Smart, confident, interested: Contributions of intelligence, self-concept, and interest to elementary school achievement

Learning and Individual Differences 62 (2018) 23–35

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Smart, confident, interested: Contributions of intelligence, self-concept, and interest to elementary school achievement☆

T

⁎

Rebecca Schneider , Christin Lotz, Jörn R. Sparfeldt Saarland University, Germany

A R T I C L E I N F O

A B S T R A C T

Keywords: Scholastic achievement Intelligence Motivation Self-concept Elementary school

Cognitive and motivational variables are significant correlates and predictors of scholastic achievement. In upper elementary school grade levels, intelligence seems to be more important compared to motivational variables. Regarding motivational variables, (competence) self-concept revealed higher path coefficients in reported grades than interest. Extending these findings to lower grade levels, the present study with N = 858 students that stemmed from grade levels 2, 3, and 4 (n = 253/321/284) revealed that, when all three predictors were jointly considered, self-concept and interest contributed substantially to the prediction of reported grades in mathematics and German beyond intelligence in all three examined grade levels, with the exception of interest of fourth graders in German. Self-concept was the numerically stronger motivational predictor. Significant grade level-related differences of the predictors were not evidenced. The importance of cognitive and motivational predictors for scholastic success in elementary school is discussed.

1. Introduction Success in school as indicated by scholastic achievement has been and still is a major topic in educational and psychological research. Because of its relevance for success in life, it seems worthwhile to examine important determinants of scholastic achievement. Prominent and frequently discussed predictors are cognitive and motivational constructs like intelligence and academic self-concept. Although intelligence is a very good predictor of achievement in, for example, mathematics and native languages (e.g., Deary, Strand, Smith, & Fernandes, 2007; Jensen, 1998; Roth et al., 2015), there is a substantial amount of variance left unexplained. Previous research with a focus on fourth graders has shown that motivational constructs like students' competence self-concept or interest substantially add to the prediction of scholastic achievement above and beyond intelligence (Spinath, Spinath, Harlaar, & Plomin, 2006; Weber, Lu, Shi, & Spinath, 2013). However, for elementary school children below grade level 4, the simultaneous prediction of scholastic achievement by cognitive and motivational variables remains a rather open question. Due to a progression in cognitive development, self-concept formation processes, and increasing scholastic experiences in the elementary school years, grade level-related differences in the prediction of scholastic

achievement by cognitive and motivational variables might occur. Scholastic achievement is typically assessed by reported grades or scholastic competence tests (Steinmayr, Meißner, Weidinger, & Wirthwein, 2014). Reported grades and competence tests usually correlate around .40 ≤ r ≤ .60 (Helmke & van Aken, 1995; Marsh, 2007), indicating substantial differences between both measures. Whereas test scores should merely reflect the performance of a student in a particular test, reported grades rely on a broader definition of achievement that additionally includes motivational aspects, volition, or effort (Willingham, Pollack, & Lewis, 2002). In contrast to competence test results, reported grades are typically well-known by (elementary school) students due to the immediate and salient feedback by teachers (e.g., overviews of reported grades after in-class examinations, report cards). They are also of high importance to students and their parents for the promotion to the next academic year. Therefore, this study focused on the statistical prediction of scholastic achievement (assessed by reported grades in two core elementary school subjects, i.e. mathematics and native language) by intelligence, competence self-concept, and interest, especially taking specific and common variances into account. Additionally, differences across elementary school grade levels 2, 3, and 4 were examined.

☆ This research was conducted with the support of the German funds “Bund-Länder-Programm für bessere Studienbedingungen und mehr Qualität in der Lehre (‘Qualitätspakt Lehre’)” [the joint program of the States and Federal Government for better study conditions and quality of teaching in higher education (“the Teaching Quality Pact”)] at Saarland University (funding code: 01PL11012). The authors developed the topic and content of this manuscript independent of this funding. ⁎ Corresponding author at: Department of Educational Science, Campus A5 4, Saarland University, D-66123 Saarbrücken, Germany. E-mail address: [email protected] (R. Schneider).

https://doi.org/10.1016/j.lindif.2018.01.003 Received 11 April 2017; Received in revised form 13 October 2017; Accepted 2 January 2018 1041-6080/ © 2018 Elsevier Inc. All rights reserved.

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domain-specific academic achievements were repeatedly reported (e.g., Arens, Trautwein, & Hasselhorn, 2011; Skaalvik & Skaalvik, 2002). Selfconcept and interest are usually substantially correlated within one domain (Arens, Trautwein, et al., 2011; Arens, Yeung, et al., 2011; Arens & Hasselhorn, 2015; Marsh et al., 1999; Möller, Pohlmann, Köller, & Marsh, 2009), but show differential relations to outcome variables: Self-concepts revealed a stronger relation to scholastic achievement, whereas interests were usually stronger related to effort or choice-related behaviors. Accordingly, the relations between interests and reported grades were numerically lower than self-concept–reported grade correlations (e.g., Arens, Yeung, et al., 2011; Eccles et al., 1993; Jansen, Lüdtke, & Schroeders, 2016; Spinath et al., 2006). Regarding differences between elementary school grade levels, selfconcept/interest–reported grade correlations are usually of higher magnitude in higher grade levels. For example, increasing manifest selfconcept–reported grade correlations were reported for 2nd/3rd/4th graders of r = .35/.40/.52 for mathematics and r = .37/.41/.50 for native language (Helmke, 1997a). Considering eagerness to learn as an indicator of interest, the manifest interest–reported grade correlations were numerically smaller compared with the self-concept–reported grade correlations, but also numerically increasing for mathematics (r = .26/.32/.35) and native language (r = .19/.31/.33). For the relations of self-concept/interest with reported grades, comparable correlation patterns were found for native language in a sample of third and fourth graders (Weidinger, Spinath, & Steinmayr, 2015). The progression in cognitive development, increasing scholastic experiences, and the onset or increase of social and dimensional comparisons with increasing age should result in more realistic self-concepts and interests (Harter, 1999; Helmke, 1999; Weidinger et al., 2015; Wigfield & Eccles, 2000; Wigfield et al., 1997). Thus, the correlation between self-concepts or interests and reported grades should increase and their predictive power on reported grades should be of higher magnitude in higher elementary school grades.

1.1. Cognitive variable: intelligence Regarding cognitive variables, intelligence is considered to be one of the most relevant predictors of academic achievement (e.g., Deary et al., 2007; Jensen, 1998; Kuncel, Hezlett, & Ones, 2004). The mean correlation of ρ = .45 for elementary school students reported in a recent meta-analysis indicates that more intelligent students get better reported grades in school (Roth et al., 2015). Concerning different grade levels, the intelligence–reported grade correlations seem not to differ substantially across elementary school levels: By using identical assessments for intelligence (non-verbal reasoning) and reported grades in different elementary school grade levels and, thereby, supporting construct equivalence, Laidra, Pullmann, and Allik (2007) reported comparably high manifest correlations of r = .54/.50/.53 (corrected for range restriction) between intelligence and grade point average for second/third/fourth graders, respectively. Unfortunately, Laidra et al. (2007) did not test for measurement invariance among grade levels due to a manifest analysis strategy. To detect meaningful differences between respective grade levels, identical assessments and measurement invariance testing are desirable. With regard to school subject-specific reported grades, Bullock and Ziegler (1997) found for third/fourth graders manifest intelligence–reported grade correlations of r = .46/.49 in mathematics and of r = .36/.41 in German as native language (general intellectual ability in 3rd grade, non-verbal reasoning in 4th grade). Other studies reported manifest correlations between reported grades and different intelligence factors of comparable magnitude for fourth graders (Spinath et al., 2006: rmathematics/English = .49/.44 [general intellectual ability]; Spinath, Spinath, & Plomin, 2008: rmathematics/English = .44/.42 [general intellectual ability]; Weber et al., 2013: rmathematics/ German = .47/.36 [non-verbal reasoning]). A numerically lower manifest correlation between reported grades and figural reasoning of r = .23 was found for German in third and fourth graders (Dresel, Fasching, Steuer, & Berner, 2010). However, analyses were not run separately for third and fourth graders and, thus, their interpretation might be impaired. To conclude, these results limit firm conclusions regarding comparisons across grade levels due to different operationalizations.

