Search

Background: Item response times in computerized assessments are frequently used to identify rapid guessing behaviour as a manifestation of response disengagement. However, non-rapid responses (i.e., with longer response times) are not necessarily engaged, which means that response-time-based procedures could overlook disengaged responses. Therefore, the identification of disengaged responses could be improved by considering additional indicators of disengagement. We investigated the extent to which decreases in individuals' item solution probabilities over the course of a test reflect disengaged response behaviour. Objectives: To disentangle different types of possibly disengaged responses and better understand non-effortful test-taking behaviour, we augmented responses-time-based procedures for identifying rapid guessing with strategies for detecting disengaged responses on the basis of performance declines in non-rapid responses. Methods: We combined item response theory (IRT) models for rapid guessing and test-taking persistence to examine the capability of response times and item positions to capture response disengagement. We used a computerized assessment in which science items were randomly distributed across positions for each student. This allowed us to estimate individual differences in test-taking persistence (i.e., the duration for which the initial level of performance is maintained) while accounting for rapid responses. Results and Conclusions: Response times did not fully explain disengagement; item responses reflected test-taking persistence even when rapid responses were accounted for. This interpretation was supported by a strong correlation of test-taking persistence with decreases in self-reported test-taking effort. Furthermore, our results suggest that IRT models for test-taking persistence can effectively account for the undesirable impact of low test-taking effort even when response times are unavailable.

Disengaged item responses pose a threat to the validity of the results provided by large-scale assessments. Several procedures for identifying disengaged responses on the basis of observed response times have been suggested, and item response theory (IRT) models for response engagement have been proposed. We outline that response time-based procedures for classifying response engagement and IRT models for response engagement are based on common ideas, and we propose the distinction between independent and dependent latent class IRT models. In all IRT models considered, response engagement is represented by an item-level latent class variable, but the models assume that response times either reflect or predict engagement. We summarize existing IRT models that belong to each group and extend them to increase their flexibility. Furthermore, we propose a flexible multilevel mixture IRT framework in which all IRT models can be estimated by means of marginal maximum likelihood. The framework is based on the widespread Mplus software, thereby making the procedure accessible to a broad audience. The procedures are illustrated on the basis of publicly available large-scale data. Our results show that the different IRT models for response engagement provided slightly different adjustments of item parameters of individuals' proficiency estimates relative to a conventional IRT model.

The 2I/E model is an extension of Marsh's (1986) classical internal/external frame of reference (I/E) model. Whereas the classical I/E model describes the formation of academic self-concept by the joint operation of social (external) and dimensional (internal) comparisons, the 2I/E model integrates temporal comparisons as an additional internal comparison process. In the 2I/E model, paths from achievement levels to self-concepts in the same subject are assumed to represent social comparisons, paths from achievement levels to self-concepts in another subject are assumed to represent dimensional comparisons, and paths from achievement changes to self-concepts in the same subject are assumed to represent temporal comparisons. The present research validated the 2I/E model in six empirical studies with a total of more than 20,000 students. Generally, there were strong positive social comparison paths, moderate negative dimensional comparison paths, and small positive temporal comparison paths. Furthermore, the relations of the 2I/E model were replicated with both grades and standardized test scores as achievement indicators (Study 1 and Study 2). Dimensional comparison effects were stronger between dissimilar subjects, like math and German, than between similar subjects, like German and English (Study 2 and Study 3). Also, the relations of the 2I/E model were shown when prior self-concepts were controlled for (Study 4). Overall, the 2I/E model seems to have the potential to enrich future theory and research on self-concept formation and comparison processes.

