estimated an-other model that also included quadratic predictor terms for both self-concepts. The interaction effect was again statistically significant, but there was no indication of curvilinearity; neither quadratic term was signi_{ficantly different from zero, b = 0.03, z = 0.76, p = .45, and} b =−0.02, z = −0.49, p = .62, for mathematics and verbal self-con-cept, respectively.

In a_{final step, we used response surface methodology to further our} understanding of the relationship between valuing of school and the predictors mathematics and verbal self-concept. Specifically, we plotted a three-dimensional surface using the coefficients obtained for first- and second-order effects of both self-concepts on valuing of school in the full model (Edwards, 2002; Edwards & Parry, 1993; seeFigure 2). The corre-sponding equation was as follows:

η1¼ b1η1þ b2η2þ b3η12þ b4η1η2þ b5η22þ ξ4

whereη3represents valuing of school andη1andη2are mathematics

and verbal self-concept, respectively;ξ3represents the residual.2

InFigure 2, mathematics and verbal self-concept are perpendicular horizontal axes and valuing of school is the vertical axis. Overall, the saddle-shaped surface is curved upward such that valuing of school in-creases as both self-concepts increase. The peak of the surface is at the point ofη1= 3 ,η2= 3; that is, valuing of school was maximized when

both self-concepts were highest. A formal analysis of the line where mathematics self-concept equals verbal self-concept (_η1=η2) revealed

that the surface was curved slightly upward along this line (b = 0.11, p = .007) and positively sloped at the mean of both self-concepts

(b = 0.22, pb .001). The value attached to school increased the more both self-concepts exceeded their respective average. To explore the ef-fect on valuing of school when mathematics and verbal self-concept maintained a compensatory relationship, we analyzed the line where mathematics self-concept equals the additive inverse of the verbal self-concept (η1=−η2). The surface wasflat along this line; neither

the curvature of the line nor the slope at the mean of both self-concepts was statistically significant (b = −0.10, p = .15, and b = 0.03, p = .69, respectively). The value attached to school remained at the same com-paratively low level whether both self-concepts were average or one was extremely low while the other was extremely high.

5. Discussion

We theorized that students' valuing of school was a function of their domain-speci_{fic self-concepts of ability. Specifically, we assumed that in} addition to their direct effects, the two major domain-specific self-con-cepts mathematics and verbal self-concept would produce an interac-tive effect on the value students attached to school when achievement in the respective domains was controlled for. The structural equation model did indeed reveal a statistically significant latent interaction. Moreover, both self-concepts exerted significant direct effects on valu-ing of school.

5.1. Academic self-concepts and valuing of school

Response surface methodology, used to describe how valuing of school varied as a function of both academic self-concepts, revealed that students' later valuing of school was not lower when both self-con-cepts were low relative to when only one of them was low. Put in neg-ative terms, however, even a single low domain-specific self-concept was associated with low valuing of school. The fact that the value at-tached to school was found to be comparable whether the student had two low self-concepts or only one might be an instance of negativity bias (e.g.,Baumeister et al., 2001). Unless students' self-concepts are high in both subjects, the lower self-concept seems to contribute dispro-portionately to the value they attach to school. Unfortunately, devaluing school does not seem to have the expected protective effect on students' self-esteem: Devaluation of academic success was not a predictor of global self-esteem as assessed three months later in a sample of low-SES students (Loose et al., 2012).

The significance of the mathematics domain is in line with previous studies (e.g.,Deary, Strand, Smith, & Fernandes, 2007; Marsh & Yeung, 1997) and might be interpreted in light of the implicit theories students endorse about academic achievement (e.g.,Dweck, Chiu, & Hong, 1995; Dweck & Leggett, 1988). Both laypeople (Meyer, Cimpian, & Leslie, 2015) as well as practitioners in thefield (Leslie, Cimpian, Meyer, & Freeland, 2015) tend to believe that mathematics requires special apti-tude, more than most other academic domains. Consequently, students may perceive their mathematics abilities to be less malleable than their verbal abilities. This notion is corroborated by the vast literature on mathematics anxiety (e.g.,Maloney & Beilock, 2012). Research on mathematics anxiety, in the absence of corresponding research in the verbal or other domains, seems to suggest that mathematics is Table 1