1.3. Prediction of reported grades by intelligence, self-concept, and interest Studies examining the simultaneous prediction of reported grades by cognitive and motivational variables, such as intelligence, self-concept, and interest in elementary school are sparse. To predict reported grades in fourth graders, some authors used conglomerates of various cognitive and motivational variables. For example, reported grades in mathematics were numerically stronger predicted by cognitive variables (conglomerate of intelligence [non-verbal reasoning] and working memory; β = 0.59) compared to motivational variables (conglomerate of self-concept and intrinsic value; β = 0.41; Weber et al., 2013). For German (native language), motivational variables turned out to be the numerically better predictor than cognitive variables (β = 0.67 vs. β = 0.34). Both, conglomerates of cognitive and motivational variables, explained R2 = .71 of the reported grade variance in mathematics and R2 = .75 in German. Helmke (1997b) reported numerically lower coefficients for both sets of predictors of reported grades (cognitive predictors: prior knowledge, intelligence [non-verbal reasoning], ability to concentrate; motivational predictors: self-concept, attitudes toward subjects, test anxiety, further variables concerning volitional and learning-related aspects): Cognitive variables (βmathematics/ German = 0.22/0.22) were numerically stronger predictors compared to motivational variables in mathematics and German (β = 0.06/0.05; for German contrary to Weber et al., 2013). Within these manifest analyses, both predictors explained R2mathematics/German = .59/.57 of the total reported grade variance. Using intelligence (verbal and non-verbal reasoning) and academic self-concept (Schicke & Fagan, 1994), intelligence accounted for 48% of the variance in reported grades (R2 = .48) and academic self-concept contributed only a small amount of variance beyond intelligence (ΔR2 = .07). So far, only one study investigated intelligence, self-concept, and interest simultaneously as separate predictors of academic achievement

1.2. Motivational variables: competence self-concept and interest Whereas intelligence is substantially related to reported grades, explaining mostly around 25% of the reported grade variance in mathematics or native language, a substantial amount of variance is left unaccounted for. Additionally, motivational constructs contributed substantially to the prediction of reported grades beyond intelligence (e.g., Steinmayr & Meißner, 2013; Steinmayr & Spinath, 2009). Salient motivational variables with close relations to scholastic achievement are competence self-concept and interest. Whereas competence selfconcept refers to students' self-perceived ability and reflects the expectancy component within the well-elaborated expectancy-value model (e.g., Eccles (Parsons) et al., 1983; Wigfield & Eccles, 2000), interest is a more subjective and intrinsic motivational-affective variable that is considered to be part of the value component. In some studies in the tradition of self-concept literature dealing with its formation, structure, and assessment (e.g., Arens, Yeung, Craven, & Hasselhorn, 2011; Marsh, Craven, & Debus, 1999), the term “affect selfconcept” was used basically as a synonym for interest. For example, affect self-concept items of the well-established Self Description Questionnaire I (SDQ I; Marsh, 1992) like “I am interested in [subject]” were used to measure interest (e.g., Schroeders, Schipolowski, Zettler, Golle, & Wilhelm, 2016). Both, self-concept and interest, are domain-specifically structured even in early grades (e.g., Arens, Yeung, et al., 2011; Eccles, Wigfield, Harold, & Blumenfeld, 1993). Correspondingly, convergent and divergent relations of domain-specific self-concepts or interests with 24

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graders, using the same operationalization for all predictors and criteria in the three grade levels. In detail, our research questions were threefold and separately tested for mathematics and German (native language). The first aim was to analyze the prediction of the reported grade by intelligence and one additional motivational variable as based on priorly mentioned studies (e.g., Spinath et al., 2006). Concerning the simultaneous prediction of the reported grade using only intelligence and self-concept, we expected to find, (1a) unique intelligence effects beyond self-concept as well as unique effects of self-concept beyond intelligence. Analogously, we expected to find, (1b) unique effects of interest beyond intelligence as well as unique intelligence effects beyond interest in a corresponding prediction model with only intelligence and interest. Second, we examined the prediction of the reported grade by intelligence, self-concept, and interest in concert. Based on prior results (Spinath et al., 2006), we expected (2a) no substantial unique effects of interest beyond intelligence and self-concept, but we assumed (2b) selfconcept and (2c) intelligence to show unique effects beyond the other two respective predictors. Third, possible developmental changes in the predictive power of intelligence, self-concept, and interest across elementary school grade levels were inspected: We assumed (3a) comparable path coefficients of intelligence on the reported grade and (3b) increasing path coefficients of self-concept/interest on the reported grade with higher elementary school grade levels.

(Spinath et al., 2006) in a sample of N = 1678 nine year old twins. Substantial path coefficients of intelligence (general intellectual ability and reasoning tests; mathematics/English: β = 0.42/0.38) and selfconcept (β = 0.29/0.31) emerged on composite achievement scores, but non-significant path coefficients of interest (β = −0.03/0.00). To evaluate the predictive power of each predictor and in order to avoid underestimating the significance of the less powerful predictor, Spinath et al. (2006) examined the proportion of variance solely explained by each predictor as well as the proportion of shared variance, relying on commonality analyses. Regarding solely intelligence and self-concept, both predictors explained R2 = .32 of the achievement variance in mathematics. Thereby, intelligence uniquely accounted for R2 = .17, self-concept for R2 = .08, and the shared variance for R2 = .07. In a second model with solely intelligence and interest, both predictors explained R2 = .29 of the achievement score variance in mathematics. In this model, intelligence uniquely accounted for R2 = .23, interest accounted for R2 = .04, and the commonly explained variance was very small (R2 = .02). For English (as native language), results were of comparable magnitude. As mentioned above, the coefficients of interest on achievement scores were non-substantial when intelligence, selfconcept, and interest were considered simultaneously as predictors. This might be due to substantial correlations between self-concept and interest (rmathematics/English = .74/.56). Regarding common variances of cognitive and motivational variables, Spinath et al. (2006) assumed mutual reinforcement processes of intelligence, self-concept, and interest. For example, students with higher intelligence scores show better reported grades and perceive higher achievements in a subject and, therefore, might experience more competence and positive intrinsic affect while working in that subject, whereas for students with lower abilities, receiving lower/weaker reported grades, the work might be more strenuous and less associated with positive affective-motivational feelings. Reversely, stronger interest or a more positive self-concept might contribute to improve the reported grade, for example, based on higher motivation to learn or practice. Therefore, it can be expected that a substantial portion of variance in reported grades is explained by the communality of selfconcept and interest. However, interest does not seem to show a substantial specific contribution to the prediction of reported grades in addition to the shared variance of intelligence and self-concept (Spinath et al., 2006). Unfortunately, communality analyses by Spinath et al. (2006) were only based on two and not on all three predictors. Thus, the analysis of specific and common variances within a simultaneous prediction of reported grades by intelligence, self-concept, and interest still calls for further research. All studies mentioned in this section examined the prediction of reported grades in fourth graders. For elementary school children in lower grades, studies are needed. Therefore, assumptions about differences in the prediction of reported grades between elementary school grade levels can only be based on differences in correlations of reported grades with intelligence, self-concept, and interest. As mentioned, the relations between reported grades and intelligence seem not to differ substantially between grade levels, whereas the relations between reported grades and self-concepts or interests were of higher magnitude in higher elementary school grade levels. Therefore, the predictive power of intelligence might remain stable across grade levels, but the predictive power of self-concept and interest might increase with higher elementary school grade levels. To examine possible differences between grade levels, intelligence, self-concepts, interests, and achievements should be assessed with the same instruments in all elementary school grade levels.

2. Method 2.1. Sample and procedure The sample consisted of N = 858 second to fourth graders (grade level 2/3/4: n = 253/321/284; age: M (SD) = 8.06 (0.51)/9.04 (0.47)/10.06 (0.50) years; n = 446 females) attending 59 classes from 16 German elementary schools in Lower Saxony, Saxony-Anhalt, and Saarland. Participation was voluntary and anonymous. School authorities, principals, and teachers approved the data collection in corresponding schools; therefore, Institution Reviewer Board approval was not required. Informed consent was obtained from the parents and informed assent from the children prior to testing. The parents of n = 143 children did not allow their child to participate; due to reasons unrelated to the study (e.g., illness) n = 119 students of the initial sample (N = 1128) did not take part. Furthermore, n = 8 students were excluded due to an unreasonably low intelligence score (see below), resulting in the mentioned sample size (N = 858). Data collection took place during regular lessons and was conducted by trained experimenters in small groups (8 to 12 students, two school hours of 45 min each). To eliminate interfering factors due to different reading levels, all self-concept and interest items were read aloud. After listening to each item, the students marked the answer directly on the questionnaire. 2.2. Instruments 2.2.1. Intelligence Intelligence was assessed with the subtests matrices, classifications, and series (15 items per subtest), stemming from the well-known and widely used German version of the Culture Fair Intelligence Test (CFT 1–R; Weiß & Osterland, 2013). All subtests tapped figural reasoning which is considered to be prototypical of intelligence (Lohmann & Lakin, 2011). Those n = 8 students (grade 2: n = 2; grade 3: n = 6) with a score corresponding to an IQ below 70 were excluded from the sample to ensure sufficient cognitive ability for an adequate comprehension and item processing. McDonalds' omega for the intelligence subtests (grade levels 2/3/4) were as follows: series ω = .85/.82/.79, classifications ω = .72/.65/.63, matrices ω = .73/.60/.57.