Tests administered in studies of student achievement often have a certain amount of not-reached items (NRIs). The propensity for NRIs may depend on the proficiency measured by the test and on additional covariates. This article proposes a semiparametric model to study such relationships. Our model extends Glas and Pimentel's item response theory model for NRIs by (1) including a semiparametric representation of the distribution of the onset of NRIs, (2) modeling the relationships of NRIs with proficiency via a flexible multinomial logit regression, and (3) including additional covariates to predict NRIs. We show that Glas and Pimentel's and our model have close connections to event history analysis, thereby making it possible to apply tools developed in this context to the analysis of NRIs. Our model was applied to a timed low-stakes test of mathematics achievement. Our model fitted the data better than Glas and Pimentel's model, and allowed for a more fine-grained assessment of the onset of NRIs. The results of a simulation study showed that our model accurately recovered the relationships of proficiency and covariates with the onset of NRIs, and reduced bias in the estimates of item parameters, proficiency distributions, and covariate effects on proficiency.

Position effects (PE) cause decreasing probabilities of correct item responses towards the end of a test. We analysed PEs in science, mathematics and reading tests administered in the German extension to the PISA 2006 study with respect to their variability at the student- and school-level. PEs were strongest in reading and weakest in mathematics. Variability in PEs was found at both levels of analysis. PEs were stronger for male students, for students with a migration background (science and mathematics), and for students with a less favourable socio-economic background (reading). At the school level, PEs were stronger in lower school tracks and in schools with a high proportion of students with a migration background. The relationships of the test scores with the covariates partly reflected the covariates' relationships with PEs. Our findings suggest that PEs should be taken seriously in large-scale assessments as they have an undesirable impact on the results.

In the present research, we investigated the relation between changes in students' state self-control capacity and their motivational test-taking effort over the course of an achievement test. Thereby, we considered trait self-control as a major predictor of achievement-related behavior as a covariate. N = 1840 apprentices repeatedly rated their state self-control capacity and the test-taking effort they invested while working on a 140-min achievement test in mathematics and science. Using growth curve analyses, our results revealed correlated decreases in state self-control capacity and the test-taking effort invested over the course of the test. Furthermore, we found that trait self-control helped to keep state self-control capacity and test-taking effort at a higher level over the course of the test. Our results support the assumption of the process model of self-control that waning self-control capacity is reflected in reduced motivational effort. Furthermore, our findings provide evidence that self-control might play a crucial role in students' test-taking behavior in large-scale assessment studies. By modeling changes in state self-control capacity and effort investment while considering trait self-control, we provide an alternative approach for investigating self-control-dependent processes and the underlying mechanisms of self-control in achievement situations.

Students evaluate their domain-specific abilities by comparing their own achievement in a certain domain with the achievement of others (social comparison), with their own prior achievement (temporal comparison), and with their own achievement in other domains (dimensional comparison). This article is the first to analyze the simultaneous effects of social, temporal, and dimensional comparisons on students' academic self-concepts of various domains in experimental and field studies. In Study 1 (N = 120), students judged their ability self-concept after having received experimentally manipulated social, temporal, and dimensional comparison feedback. In Study 2 (N = 924), students had to rate their math and German self-concept and were asked to directly compare their achievement to social, temporal, and dimensional comparison standards. In the longitudinal Study 3a (N = 3,054) and 3b (N = 14,008), the three types of comparisons were modeled in an extended internal/external frame of reference model (Marsh, 1986) containing paths from math and verbal achievement level and achievement change to math and verbal self-concept. In all studies, social, temporal, and dimensional comparisons showed significant effects on self-concept. For each comparison process, downward comparisons with worse-off standards resulted in higher self-concepts, whereas upward comparisons with better-off standards resulted in lower self-concepts. These results are in accordance with the theories underlying social, temporal, and dimensional comparison processes and support their integration into a combined framework.

We present factor extension procedures for confirmatory factor analysis that provide estimates of the relations of common and unique factors with external variables that do not undergo factor analysis. We present identification strategies that build upon restrictions of the pattern of correlations between unique factors and external variables. The first restriction minimizes the sum of squared correlations between unique factors and external variables. This approach is similar to the traditional factor extension procedure. The second restriction minimizes the complexity of the pattern of external correlations of unique factors. This approach has similarities with the simple structure ideal imposed on most factor rotation strategies. The procedures are illustrated with a real data example that demonstrates their applicability to real-world research questions.