Means and standard deviations by cohort

Cohort 1 Cohort 2 M SD M SD T1 Mathematics achievement –0.32 1.03 0.25 0.90 Reading achievement –0.38 0.93 0.29 0.94 Mathematics self-concept 0 0.85 –0.01 0.88 Verbal self-concept 0 0.87 0.03 0.82 T2 Valuing of school 0 0.68 –0.10 0.68

Note. Cohort 1 = Grade 5, Cohort 2 = Grade 7 at thefirst measurement point, respectively; T1 =first measurement point; T2 = second measurement point. Both achievement scores were observed variables; the domain-specific self-concepts and valuing of school were la-tent variables. The lala-tent factor means werefixed at zero in Cohort 1 and were estimated in Cohort 2.

Table 2

(Latent) Bivariate correlations (and standard errors)

(2) (3) (4) (5) (1) Mathematics achievement .64 (.06) .31 (.03) .17 (.03) –.12 (.03) (2) Reading achievement – .22 (.03) .26 (.03) –.10 (.03) (3) Mathematics self-concept – .27 (.04) .09 (.04) (4) Verbal self-concept – .09 (.04) (5) Valuing of school –

Note. All constructs but valuing of school were assessed concurrently; valuing of school was assessed with a time lag of 2 years. Standard errors are corrected for non-indepen-dence of observations for students in the same class.

2

The partial coefficients were additionally controlled for the effects of mathematics achievement and reading comprehension on both self-concepts and on valuing of school.

specifically associated with the threat of feeling deficient (i.e., lacking what it takes) and negative affect. When their mathematics self-concept is low, students will judge the prospect of improving their performance to be particularly dismal (Fredricks & Eccles, 2002; Jacobs et al., 2002). It is conceivable that these negative experiences mar the overall school experience.

As for the verbal domain, reading is recognized to be a key com-petence that contributes to success in other domains. In a cross-sec-tional study of upper secondary school students, Kessels and Steinmayr (2013)found that self-concept in German was an even stronger predictor of valuing of school than mathematics self-con-cept. Unlike the students in the present study, upper secondary school students have more freedom to determine their own sched-ules; they may shape their academic self-concept by selecting courses that emphasize personal strengths and downplaying the im-portance of school subjects in which they perceive their abilities to be comparatively low. So upper secondary school students with a low mathematics self-concept may reduce the psychological central-ity of mathematics, thereby making it unnecessary for them to attach a similarly low value to school.

5.2. Academic achievement and valuing of school

Contrary to expectations, achievement on the standardized mathe-matics test negatively predicted valuing of school, necessitating a dis-cussion of the signi_{ficance of achievement for the value attached to}

school. Reading achievement was not a significant predictor of valuing of school in the structural equation model; however, the bivariate corre-lation was also significantly negative. Still, there is no reason to believe that the tests have been compromised. They were compiled from curricularly valid established measures, and the comparisons of the two cohorts' mean achievements yielded plausible results. An impor-tant task for future research is therefore to investigate the conditions under which high achievement entails devaluation of school. One might speculate that schools have failed to meet the needs and interests of high-achieving students. Another possible explanation might be that students in the current sample devalued school out of concern for their reputation. Previous research has shown students' disengagement from a particular subject to be a function of the disengagement they perceive in their classmates (Martin et al., 2012). Indifference to academic achievement might be a perceived peer norm. To the extent that aca-demic motivation is perceived as incompatible with popularity (Juvonen & Murdock, 1995), adhering to that norm might be particular-ly important for high-achieving students. Attaching a low value to school might then be viewed as indicating that achievement is the result not of effort, but of ability. Assuming that such norms are internalized, they may also have an impact on students' responses to confidential questionnaires. Because such norms might be particularly strong in middle school and in learning environments with a large number of so-cioeconomically disadvantaged students (Martin et al., 2012), it would be desirable to replicate the present results with a more heterogeneous sample.