1.4. The present investigation This study examined the statistical prediction of the reported grade as an important indicator of scholastic achievement by intelligence, (competence) self-concept, and interest in second, third, and fourth 25

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Geiser, 2013, p. 99 ff.). To test for metric invariance, the model with all factor loadings and intercepts freed across the three grade levels (configural model) was compared to a model with factor loadings constrained to be equal across grade levels (using χ2-based SatorraBentler correction [test value T; Satorra, 2000] and ΔCFI < .005 [Chen, 2007]). Regarding research question (1a), we first established separately for each grade level a latent model consisting of an intelligence and a selfconcept factor as predictors and the reversely scored manifest reported grade as the criterion (intelligence–self-concept model). Path coefficients relating intelligence, self-concept, and the criterion were examined. To inspect whether path coefficients of the predictors on the reported grade differed significantly in magnitude, we imposed equality constraints on the parameters from the predictors on the reported grade and performed a Wald test (test value Tw). If the Wald test revealed to be significant (p < .05), the equality constraints would worsen the model fit substantially. Second, to inspect the unique effects of each predictor in terms of incremental predictive validity as well as the portion of common variance explained by the predictors, we used the Cholesky approach (De Jong, 1999; Loehlin, 1996). This approach allows the orthogonal decomposition of the explained variances (i.e., separating the independent contributions of each factor) without altering the model fit or affecting the measurement part of the model. To investigate the self-concept increment that is independent of intelligence (2-predictor self-concept increment model, see Fig. 1), the intelligence-factor's Cholesky factor (Ch_intelligence) was assigned first priority to predict the reported grade variance by intelligence and as much of the self-concept factor as possible. The self-concept factor's Cholesky factor (Ch_competence SC) then represented the increment of self-concept after intelligence was partialled out and explained the remaining reported grade variance. Similarly and to investigate the increment of intelligence beyond self-concept, we established another model in which first priority was assigned to self-concept and second to intelligence. Significant path coefficients of the particular Cholesky factors with second priority indicated that the particular predictor explained the reported grade substantially beyond the other predictor. Squared regression coefficients can be interpreted as the proportion of uniquely explained variance by each predictor on the reported grade. The common variance of the two predictors on the reported grade was calculated by subtracting the specific variances of both predictors from the total explained variance (i.e., R2common = R2total − R2intelligence in2 crement − Rself-concept increment). Concerning research question (1b), we

2.2.2. Competence self-concept Competence self-concept for mathematics and reading (corresponding to native language because the SDQ I does not specifically assess self-concepts in the native language) was assessed with the corresponding four items of the Self Description Questionnaire I (SDQ I; Marsh, 1992; German translation by Arens, Trautwein, et al., 2011), for example, “I am good at mathematics”. Regarding another research question, students responded to these self-concept items on a 3-, 4- or 5point Likert-type scale (randomized within each class). For the following analyses, the item scores were z-standardized per response format and grade level. McDonalds' omega for the three grade levels (2/ 3/4) was at least good for mathematics (ω = .91/.90/.92) and reading (ω = .86/.90/.88). 2.2.3. Interest Interest in mathematics and reading was assessed with the corresponding four affect self-concept items of the Self Description Questionnaire I (SDQ I; Marsh, 1992; German translation by Arens, Trautwein, et al., 2011; interest and affect self-concept are used synonymously), for example, “I am interested in reading”. Again, students responded to these items on a 3-, 4- or 5-point Likert-type scale (randomized within each class). Item scores were z-standardized per response format and grade level. McDonalds' omega for the three grade levels (2/3/4) was at least good for mathematics (ω = .91/.94/.94) and reading (ω = .87/.91/.90). 2.2.4. Scholastic achievement Scholastic achievement was operationalized by reported grades in the core elementary school subjects mathematics and German. The teachers provided the actual reported grades from their students' last midterm report cards. In the German grading system, reported grades range from 1 (very good) to 6 (insufficient) whereas numerically lower reported grades indicate better scholastic achievements. To facilitate meaningful interpretation, reported grades were reversely scored so that higher numerical values indicated higher scholastic achievement. 2.3. Analyses All analyses were run separately for mathematics and German. In all models, the latent intelligence factor was indicated by the sum scores of the three intelligence subtests. The self-concept and interest factors were indicated by the corresponding subject-specific items. The nonstandardized loadings of the first indicator of a corresponding latent factor were freed and factor variances restricted to 1. We used the maximum likelihood robust estimator in MPlus (7.11; Muthén & Muthén, 1998–2013), the “type = complex” specification to control for potential effects due to school class affiliation and clustering of the data (students in classes), and the full-information maximum likelihood estimation to handle the few missing values (maximum per variable: 3.5%). Univariate normality of the standardized self-concept and interest items was not severely violated (skewness: −0.31 to 0.26, median = −0.08; kurtosis: −1.01 to −0.33, median = −0.73). Such values are considered not to undermine the robustness of ML-estimation (Finney & DiStefano, 2006). Preliminarily and in order to examine the relationship among intelligence, self-concept, interest, and reported grade, we specified a correlation model with the latent variables intelligence, self-concept, and interest, as well as the manifest reported grade separately for each grade level. To describe the model fit, χ2 values with df were supplemented by CFI, TLI, RMSEA, and SRMR. CFI and TLI above .90 (.95), and RMSEA and SRMR values below .08 (.05) typically signify an acceptable (good) fit (e.g., Marsh et al., 1999; Schreiber, Stage, King, Nora, & Barlow, 2006). Furthermore and as a prerequisite to analyze whether path coefficients relating the three predictors and the reported grades differed significantly between grade levels, we inspected measurement invariance among grade levels using the 3-predictor models (see below;

Fig. 1. 2-predictor self-concept increment model. Ch = Cholesky factor, SC = self-concept.

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Fig. 2. 3-predictor model with path coefficients separately for each grade level (2/3/4) and the two school subjects mathematics (above) and German (below). SC = self-concept. *p < .05.

(Ch_competence SC) to explain the remaining reported grade variance by self-concept and the interest factor after intelligence was partialled out. Finally, the interest factor's Cholesky factor (Ch_interest) represented the increment of interest after intelligence and self-concept were partialled out and explained the remaining reported grade variance. Investigating the self-concept increment beyond intelligence and interest (research question 2b; 3-predictor self-concept increment model), we assigned first priority to intelligence, second to interest, and third to self-concept. Examining the intelligence increment (research question 2c; 3-predictor intelligence increment model), first priority was assigned to self-concept, second to interest, and third to intelligence. Finally, the common variance (consisting of pairwise shared variance and shared variance of all three predictors) on the reported grade was calculated by subtracting the specific variances of the three predictors from the total explained variance (R2common = R2total − R2intelligence increment − R2self-concept increment − R2interest increment). To analyze whether path coefficients relating the three predictors (intelligence, self-concept, interest) and reported grades differed significantly between grade levels (research question 3; on the premise of measurement invariance across grade levels), a sequential approach was used for comparing the path coefficients across grade levels, using the metric multi-group model as the baseline model. For all prediction models used in this approach, we imposed equality constraints on the corresponding predictor intercorrelations across grade levels (Fig. 2). First, in an omnibus test (Wald test with α < .05), a multi-group prediction model with all unidirectional paths between intelligence, self-concepts and interests, and reported grades constrained to be equal across the three elementary school levels was compared to a multigroup model without these constraints (multi-group standard model). Second, in case of a significant Wald test, we further searched for differences between respective grade levels' path coefficients. Therefore, two-group models between two respective grade levels with again all unidirectional paths between the three predictors and reported grades constrained to be equal between grade levels were compared with the corresponding two-group models with unidirectional path coefficients that were allowed to vary (two-group standard model; two-tailed, 3 comparisons, adjusted α < .017). Finally and in order to analyze which specific path coefficients differed significantly between two respective levels, two-group models with one path coefficient constrained to be equal between grade levels was compared to the two-group standard model (two-tailed, 3 comparisons, adjusted α < .017).

established latent models with an equivalent structure to the models of research question (1a), except that the self-concept factor was replaced by the interest factor (intelligence–interest model, 2-predictor interest increment model). Regarding the prediction of the reported grade by intelligence, selfconcept, and interest in concert (research question 2), we first specified 3-predictor models (Fig. 2) with intelligence, self-concept, and interest factors as predictors and the reversely coded manifest reported grade as criterion separately for each elementary school level. Path coefficients relating the predictors to the criterion were examined. To inspect whether path coefficients of the three predictors on the reported grade differed significantly, a sequential approach was used: In an omnibus test (Wald test with α < .05), we imposed equality constraints on all regression coefficients of the three predictors on the reported grade. In case of a significant omnibus test, we further performed pairwise equality constraints to analyze which two coefficients differed significantly (two-tailed, 3 comparisons, Wald test with α < .017). Second, inspecting the unique effects of each variable and the portion of common variance explained by the three predictors, we specified three increment models – again separately for each grade level and again by using the Cholesky approach. To investigate the increment of interest that is independent of intelligence and self-concept (research question 2a; 3-predictor interest increment model; see Fig. 3), the intelligencefactor's Cholesky factor (Ch_intelligence) was assigned first priority to predict the reported grade variance by intelligence and as much of the self-concept factor and the interest factor as possible. Then, second priority was given to the self-concept factor's Cholesky factor

Fig. 3. Interest increment model in the Cholesky approach. Intelligence is given first priority, self-concept second, and interest third priority. Ch = Cholesky factor, SC = selfconcept.