Background: In low-stakes educational assessments, test takers might show a performance decline (PD) on end-of-test items. PD is a concern in educational assessments, especially when groups of students are to be compared on the proficiency variable because item responses gathered in the groups could be differently affected by PD. In order to account for PD, mixture item response theory (IRT) models have been proposed in the literature. Methods: In this article, multigroup extensions of three existing mixture models that assess PD are compared. The models were applied to the mathematics test in a large-scale study targeting school track differences in proficiency. Results: Despite the differences in the specification of PD, all three models showed rather similar item parameter estimates that were, however, different from the estimates given by a standard two parameter IRT model. In addition, all models indicated that the amount of PD differed between tracks, in that school track differences in proficiency were slightly reduced when PD was accounted for. Nevertheless, the models gave different estimates of the proportion of students showing PD, and differed somewhat from each other in the adjustment of proficiency scores for PD. Conclusions: Multigroup mixture models can be used to study how PD interacts with proficiency and other variables to provide a better understanding of the mechanisms behind PD. Differences between the presented models with regard to their assumptions about the relationship between PD and item responses are discussed.

We consider the conformal decomposition of Einstein’s constraint equations introduced by Lichnerowicz and York, on a closed manifold. We establish existence of non-CMC weak solutions using a combination of priori estimates for the individual Hamiltonian and momentum constraints, barrier constructions and fixed-point techniques for the Hamiltonian constraint, Riesz-Schauder theory for the momentum constraint, together with a topological fixed-point argument for the coupled system. Although we present general existence results for non-CMC weak solutions when the rescaled background metric is in any of the three Yamabe classes, an important new feature of the results we present for the positive Yamabe class is the absence of the near-CMC assumption, if the freely specifiable part of the data given by the traceless-transverse part of the rescaled extrinsic curvature and the matter fields are sufficiently small, and if the energy density of matter is not identically zero. In this case, the mean extrinsic curvature can be taken to be an arbitrary smooth function without restrictions on the size of its spatial derivatives, so that it can be arbitrarily far from constant, giving what is apparently the first existence results for non-CMC solutions without the near-CMC assumption. Using a coupled topological fixed-point argument that avoids near-CMC conditions, we establish existence of coupled non-CMC weak solutions with (positive) conformal factor ϕ ∈ W s,p , where p ∈ (1,∞) and s(p) ∈ (1 + 3/p,∞). In the CMC case, the regularity can be reduced to p ∈ (1,∞) and s(p) ∈ (3/p, ∞) ∩ [1,∞). In the case of s = 2, we reproduce the CMC existence results of Choquet-Bruhat [10], and in the case p = 2, we reproduce the CMC existence results of Maxwell [33], but with a proof that goes through the same analysis framework that we use to obtain the non-CMC results. The non-CMC results on closed manifolds here extend the 1996 non-CMC result of Isenberg and Moncrief in three ways: (1) the near-CMC assumption is removed in the case of the positive Yamabe class; (2) regularity is extended down to the maximum allowed by the background metric and the matter; and (3) the result holds for all three Yamabe classes. This last extension was also accomplished recently by Allen, Clausen and Isenberg, although their result is restricted to the near-CMC case and to smoother background metrics and data.