Figure 1. Structural equation model predicting valuing of school for the total sample. Achievement scores and self-concepts as assessed at thefirst measurement point (Grade 5 and 7, respectively), valuing of school as assessed 2 years later. Dashed arrows indicate paths that were not statistically significant.

5.3. Limitations and future directions

To the best of our knowledge, our study was the_{first to investigate} how verbal and mathematics ability self-concepts interact to affect the value students attach to school at a domain-general level. In particular, we modeled a latent interaction effect, while controlling for students' scores on standardized achievement tests, using a longitudinal design. Response surface methodology enabled us to conduct a sound investi-gation of the relationship between valuing of school and the predictors mathematics and verbal self-concept. It compares favorably to the more conventional simple slope analysis in providing insights into the nature of the interaction effect. Although it has been applied in organizational psychology (e.g.,Edwards & Cable, 2009), to the best of our knowledge response surface methodology has not yet been used in educational re-search. We strongly recommend more extensive usage of these techniques.

At least two aspects, however, need to be mentioned as limitations of the current study. A caveat of our design for modeling the effects of students' self-concepts on later valuing of school was the absence of a measure of the value attached to school for thefirst measurement point. As the scale had only been introduced at the last measurement point of the multioccasion study, it was not possible to include prior val-uing of school. Moreover, inclusion of a domain-general measure of stu-dents' academic self-concepts in future studies would allow for an insightful comparison: Students need to aggregate their cognitive rep-resentations of their academic abilities to arrive at a domain-general ap-praisal. The predictive value of ability-related beliefs is usually higher when their level of specificity matches the level of the criterion variable. A further limitation of our study concerns the generalizability of the observed effects. Our sample overrepresented students from families with a comparatively low socioeconomic status and students with an immigrant background. To the extent that parents' educational aspira-tions and involvement vary as a function of family background, this will also affect how readily students devalue school. Whether the effects of students' self-concepts on their valuing of school replicate with stu-dents from more diverse family backgrounds is a question for future re-search. If the association between students' domain-specific self-concepts and their valuing of school was indeed moderated by the family's socioeconomic status, this would contribute to maintaining in-equity in education.

6. Conclusion

Devaluing school is a rather radical strategy, which students—because of its self-reinforcing nature_{—are not likely to abandon in the absence of} environmental changes or explicit interventions. Once students perceive school to be of little importance to their self-concept and disengage their self-esteem from academic achievement (i.e., they disengage from school) they will further reduce their learning behavior. This, in turn, per-petuates low achievement and reduces job opportunities and life options. It is therefore imperative that we gain a better understanding of the psy-chological processes underlying motivated devaluation of school and how to discourage it. Encouraging students to refrain from comparing themselves with their classmates with regard to academic achievement (Huguet et al., 2009), thereby mitigating potentially detrimental effects on ability self-concepts—a recommendation that is equally valid for dif-ferent kinds of ability grouping—might help to achieve this goal. Rather, students should be encouraged to draw temporal comparisons. Strategies to promote students' engagement with school might also include provid-ing feedback on their progress and acknowledgprovid-ing effort. Ultimately, all students need to (re)frame their goals in the major school subjects so that they are attainable (cf. e.g.,Meece, Anderman, & Anderman, 2005; Pintrich, 2000, for a related discussion of mastery as opposed to perfor-mance goals). The present results suggest that harmful consequences of even one low ability self-concept are not confined to the respective do-mains; they affect the value students attach to school on a global level.

Students who experience progress towards their goals across subjects will be less likely to devalue school.

Acknowledgements

We gratefully acknowledge Gabriel Nagy for suggesting response surface methodology as a way of investigating the interaction effect of mathematics and verbal self-concept on valuing of school.

The research reported in this article is part of the project “Entwicklung und Implementierung eines neuen Konzeptes zur Eingliederung Jugendlicher in die Berufs- und Arbeitswelt in Schulen mit erhöhtem Förderbedarf (EIKA) [Development and Implementation of a School-to-Work Transition Concept for Schools Serving Disadvantaged Communities]” directed by Olaf Köller. The project was funded by the Senator for Education and Science of the Free Hanseatic City of Bremen and co-_{financed by the European Regional Development} Fund (ERDF).

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