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Table 1 Fit indices for the correlation models, the intelligence–self-concept models, the intelligence–interest models, and the 3-predictor models for each elementary school grade level as well as fit indices for the measurement invariance models and the group comparisons between grade levels for mathematics.

Correlation model

Intelligence–self-concept modela

Intelligence–interest modela

3-Predictor modela

Measurement invariance testing of the 3-predictor model Configural Metric Group comparisons of the 3-predictor model

Grade level

χ2

df

CFI

TLI

RMSEA

SRMR

2 3 4 2 3 4 2 3 4 2 3 4

54.23⁎ 84.11⁎ 59.79⁎ 27.71⁎ 40.69⁎ 39.97⁎ 13.26⁎ 23.08⁎ 7.20⁎ 54.23⁎ 84.11⁎ 59.79⁎

49 49 49 18 18 18 18 18 18 49 49 49

.996 .980 .993 .986 .969 .971 1.000 .995 1.000 .996 .980 .993

.994 .973 .990 .978 .952 .956 1.011 .992 1.025 .994 .973 .990

.021 .047 .028 .046 .063 .066 .000 .030 .000 .021 .047 .028

.037 .037 .030 .041 .037 .032 .030 .026 .016 .037 .037 .030

2 to 4

152.43⁎ 166.43⁎ 222.87⁎

123 139 179

.993 .993 .991

.990 .992 .990

.029 .026 .029

.032 .035 .046

Notes. χ = chi-square goodness-of-fit statistic; df = degrees of freedom; CFI = comparative fit index; TLI = Tucker-Lewis index; RMSEA = root mean square error of approximation; SRMR = standardized root mean squared residual. a Corresponding Cholesky factor models do not alter the model fit or affect the measurement part of the model, Cholesky model fit indices are therefore equal to the models without Cholesky factors presented in this table. ⁎ p < .05. 2

3. Results

levels, the reported grade was significantly predicted by intelligence (grade level 2/3/4: β = 0.46/0.45/0.40; p's < .05) and self-concept (grade level 2/3/4: β = 0.42/0.45/0.43; p's < .05). Intelligence and self-concept did not differ significantly in their regression coefficients (grade level 2/3/4: Tw = 0.12/ < 0.01/0.04, all df = 1, p's ≥ .73). In total, they explained R2 = .46/.52/.51 of the reported grade variance. Within the 2-predictor self-concept increment model, in grade level 2/ 3/4 the self-concept increment explained ΔR2 = .18/.18/.14 (p's < .05) of the reported grade variance beyond intelligence. The intelligence increment accounted for ΔR2 = .20/.18/.12 (p's < .05) beyond self-concept within the 2-predictor intelligence increment model. The common variance of intelligence and self-concept accounted for R2 = .08/.16/.25 (Table 5).

3.1. Preliminary analyses The correlation models with intelligence, self-concept, and interest as well as the reported grade in mathematics (Table 1) and German (Table 2) showed good fit statistics for grades 2 to 4. Details regarding the factor loadings for the intelligence subtests, subject-specific selfconcept, and interest items are presented in Table 3. For mathematics, correlations between intelligence as well as self-concept with the reported grade were substantial and of high magnitude in all three grade levels (intelligence–reported grade: .54 ≤ r ≤ .61; self-concept–reported grade: .52 ≤ r ≤ .62); correlations between interest and the reported grade were also substantial, but in contrast, of medium magnitude (.29 ≤ r ≤ .34). Intercorrelations of self-concept and interest were of high magnitude in all grade levels (.77 ≤ r ≤ .87; Table 4). For German, correlations between intelligence as well as selfconcept with the reported grade were substantial and of medium to high magnitude in all three grade levels (intelligence–reported grade: .36 ≤ r ≤ .50; self-concept–reported grade: .31 ≤ r ≤ .41) whereas the correlations between interest and the reported grade were also substantial, but of small magnitude (.11 ≤ r ≤ .28). Intercorrelations of self-concept and interest were again of high magnitude (.73 ≤ r ≤ .89; Table 4). Regarding measurement invariance, the configural and metric models with intelligence, self-concept, and interest factors yielded a good fit in mathematics (Table 1) and German (Table 2). Measurement invariance tests revealed to be non-significant; therefore, metric measurement invariance was assumed for both subjects (mathematics configural–metric: T = 12.02, df = 16, p = .74, ΔCFI < .001; German configural–metric: T = 12.36, df = 16, p = .72, ΔCFI < .001).1

3.2.2. Intelligence–interest models Concerning the intelligence–interest models (1b), the models also yielded good fits (Table 1; for factor loadings see Table 3). Intelligence (grades 2/3/4: β = 0.51/0.56/0.58; p's < .05) showed significant regression coefficients on the reported grade. The interest coefficients were substantial in grades 2 and 3 (grade level 2/3: β = 0.24/0.21; p's < .05), but not in grade level 4 (β = 0.12, p = .11). In all grade levels, the regression coefficients of intelligence on the reported grade were significantly higher than the coefficients of interest (grade level 2/ 3/4: Tw = 6.07/7.52/8.33, all df = 1, p's ≤ .01). In total, both predictors explained R2 = .34/.40/.40 of the reported grade variance. Within the 2-predictor interest increment model, in grades 2 and 3 the interest increment substantially explained ΔR2 = .06/.04 (p's < .05) of the reported grade variance beyond intelligence. For grade 4, the interest increment did not significantly contribute to the prediction (ΔR2 = .01, p = .11). The intelligence increment accounted for ΔR2 = .26/.30/.30 (p's < .05) beyond interest. The common variances of intelligence and interest were small (R2 = .02/.06/.09; for further information regarding the residual models see Table 6).

3.2. Mathematics 3.2.1. Intelligence–self-concept models The models from research question (1a) yielded good fits for all three grades (Table 1; for factor loadings see Table 3). In all grade

3.2.3. The 3-predictor models The models with intelligence, self-concept, and interest as predictors (Fig. 2; research question 2) showed good fit statistics (Table 1). Factor loadings for the intelligence subtests, self-concept, and interest items were identical with the factor loadings of the factors in the correlation model (Table 3). In all grade levels, intelligence (0.38 ≤ β1 ≤ 0.43) and self-concept (0.65 ≤ β2 ≤ 0.89) were

1 Additionally, non-significant nested comparison values indicated scalar measurement invariance for mathematics (metric–scalar: T = 3.34, df = 16, p > .99, ΔCFI = .003) and German (T = 3.93, df = 16, p = .99, ΔCFI = .004).

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Table 2 Fit indices for the correlation models, the intelligence–self-concept models, the intelligence–interest models, and the 3-predictor models for each elementary school grade level as well as fit indices for the measurement invariance models and the group comparisons between grade levels for German.

Correlation model

Intelligence–self-concept modela

Intelligence–interest modela

3-Predictor modela

Measurement invariance testing of the 3-predictor model Configural Metric Group comparisons of the 3-predictor model

Grade level

χ2

df

CFI

TLI

RMSEA

SRMR

2 3 4 2 3 4 2 3 4 2 3 4

103.89⁎ 82.05⁎ 64.57⁎ 22.51⁎ 32.24⁎ 24.54⁎ 44.21⁎ 33.78⁎ 23.00⁎ 103.89⁎ 82.05⁎ 64.57⁎

49 49 49 18 18 18 18 18 18 49 49 49

.940 .980 .987 .991 .983 .985 .951 .982 .992 .940 .980 .987

.920 .973 .983 .985 .974 .977 .923 .973 .987 .920 .973 .983

.067 .046 .033 .031 .050 .036 .076 .052 .031 .067 .046 .033

.046 .033 .033 .035 .028 .034 .033 .032 .028 .046 .033 .033

2 to 4

229.62⁎ 244.27⁎ 278.71⁎

123 139 179

.970 .970 .974

.960 .965 .971

.055 .051 .044

.037 .042 .049

Notes. χ = chi-square goodness-of-fit statistic; df = degrees of freedom; CFI = comparative fit index; TLI = Tucker-Lewis index; RMSEA = root mean square error of approximation; SRMR = standardized root mean squared residual. a Corresponding Cholesky factor models do not alter the model fit or affect the measurement part of the model, Cholesky model fit indices are therefore equal to the models without Cholesky factors presented in this table. ⁎ p < .05. 2