We provide an elementary proof of the Schauder-Tychonoff Fixed Point Theorem, using basic notions of General Topology and Convex Analysis. [ABSTRACT FROM AUTHOR]

This study examined predictors of the quality of parental homework involvement and reciprocal relations between the quality of parental homework involvement and students' reading achievement and academic functioning in a reading-intensive subject (German). Data from 2,830 students in nonacademic tracks and their parents who were surveyed in both Grades 5 and 7 were analyzed. The quality of parental homework involvement was assessed via student reports. It was conceptualized as a multidimensional construct and measured by 3 dimensions proposed by self-determination theory: parental control, parental responsiveness, and parental structure. Whereas students' academic functioning in Grade 5 predicted the way parents became involved in the homework process in Grade 7, the quality of parents' help with homework did not depend on their socioeconomic background. Reciprocal relations between the quality of parental homework involvement and children's academic functioning were observed: Low academic functioning of students in Grade 5 resulted in more parental control in Grade 7, and more parental control in Grade 5 was associated with lower academic functioning in Grade 7. Similarly, high academic functioning in Grade 5 resulted in more parental responsiveness and structure in Grade 7, and more parental responsiveness and structure in Grade 5 were associated with better academic functioning in Grade 7.

Background: Vocational interests play a central role in the vocational decision-making process and are decisive for the later job satisfaction and vocational success. Based on Ackerman's (1996) notion of "trait complexes," specific interest profiles of gifted high-school graduates can be expected. Aims: Vocational interests of gifted and highly achieving adolescents were compared to those of their less intelligent/achieving peers according to Holland's (1997) RIASEC model. Further, the impact of intelligence and achievement on interests were analysed while statistically controlling for potentially influencing variables. Changes in interests over time were investigated. Sample: "N" = 4,694 German students (age: "M" = 19.5, "SD" = 0.80; 54.6% females) participated in the study (TOSCA; Koller, Watermann, Trautwein, & Ludtke, 2004). Method: Interests were assessed in participants' final year at school and again 2 years later ("N" = 2,318). Results: Gifted participants reported stronger investigative and realistic interests, but lower social interests than less intelligent participants. Highly achieving participants reported higher investigative and (in wave 2) higher artistic interests. Considerable gender differences were found: gifted girls had a flat interest profile, while gifted boys had pronounced realistic and investigative and low social interests. Multilevel multiple regression analyses predicting interests by intelligence and school achievement revealed stable interest profiles. Beyond a strong gender effect, intelligence and school achievement each contributed substantially to the prediction of vocational interests. Conclusions: At the time around graduation from high school, gifted young adults show stable interest profiles, which strongly differ between gender and intelligence groups. These differences are relevant for programmes for the gifted and for vocational counselling. (Contains 5 tables and 4 figures.)

Using the theoretical framework of achievement goal theory, this study investigated the accuracy of teachers' judgments of their students' motivation. Self-report data were gathered on the mastery, performance-approach, and performance-avoidance goals of 1140 German secondary school students (mean age = 14.24) in five academic subjects (English, Mathematics, German, second foreign language, and Biology). Their teachers in each of the five subjects (N = 176) were asked to judge students' achievement goals. Multilevel regression analyses revealed that teacher ratings of students' motivation statistically significantly predicted student ratings in all five subjects for mastery and performance-approach motivation, but not for performance-avoidance motivation. Assessment of differences in teachers' judgment accuracy across classrooms revealed some variability in teachers' ability to judge their students' mastery and performance-approach goals. Exploratory analyses showed that teaching experience, teacher gender, student age, and student gender did not systematically explain variation in judgment accuracy. Future research should examine other characteristics potentially influencing teachers' judgment accuracy and investigate the effect of teachers' judgment accuracy on students' motivation. (Contains 5 tables.)

In this article, the authors develop and test a differential effects model of university entry versus major selection using a set of common predictors, including background factors (gender and socioeconomic status), academic achievement, and academic self-concept. The research used data from 2 large longitudinal databases from Germany (N = 5,048) and England (N = 15,995) to explore the generalizability of the hypothesized model in 2 cultural contexts. For both countries, the results suggested that (a) socioeconomic status was a key predictor of university entry, whereas gender was a key predictor of major selection; (b) achievement and self-concept in both math and English were positive predictors of university entry; and (c) math achievement and self-concept predicted math-intensive major choice and lower likelihood of entering verbal-intensive majors (and vice versa). Implications for theory and practice are discussed. (Contains 7 tables and 2 footnotes.)