Table 3 Standardized factor loadings (min/max) of the intelligence subtests on the intelligence factor, self-concept items on the self-concept factor, and interest items on the interest factor in the correlation models, the intelligence–self-concept models, and the intelligence–interest models – separately for each grade level and the two subjects mathematics and German. Mathematics Grade level Correlation model

REA CSC INT REA CSC REA INT

Intelligence–self-concept model Intelligence–interest model

German

2

3

4

2

3

4

.54/.74 .82/.90 .80/.89 .54/.74 .82/.90 .54/.74 .80/.90

.55/.64 .79/.92 .87/.93 .55/.64 .79/.91 .54/.65 .87/.93

.56/.63 .80/.92 .87/.91 .57/.64 .79/.92 .56/.63 .87/.91

.56/.73 .67/.85 .70/.86 .56/.73 .70/.82 .56/.73 .68/.84

.53/.71 .76/.90 .71/.89 .53/.71 .77/.90 .53/.72 .71/.91

.58/.63 .78/.87 .74/.89 .58/.63 .79/.85 .58/.63 .72/.91

Notes. REA = reasoning/intelligence, CSC = competence self-concept, INT = interest. All factor loadings p < .05.

statistics in all grade levels (Table 7). Subsequent pairwise constraints showed that for second graders self-concept was a substantially stronger predictor than intelligence and interest, whereas intelligence was a better predictor than interest. For third and fourth graders, intelligence and self-concept were comparably strong predictors, whereas both were better predictors than interest. When interest was assigned last priority, the interest increment (research question 2a) explained a small (but still substantial) proportion of reported grade variance in second graders, ΔR2 = .07. The selfconcept increment (research question 2b) uniquely explained ΔR2 = .19, the intelligence increment (research question 2c) contributed ΔR2 = .17 to reported grade variance in second graders. For third and fourth graders, regression coefficients of the increments in the reported grade were of the same magnitude as for second graders (Table 8). The common variance of the three predictors in grade level 2/3/4 accounted for R2 = .11/.16/.26. Path coefficients relating the three predictors and reported grades did not differ significantly among grade levels (research question 3; Tw = 5.90, df = 6, p = .43).

Table 4 Latent correlations of intelligence, self-concepts, interests, and reported grades, done separately for each elementary school grade level and for the subjects mathematics (below each diagonal) and German (above each diagonal). Grade level 2

3

4

REA CSC INT RG REA CSC INT RG REA CSC INT RG

REA

CSC

INT

RG

– .19 .09 .54⁎ – .28⁎ .17 .57⁎ – .50⁎ .33⁎ .61⁎

.03 – .87⁎ .52⁎ .20⁎ – .78⁎ .58⁎ .10⁎ – .77⁎ .62⁎

−.01 .79⁎ – .29⁎ .18⁎ .73⁎ – .31⁎ .06⁎ .89⁎ – .34⁎

.45⁎ .31⁎ .11⁎ – .50⁎ .41⁎ .22⁎ – .36⁎ .38⁎ .28⁎ –

Notes. REA = reasoning/intelligence, CSC = competence self-concept, INT = interest, RG = reported grade. ⁎ p < .05.

statistically significant (positive) predictors of the reported grade in mathematics. The regression coefficients of interest were substantially negative in all three levels (−0.52 ≤ β3 ≤ −0.29; Fig. 2). Concerning the comparison of regression coefficients among the three predictors, initially conducted omnibus Wald tests (constraining the regression coefficients of all three predictors to be equal) revealed significant test

3.3. German 3.3.1. Intelligence–self-concept models The models from research question (1a) yielded acceptable fit statistics for the second grade level and good fit indices for grade levels 3 and 4 (Table 2; for factor loadings see Table 3). Intelligence (grade level 29

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Table 5 Standardized path coefficients of the 2-predictor self-concept increment models and the 2-predictor intelligence increment models complemented by explained variances of the reported grade by the predictors – separately for elementary school grade levels and the two subjects mathematics and German. Grade level 2

3

4

Residual

CSC

REA

CSC

REA

CSC

REA

Priority

(1) REA (2) Ch_CSC

(1) CSC (2) Ch_REA

(1) REA (2) Ch_CSC

(1) CSC (2) Ch_REA

(1) REA (2) Ch_CSC

(1) CSC (2) Ch_REA

Mathematics Relational pattern of predictors REA → CSC Ch_CSC → CSC CSC → REA Ch_REA → REA Path coefficients of predictors on the reported grade REA → RG Ch_REA → RG CSC → RG Ch_CSC → RG Explained variances R2 (1) ΔR2 (2) R2 (1, 2) German Relational pattern of predictors REA → CSC Ch_CSC → CSC CSC → REA Ch_REA → REA Path coefficients of predictors on the reported grade REA → RG Ch_REA → RG CSC → RG Ch_CSC → RG Explained variances R2 (1) ΔR2 (2) R2 (1, 2)

0.29⁎ 0.96⁎

0.19 0.98⁎

0.29⁎ 0.96⁎

0.19 0.98⁎ 0.54⁎

0.58⁎ 0.45⁎ 0.51⁎

0.42⁎ .29⁎ .18⁎ .46a,⁎

.26⁎ .20⁎ .46⁎

.34⁎ .18⁎ .52⁎

0.61⁎

.34⁎ .18⁎ .52⁎

0.10 1.00⁎ 0.36⁎

0.43⁎ 0.41⁎ 0.32⁎ .26⁎ .10⁎ .36⁎

.40⁎ .12⁎ .51a,⁎

0.10⁎ 1.00⁎

0.51⁎ 0.44⁎ 0.31⁎

.10⁎ .19⁎ .29⁎

.37⁎ .14⁎ .51⁎

0.20⁎ 0.98⁎

0.03 1.00⁎

0.30⁎

0.34⁎ 0.63⁎ 0.37⁎

0.20⁎ 0.98⁎

0.45⁎

0.51⁎ 0.86⁎

0.43⁎ 0.58⁎ 0.43⁎

0.03 1.00⁎

.20⁎ .09⁎ .29⁎

0.51⁎ 0.86⁎

0.32⁎ 0.37⁎ 0.34⁎

.17⁎ .18⁎ .36a,⁎

.13⁎ .12⁎ .24a,⁎

.14⁎ .10⁎ .24⁎

Notes. REA = reasoning/intelligence, CSC = competence self-concept, RG = reported grade, → unidirectional coefficients. Variances (R2) uniquely explained by the predictor are printed in bold. a Due to rounding procedure, specific values might not correspond exactly to the total explained variance. ⁎ p < .05.

2/3/4: β = 0.44/0.44/0.33; p's < .05) and self-concept (grade level 2/ 3/4: β = 0.30/0.33/0.40; p's < .05) showed significant regression coefficients on the reported grade in all grade levels. In all grade levels, intelligence and self-concept did not differ significantly in their regression coefficients (grade levels 2/3/4: Tw = 2.30/1.49/ < 0.01, all df = 1, p's ≥ .13). In total, they explained R2 = .29/.36/.24 of the reported grade variance in German. In the 2-predictor self-concept increment models in grade levels 2/3/4, the self-concept increment uniquely explained ΔR2 = .09/.10/.12 (p's < .05) of the reported grade variance beyond intelligence, whereas the intelligence increment accounted for ΔR2 = .19/.18/.10 (p's < .05) beyond self-concept. The common variance of intelligence and self-concept accounted for R2 = .01/.08/.02 (Table 5).

between the coefficients occurred (Tw = 0.63, df = 1, p = .43). In total, the predictors explained .19 ≤ R2 ≤ .28 of the reported grade variance. In grade level 2, the interest increment did not significantly contribute to the prediction (ΔR2 = .01, p = .11) beyond intelligence. In grade levels 3 and 4, the interest increment substantially explained ΔR2 = .02/.06 (p's < .05) of the reported grade variance beyond intelligence. The intelligence increment accounted for ΔR2 = .20/.24/.12 (p's < .05) beyond interest. The common variances of intelligence and interest were very small, R2 = .00/.03/.01 (Table 6). 3.3.3. The 3-predictor models The 3-predictor models (research question 2) showed acceptable fit statistics for the second grade and good fit indices for grade levels 3 and 4 (Table 2). Factor loadings for the intelligence subtests, self-concept, and interest items were identical with the factor loadings of the factors in the correlation model (Table 3). Again and in all grade levels, intelligence (0.32 ≤ β1 ≤ 0.44) and self-concept (0.47 ≤ β2 ≤ 0.55) were statistically significant (positive) predictors of the reported grade in German. In turn, the regression coefficients of interest were substantially negative in grades 2 and 3 (−0.52 ≤ β3 ≤ −0.22), but nonsubstantial in grade 4 (β = −0.20; Fig. 2). Concerning path coefficients comparisons, initially conducted omnibus Wald tests (constraining the regression coefficients of all three predictors to be equal) revealed significant test statistics in all grade levels (Table 7). Subsequent pairwise constraints showed that intelligence and self-concept did not differ

3.3.2. Intelligence–interest models Concerning research question (1b), the models yielded an acceptable fit for grade level 2 and good fits for grade levels 3 and 4 (Table 1; for factor loadings see Table 3). Intelligence (grade level 2/3/4: β = 0.45/0.50/0.34; p's < .05) showed significant regression coefficients with the reported grade in all grade levels. The interest coefficients were substantial in grade levels 3 and 4 (β = 0.13/0.25; p's < .05), but not in grade level 2 (β = 0.11, p = .09). In grade levels 2 and 3, the regression coefficients between intelligence and reported grade were higher than the coefficients of interest (Tw = 11.81/16.11, all df = 1, p < .01). In grade level 4, no significant differences 30

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Table 6 Standardized path coefficients of the 2-predictor interest increment models and the 2-predictor intelligence increment models complemented by explained variances of the reported grade by the predictors – separately for elementary school grade levels and the two subjects mathematics and German. Grade level 2

3

4

Residual

INT

REA

INT

REA

INT

REA

Priority

(1) REA (2) Ch_INT

(1) INT (2) Ch_REA

(1) REA (2) Ch_INT

(1) INT (2) Ch_REA

(1) REA (2) Ch_INT

(1) INT (2) Ch_REA

Mathematics Relational pattern of predictors REA → INT Ch_INT → INT INT → REA Ch_REA → REA Path coefficients of predictors on the reported grade REA → RG Ch_REA → RG INT → RG Ch_INT → RG Explained variances R2 (1) ΔR2 (2) R2 (1, 2) German Relational pattern of predictors REA → INT Ch_INT → INT INT → REA Ch_REA → REA Path coefficients of predictors on the reported grade REA → RG Ch_REA → RG INT → RG Ch_INT → RG Explained variances R2 (1) ΔR2 (2) R2 (1, 2)

0.17⁎ 0.99⁎

0.09 1.00⁎ 0.09⁎ 1.00⁎ 0.53⁎

0.17⁎ 0.99⁎ 0.59⁎

0.51⁎ 0.29⁎ 0.24⁎ ⁎

.28 .06⁎ .34⁎

⁎

⁎

.08 .26⁎ .34⁎

.35 .04⁎ .40a,⁎

0.62⁎

.09 .30⁎ .40a,⁎

0.52⁎

0.07 1.00⁎ 0.36⁎

0.49⁎ 0.22⁎ 0.13⁎ .27⁎ .02⁎ .29⁎

.10⁎ .30⁎ .40⁎

0.07 1.00⁎ 0.18 0.98⁎

0.45⁎ 0.10

.01 .20⁎ .21⁎

.38⁎ .01 .40a,⁎

⁎

−0.01 1.00⁎

0.11

0.55⁎ 0.32⁎ 0.12

⁎

0.18⁎ 0.98⁎

0.45⁎

0.33⁎ 0.94⁎

0.55⁎ 0.30⁎ 0.21⁎

−0.01 1.00⁎

.20⁎ .01 .21⁎

0.33⁎ 0.94⁎

0.34⁎ 0.27⁎ 0.25⁎

.05⁎ .24⁎ .29⁎

.13⁎ .06⁎ .19⁎

.07⁎ .12⁎ .19⁎

Notes. REA = reasoning/intelligence, INT = interest, RG = reported grade, → unidirectional coefficients. Variances (R2) uniquely explained by the predictor are printed in bold. a Due to rounding procedure, specific values might not correspond exactly to the total explained variance. ⁎ p < .05.

levels. Therefore, we analyzed the statistical prediction of reported grades by intelligence, self-concept, and interest, separately for two core elementary school subjects (mathematics, German as native language) and separately for elementary school grade levels 2, 3, and 4. Evaluating the increments of motivational variables for reported grades, the present findings underline the significance of motivational variables beyond intelligence. Specifically, self-concepts contributed substantially to the prediction of reported grades in mathematics and German beyond intelligence in elementary school grade levels 2, 3, and 4.

significantly. In grade levels 2 and 3, both were better predictors than interest. When interest was assigned last priority, the interest increment (2a) only explained a small (but still substantial) proportion of reported grade variance in the second graders, ΔR2 = .04, whereas the selfconcept increment (2b) uniquely explained ΔR2 = .12 and the intelligence increment (2c) explained ΔR2 = .18. For the third graders, regression coefficients of the increments on the reported grade were of numerically comparable magnitude (Table 9). Regarding the fourth graders, the interest increment did not substantially contribute to the prediction of reported grade variance (ΔR2 = .01), path coefficients of self-concept and intelligence increments on the reported grade were numerically smaller compared with grades 2 and 3 (see Table 9). The common variance of the three predictors accounted for R2 = .07/.09 in grades 3 and 4. For the second graders, the predictors did not share substantial amounts of common variance. Analyses whether path coefficients relating the three predictors to reported grades differed significantly among grade levels revealed no such differences (research question 3; Tw = 3.49, df = 6, p = .75).

4.1. Statistical prediction of reported grades by intelligence, self-concept, and interest Regarding the statistical prediction of reported grades by using only intelligence and competence self-concept, both were substantial predictors of reported grades in mathematics and German. Within the intelligence–interest model, interest only partially contributed to the prediction of reported grades beyond intelligence. Although substantial, the specific contributions of interest were rather small (R2 ≤ .06). Concerning prediction models with intelligence, self-concept, and interest in concert, intelligence and self-concept were substantial (positive) predictors of the reported grades, whereas the regression coefficients of interests in mathematics and German were (substantially) negative in all three grade levels. In contrast to

4. Discussion The aim of this study was to contribute to the knowledge about the roles of cognitive and motivational variables for scholastic achievement assessed by reported grades across different elementary school grade 31

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consistently emerged in (almost) all grade levels as well as in mathematics and German, the occurrence of a statistical artifact (e.g., due to the sample) appears unlikely. This rather points toward a suppression phenomenon (Conger, 1974): In all grade levels, self-concepts and interests were very closely correlated (mathematics: .77 ≤ r ≤ .87; German: .73 ≤ r ≤ .89, see Table 4) and in separate models with intelligence (intelligence–self-concept model; intelligence–interest model), both variables showed positive regression coefficients for reported grades corresponding to the substantial positive reported grade–interest correlations. When entering both motivational components simultaneously into the statistical regression, the self-concept coefficients increased (in comparison to the self-concept coefficients of the intelligence–self-concept model), whereas the interest path coefficients decreased (in comparison to the interest path coefficients of the intelligence–interest model) and even became substantially negative. Because of this suppressor effect, analyses of the common and specific contributions of each predictor are important complements to appropriately evaluate the significance of each predictor (see Section 4.2). Regarding the magnitude of path coefficients of the predictors on composite achievement scores, Spinath et al. (2006) found that intelligence was a stronger predictor in fourth graders than self-concept and interest in mathematics and English. In contrast, the path coefficients of intelligence and self-concept on reported grades in mathematics and German did not differ substantially from each other in grade level 4 nor in levels 2 and 3 in this study (see also Table 5). Regarding the intelligence–interest models and in conformity with Spinath et al. (2006), intelligence revealed higher path coefficients with reported grades compared to interest in the examined elementary school grade levels. A possible reason for the partially different relation patterns might be the assessment of intelligence. Whereas we administered the well-known CFT (consisting of figural reasoning subtests; Weiß & Osterland, 2013) by trained experimenters, Spinath et al. (2006) provided participants' parents with booklets for in-home testing,

Table 7 Results of the Wald tests for comparing the regression coefficients of the 3-predictor models – separately for each grade level and the subjects mathematics and German. Grade level Mathematics 2

3

4

German 2

3

4

Models

Wald Tw

df

p

β1 = β2 = β3 β1 = β2 β1 = β3 β2 = β3 β1 = β2 = β3 β1 = β2 β1 = β3 β2 = β3 β1 = β2 = β3 β1 = β2 β1 = β3 β2 = β3

39.39 7.69 33.41 20.50 46.67 3.64 43.35 30.65 73.11 1.56 46.12 24.41

2 1 1 1 2 1 1 1 2 1 1 1

< .01 < .01 < .01 < .01 < .01 =.06 < .01 < .01 < .01 =.21 < .01 < .01

β1 = β2 = β3 β1 = β2 β1 = β3 β2 = β3 β1 = β2 = β3 β1 = β2 β1 = β3 β2 = β3 β1 = β2 = β3 β1 = β2 β1 = β3 β2 = β3

45.86 1.01 45.74 25.71 38.42 0.08 34.29 29.67 7.97 0.48 6.24 2.59

2 1 1 1 2 1 1 1 2 1 1 1

< .01 =.31 < .01 < .01 < .01 =.78 < .01 < .01 =.02 =.49 =.01 =.11

Notes. Wald Tw = chi-square statistics of the Wald tests; df = degrees of freedom of the Wald tests.