In modern expectancy-value theory (EVT) in educational psychology, expectancy and value beliefs additively predict performance, persistence, and task choice. In contrast to earlier formulations of EVT, the multiplicative term Expectancy x Value in regression-type models typically plays no major role in educational psychology. The present study used latent moderated structural equation modeling to explore whether there is empirical support for a multiplicative effect in a sample of 2,508 students at the end of secondary education. Expectancy and four facets of value beliefs (attainment, intrinsic, and utility value as well as cost) predicted achievement when entered separately into a regression equation. Moreover, in models with both expectancy and value beliefs as predictor variables, the expectancy component as well as the multiplicative term Expectancy x Value were consistently found to predict achievement positively. (Contains 3 tables, 2 figures and 4 footnotes.)

This article examines the development of social and ethnic disparities in academic achievement in elementary schooling. It investigated whether reading and mathematics development in 136 mixed-ability classes shows path-dependent processes of cumulative advantage (Matthew effects) from Grades 4 to 6 (Grade 4 mean age = 10.62, SD = 0.57) resulting in growing inequality. Status-dependent processes of cumulative advantage, their interaction with path-dependent processes, and consequences for the degree of social and ethnic inequality are examined. Two complementary methods for analyzing multilevel data are used: growth curve and quasi-simplex models. No evidence for a Matthew effect was found in either domain. A compensation effect emerged for reading, to the benefit of ethnic minorities. A fan-spread effect was found for mathematics, partly attributable to status-dependent processes of cumulative advantage. (Contains 5 tables and 2 figures.)

In Germany, the "Abitur" grades awarded at the end of upper secondary education are critical in the allocation of sought-after university places. Drawing on a representative sample of 3526 grade 13 "Abitur" students in the German state of Baden-Wurttemberg, this article examines whether and to what extent grading is affected by the mean achievement of the school serving as frame of reference ("group-referenced grading"), and to what extent this influence differs for coursework and examination grades in mathematics and English as a foreign language. Overall, the results indicate that the higher level of standardization of the central "Abitur" examinations makes examination grades less susceptible to frame-of-reference effects than are coursework grades. (Contains 4 tables.)

Enthusiasm is considered an important characteristic of effective teachers. However, the conceptualization of the term in the research literature is inconsistent. Whereas most studies use the term "enthusiasm" to describe features of instruction, some have used it to describe a characteristic of teachers. This research seeks to clarify the concept of teacher enthusiasm, examining its dimensionality and context specificity. The study draws on three samples of teachers who were administered questionnaire measures of enthusiasm. In two samples (N = 205 and 332), it was possible to match teacher data with data on the students taught. In another sample (N = 113), additional measures of work-related wellbeing were implemented. Confirmatory multigroup factor analyses showed that two dimensions of teacher enthusiasm can be distinguished, namely enthusiasm for teaching and enthusiasm for the subject. These dimensions differed in their meaning and context specificity. Whereas teaching enthusiasm was systematically linked to occupational wellbeing and to classroom variables, subject enthusiasm related only moderately to other measures of occupational wellbeing and was independent of characteristics of the classes taught. (Contains 5 tables and 3 figures.)

Gender differences in the development of children's and adolescents' academic self-perceptions have received increasing attention in recent years. This study extends previous research by examining the development of mathematics self-concept across grades 7-12 in three cultural settings: Australia (Sydney; N = 1,333), the United States (Michigan; N = 2,443), and Germany (four federal states; N = 4,688). Results of latent growth curve models document very similar patterns of self-concept development in males and females in the three settings. First, gender differences in favor of boys were observed at the beginning of the observation period (grade 7). Second, gender was not significantly related to self-concept change in either group, meaning that initial differences persisted across time. Third, the results provided no evidence that the form of the longitudinal change trajectories for mathematics self-concept differed across the cultural settings. This pattern of results is inconsistent with explanatory models that predict converging or diverging gender differences in mathematics self-concept. Furthermore, the results indicate that self-concept development may be highly similar across western cultural settings.