expectations, this means that in the 3-predictor model being less interested in mathematics/reading went along with better reported grades in mathematics/German. Because this relation pattern

Table 8 Standardized path coefficients of the 3-predictor increment models in the Cholesky approach as well as explained variances of the reported grade in mathematics by the predictors, done separately for each elementary school grade level. Grade level

2

Increment

INT

CSC

REA

INT

CSC

REA

INT

CSC

REA

Priority

(1) Ch_REA (2) Ch_CSC (3) Ch_INT

(1) Ch_REA (2) Ch_INT (3) Ch_CSC

(1) Ch_CSC (2) Ch_INT (3) Ch_REA

(1) Ch_REA (2) Ch_CSC (3) Ch_INT

(1) Ch_REA (2) Ch_INT (3) Ch_CSC

(1) Ch_CSC (2) Ch_INT (3) Ch_REA

(1) Ch_REA (2) Ch_CSC (3) Ch_INT

(1) Ch_REA (2) Ch_INT (3) Ch_CSC

(1) Ch_CSC (2) Ch_INT (3) Ch_REA

1⁎ 0.19 0.09

0.97⁎

1⁎ 0.28⁎ 0.17⁎

1⁎ 0.17⁎ 0.28⁎

0.95⁎

1⁎ 0.50⁎ 0.34⁎

1⁎ 0.34⁎ 0.50⁎

0.86⁎

0.19 1⁎ 0.87⁎ −0.14

0.96⁎ 0.77⁎

0.60⁎

0.87⁎ 0.70⁎

0.58⁎

0.50⁎

0.62⁎

0.75⁎ 0.99⁎

0.28⁎ 1⁎ 0.78⁎ −0.09 0.62⁎

0.63⁎

0.64⁎ 0.94⁎

Path coefficients of predictors on the reported grade Ch_REA → RG 0.54⁎ 0.54⁎ Ch_CSC → RG 0.43⁎ 0.24⁎ Ch_INT → RG −0.26⁎ 0.44⁎

0.41⁎ 0.52⁎ −0.32⁎

0.57⁎ 0.43⁎ −0.19⁎

0.57⁎ 0.21⁎ 0.42⁎

0.41⁎ 0.58⁎ −0.23⁎

0.61⁎ 0.36⁎ −0.18⁎

0.61⁎ 0.15⁎ 0.38⁎

0.33⁎ 0.62⁎ −0.22⁎

Explained variances R2 (1) ΔR2 (2) R2 (1, 2) ΔR2 (3) R2 (1, 2, 3)

.27⁎ .10⁎ .37⁎ .17⁎ .54⁎

.32⁎ .18⁎ .50⁎ .04⁎ .55a,⁎

.32⁎ .04⁎ .36⁎ .18⁎ .55a,⁎

.34⁎ .05⁎ .39⁎ .17⁎ .55a,⁎

.37⁎ .13⁎ .50⁎ .03⁎ .54a,⁎

.37⁎ .02⁎ .39⁎ .14⁎ .54a,⁎

.38⁎ .05⁎ .43⁎ .11⁎ .54⁎

Relational pattern of predictors Ch_REA → REA 1⁎ Ch_REA → CSC 0.19 Ch_REA → INT 0.09 Ch_CSC → REA Ch_CSC → CSC 0.98⁎ Ch_CSC → INT 0.86⁎ Ch_INT → REA Ch_INT → CSC Ch_INT → INT 0.50⁎

.29⁎ .18⁎ .47⁎ .07⁎ .54⁎

3

0.49⁎

0.85⁎ 1⁎

.29⁎ .06⁎ .35⁎ .19⁎ .54⁎

4

0.50⁎ 1⁎ 0.77⁎ −0.08 0.64⁎

Notes. REA = reasoning/intelligence, CSC = competence self-concept, INT = interest, RG = reported grade, → unidirectional coefficients. Variances (R2) uniquely explained by the predictor are printed in bold. a Due to rounding procedure, specific values might not correspond exactly to the total explained variance of the reported grade. ⁎ p < .05.

32

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Table 9 Standardized path coefficients of the 3-predictor increment models in the Cholesky approach as well as explained variances of the reported grade in German by the predictors, done separately for each elementary school grade level. Grade level

2

Increment

INT

CSC

REA

INT

CSC

REA

INT

CSC

REA

Priority

(1) Ch_REA (2) Ch_CSC (3) Ch_INT

(1) Ch_REA (2) Ch_INT (3) Ch_CSC

(1) Ch_CSC (2) Ch_INT (3) Ch_REA

(1) Ch_REA (2) Ch_CSC (3) Ch_INT

(1) Ch_REA (2) Ch_INT (3) Ch_CSC

(1) Ch_CSC (2) Ch_INT (3) Ch_REA

(1) Ch_REA (2) Ch_CSC (3) Ch_INT

(1) Ch_REA (2) Ch_INT (3) Ch_CSC

(1) Ch_CSC (2) Ch_INT (3) Ch_REA

1⁎ 0.03 − 0.01

1⁎

1⁎ 0.20⁎ 0.18⁎

1⁎ 0.20⁎ 0.18⁎

0.98⁎

1⁎ 0.10 0.06

1⁎ 0.10 0.06

0.99⁎

0.03 1⁎ 0.79⁎ −0.06

0.98⁎ 0.70⁎

0.69⁎

0.20⁎ 1⁎ 0.73⁎ 0.05

1⁎ 0.89⁎

0.45⁎

0.61⁎

0.69⁎

0.70⁎ 0.98⁎

0.69⁎

0.45⁎

0.89⁎ 1⁎

Path coefficients of predictors on the reported grade Ch_REA → RG 0.45⁎ 0.45⁎ Ch_CSC → RG 0.30⁎ 0.34⁎ Ch_INT → RG −0.20⁎ 0.12⁎

0.43⁎ 0.31⁎ −0.22⁎

0.50⁎ 0.32⁎ −0.14⁎

0.50⁎ 0.32⁎ 0.13⁎

0.43⁎ 0.41⁎ −0.12⁎

0.36⁎ 0.33⁎ −0.09

0.36⁎ 0.23⁎ 0.26⁎

0.32⁎ 0.37⁎ −0.11

Explained variances R2 (1) ΔR2 (2) R2 (1, 2) ΔR2 (3) R2 (1, 2, 3)

.10⁎ .05⁎ .15⁎ .18⁎ .33⁎

.25⁎ .10⁎ .35⁎ .02⁎ .37⁎

.25⁎ .02⁎ .27⁎ .10⁎ .37⁎

.17⁎ .01⁎ .18⁎ .18⁎ .37a,⁎

.13⁎ .11⁎ .24⁎ .01 .25⁎

.13⁎ .07⁎ .20⁎ .05⁎ .25⁎

.14⁎ .01 .15⁎ .10⁎ .25⁎

Relational pattern of predictors Ch_REA → REA 1⁎ Ch_REA → CSC 0.03 Ch_REA → INT −0.01 Ch_CSC → REA Ch_CSC → CSC 1⁎ Ch_CSC → INT 0.79⁎ Ch_INT → REA Ch_INT → CSC Ch_INT → INT 0.61⁎

.20⁎ .09⁎ .29⁎ .04⁎ .33⁎

3

0.61⁎

0.79⁎ 1⁎

.20⁎ .01⁎ .21⁎ .12⁎ .33⁎

4

0.10 1⁎ 0.89⁎ −0.06 0.45⁎

Notes. REA = reasoning/intelligence, CSC = competence self-concept, INT = interest, RG = reported grade, → unidirectional coefficients. Variances (R2) uniquely explained by the predictor are printed in bold. a Due to rounding procedure, specific values might not correspond exactly to the total explained variance of the reported grade. ⁎ p < .05.

minor role compared to intelligence and self-concepts if interpretations are based on the 3-predictor models. Common variances within the 2-predictor models of our analyses were of comparable magnitude to common variances found by Spinath et al. (2006) in mathematics. For German, common variances were numerically smaller in comparison to Spinath et al. as well as in comparison to mathematics. As mentioned, mutual reinforcement processes of intelligence, self-concept, and interest can be assumed, at least for third and fourth graders. In our data, cognitive and motivational variables were not significantly related in second graders. Contrary, substantial positive correlations between intelligence, self-concept, and interest were found in third and fourth graders. This differential overlap between cognitive and motivational variables across different grade levels should be investigated longitudinally to further contribute to the discussion about the role of motivational variables for the development of reported grades.

containing tests adapted from the Wechsler Intelligence Scale for children and the Cognitive Abilities Test 3 (for further details see Spinath et al., 2006). Higher path coefficients of intelligence on reported grades could have been expected if this study would have used verbal or mixed (non-verbal and verbal) intelligence subtests (e.g., Roth et al., 2015). Nevertheless, reasoning tests are considered to be very good markers of intelligence and provide an effective and efficient instrument for assessing intelligence in groups of elementary school children. 4.2. Specific and common variances in predicting reported grades Concerning the specific contributions to the prediction of reported grade variance, intelligence, competence self-concept, and interest increments within the Cholesky models added incrementally to the explanation of reported grade variance (with the exception that only the interest increment in fourth graders in the native language did not contribute substantially). These results spotlight the importance of motivational variables for the prediction of reported grades. In theoretical conformity with the expectancy-value model and replicating recent findings (e.g., Trautwein et al., 2012), the expectancy component (self-concept) was more closely related to scholastic achievement than the value component (interest) in all examined elementary school grade levels. Moreover, contributions of self-concept to reported grade variances were of higher magnitude compared to interest. Nevertheless and in contrast to our expectations, interest (mostly) contributed substantially to the explanation of reported grade variance, underlining its significance beyond intelligence and self-concept even though the specific variance proportions were small. As mentioned earlier, interest was negatively related to reported grades in the 3-predictor model which might be a consequence of the suppressor effect. Therefore, the interpretability of the interest's contribution in the 3-predictor model calls for further research. At least, in our sample of elementary school children from second, third, and fourth grades, interests seem to play a

4.3. Subject-specific differences in the prediction of reported grades Regarding the separate analyses for the school subjects mathematics and German, our findings indicated partially differential relation patterns: In line with prior findings (Bullock & Ziegler, 1997; Roth et al., 2015), the relation between intelligence and reported grades was closer in mathematics compared to German. Roth et al. (2015) assumed that mathematics might be more strongly associated with tasks requiring logical thinking, which, in turn, is the main component of intelligence tests (Deary et al., 2007). Furthermore, concerning intelligence, selfconcept, and interest simultaneously, the predictive validity of intelligence and self-concept seemed to be comparable in magnitude whereas interest uniquely explained numerically less (but still substantial) variance of reported grades in mathematics. In German, however, intelligence explained numerically more variance in the reported grade compared to the other predictors. The numerically lower 33

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Baumert, Lüdtke, Trautwein, & Brunner, 2009; Roth et al., 2015). Concerning motivational variables, empirical studies gave evidence for their closer relation with reported grades than competence tests (e.g., Marsh, Trautwein, Lüdtke, Köller, & Baumert, 2005). Thus, past studies conducted with secondary school students regarding the differential relevance of cognitive and motivational variables for educational success showed that intelligence was more relevant than motivational variables for competence tests, whereas motivational variables were more relevant than intelligence for reported grades (Jansen et al., 2016; Steinmayr & Meißner, 2013). Comparable relations could be expected for elementary school students, but remain an open question for further research. Regarding policy implications, it is well-known that different teachers use more or less different evaluation standards while grading students' achievements. Reported grades are influenced by such effects and evaluation tendencies (e.g., Harlen, 2005; Steinmayr et al., 2014; Trautwein, 2009). In comparison with teacher-given reported grades, competence tests are less influenced by such evaluation tendencies and corresponding construct-irrelevant variance (Steinmayr et al., 2014). In order to increase the comparability of reported grades across classes, more standardized competence assessments and grading procedures are recommended (cf. Tent, 2006). Additionally, schools and classes impact motivational constructs as, for example, students' self-concepts (e.g., big-fish-little-pond effect; Marsh, 1987). It remains an open question whether an increase of the comparability of reported grades across classes affects motivational constructs as well.

predictive power of self-concept/interest in German compared to mathematics might be explained by the operationalization of the SDQ I (Marsh, 1992) that contained items to assess competence self-concepts and interests in reading instead of the more general verbal (German) self-concepts/interests. Although reading and verbal self-concepts/interests do not correspond perfectly, reading plays a more important role in the verbal curriculum for elementary school children compared to secondary school students (Arens, Yeung, & Hasselhorn, 2014). In elementary school, obtaining the ability to read is an essential learning goal and reading is a prerequisite for higher learning goals like poetry analyses in secondary school. Accordingly, Arens et al. (2014) argued that the verbal self-concept/interest structure in elementary school children might be characterized by less important verbal self-concepts and interests, but might be accompanied by more prominent reading self-concept/interest components. To what extent the assessment of reading vs. verbal self-concept/interest affects the predictive power of the corresponding components in German (or other native languages) in elementary school children is an issue for further research. 4.4. Grade level- and achievement indicator-related differences Substantial differences in the prediction of reported grades depending on students' grade level were not found. Due to latent modeling, a confounding of measurement variance (measurement model) and structural variance (statistical prediction model) across grade levels was avoided. Because measurement invariance was assumed, potential prediction differences would have been assignable to structural invariances. While interpreting our empirical results among grade levels, one should keep in mind that we used cross-sectional data. Cross-sectional data do not allow firm conclusions about the causal ordering of variables. To allow interpretations about the causal ordering of variables, experimental and/or longitudinal data would have been desirable. At least regarding self-concepts, for example, the reciprocal effects model (REM; for elementary school children see e.g., Guay, Marsh, & Boivin, 2003; Weidinger et al., 2015) suggests that academic self-concepts and academic achievements are reciprocally related. In this paper, we focused on the statistical prediction of reported grades by selfconcepts (and intelligence) as well as unique and shared variance proportions of the predictors; within the internal/external frame of reference model (I/E model; e.g., Möller et al., 2009) the impact of reported grades on the formation of subject-specific self-concepts is investigated. In the first school years, students get their first reported grades that provide first sources of salient feedback of scholastic achievements to them, thereby, allowing them to normatively evaluate their own performances by social comparisons (e.g., Möller et al., 2009). These comparison processes increase with age, especially in elementary school in the course of increasing experiences with reported grades and cognitive development (see Harter, 2006; Skaalvik & Skaalvik, 2002) which should definitely impact (the formation of) the self-concept. Both strands of research (REM and I/E) can be brought together within a reciprocal internal/external frame of reference model (cf. Möller, Retelsdorf, Köller, & Marsh, 2011; Möller, Zimmermann, & Köller, 2014), calling for further longitudinal research. While interpreting our empirical results, one should keep in mind that different operationalizations of scholastic achievement might go hand in hand with a (partially) different prediction pattern of cognitive and motivational variables in elementary school students. As mentioned above, test scores should merely reflect the performance of a student, whereas reported grades are multi-dimensional including behavioral and attitudinal elements (Willingham et al., 2002). Therefore, student characteristics like self-concepts, interests, effort, and persistence seem to more likely influence school-based performance measures like reported grades than competence tests. Empirical studies addressing intelligence and achievement measures showed that the intelligence–achievement/competence test coefficients typically exceeded the average intelligence–reported grade coefficients (e.g.,

5. Conclusion In summary, this study was the first to simultaneously inspect the statistical prediction power of intelligence, competence self-concept, and interest for reported grades across different elementary school grade levels. Thereby, we took specific and common variances into account, separately for two core elementary school subjects (mathematics, German) and the elementary school grade levels 2, 3, and 4. For all examined elementary school levels, the present findings underline the significance of self-concept above and beyond intelligence, whereas interest seems to play a minor role for the prediction of reported grades. This study found that motivational variables, especially self-concept, are relevant for scholastic achievement in addition to intelligence, but also that these constructs overlap (especially self-concepts and interests). Noteworthy, we found no substantial differences in the prediction of reported grades between students' grade levels. In conclusion, the results of this study indicated that in different elementary school grade levels intelligence substantially predicts scholastic achievement, but that motivational variables have the potential to substantially contribute to the prediction alongside intelligence regardless of the elementary school grade level. References Arens, A. K., & Hasselhorn, M. (2015). Differentiation of competence and affect selfperceptions in elementary school students: Extending empirical evidence. European Journal of Psychological Education, 30, 405–419. http://dx.doi.org/10.1007/s10212015-0247-8. Arens, A. K., Trautwein, U., & Hasselhorn, M. (2011). Erfassung des Selbstkonzepts im mittleren Kindesalter: Validierung einer deutschen Version des SDQ I [Self-concept acquisition for middle aged children: Validation of a German version of the SDQ I]. Zeitschrift für Pädagogische Psychologie, 25, 131–144. http://dx.doi.org/10.1024/ 1010-0652/a000030. Arens, A. K., Yeung, A. S., Craven, R. G., & Hasselhorn, M. (2011). The twofold multidimensionality of academic self-concept: Domain specificity and separation between competence and affect components. Journal of Educational Psychology, 103, 970–981. http://dx.doi.org/10.1037/a0025047. Arens, A. K., Yeung, A. S., & Hasselhorn, M. (2014). Native language self-concept and reading self-concept: Same or different? The Journal of Experimental Education, 82, 229–252. http://dx.doi.org/10.1080/00220973.2013.813362. Baumert, J., Lüdtke, O., Trautwein, U., & Brunner, M. (2009). Large-scale student assessment studies measure the results of processes of knowledge acquisition: Evidence in support of the distinction between intelligence and student achievement. Educational Research Review, 4, 165–176. http://dx.doi.org/10.1016/j.edurev.2009.

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