The cross-cultural generalizability of vocational interest structures has received significant attention in recent years. This article adds to this research in four respects. First, data from a context that has not previously been investigated (Germany) was analyzed. Second, students at different stages of their educational career were examined. Third, the interest structure in male and females was compared. Fourth, two methods--the randomization test of hypothesized order relations (RTOR) and confirmatory factor analysis (CFA)--were applied to three competing structural conceptions: Holland's circular representation, Gati's hierarchical model, and Rounds and Tracey's alternative hierarchical model. RTOR supported all three representations, whereas CFA supported only Holland's model. CFAs indicated that the interest structure is reasonably invariant between high school and university students, but that the configurations for high school females and males differ. Substantive and methodological implications are discussed. (Contains 9 tables and 5 figures.)

Whether sequence learning entails a single or multiple memory systems is a moot issue. Recently, D. R. Shanks, L. Wilkinson, and S. Channon advanced a single-system model that predicts a perfect correlation between true (i.e., error free) response time priming and recognition. The Shanks model is contrasted with a dual-process model that incorporates both response time priming and reportable sequence knowledge as predictors of recognition. The models were tested by applying confirmatory factor analysis to data obtained from a recognition test that was administered under both speed and accuracy conditions. The Shanks model accounted for the data in the speed condition, whereas the dual-process model provided a better fit in the accuracy condition. The results are compatible with the notion that cognitive processes were engaged differentially in recognition judgments under speed and accuracy conditions. (Contains 4 figures and 3 footnotes.)

This study examines the relationships of vocational interests and mathematical literacy both cross-sectionally and longitudinally. Extending previous research, the results of Holland's RIASEC (Realistic, Investigative, Artistic, Social, Enterprising, and Conventional) scale scores are compared with results from a reductionist approach using individual interest profiles (including the parameters level, differentiation, and orientation). Both analyses find significant relations between interests and mathematical literacy. The scale score analyses reveal positive associations of Realistic interests with mathematical literacy, whereas Artistic interests show a negative association. Interest profiles from a dimensional representation show individuals with interest orientations close to the Realistic domain score highest on mathematical literacy, with those with interests in both Artistic and Social domains scoring lowest. Results from profile analyses suggest that interest differentiation moderates the interest-ability relation. Only interest profiles are predictive for mathematical literacy over and above covariates, indicating that interest profiles are more robust predictors than the scale scores. Analyses show that interest profiles are a valid reduction of the scale score models. (Contains 4 figures and 5 tables.)

Predictions about processes linking gender to students' choices of advanced courses were derived from the internal/external frame of reference (I/E) model and expectancy value (EV) theory. The predictions were tested for the domains of mathematics and biology using data from 1,148 students attending academically oriented secondary schools in Germany. Results revealed substantial gender differences on measures gathered in Grade 10. Males outperformed females on the mathematics and biology achievement tests, and reported higher math self-concepts and intrinsic values. Females scored higher on the biology self-concept and intrinsic value scales. Consistent with our expectations, gender differences in Grade 10 mediated the effect of gender on course enrollment in Grade 12. In line with the EV model, self-concepts and intrinsic values had substantial effects on subsequent course choices. As predicted by the I/E model, domain-specific self-concepts and intrinsic values were positively related to course choices in the same domain, but negatively related to choices in the other domain. In addition, results of multigroup structural equation models revealed that the processes underlying course choices were different for males and females. Finally, students' choices of specialized courses were related to their aspired field of college education. (Contains 3 tables, 4 figures and 1 note.)

Results from prior research indicate that a student's academic self-concept is negatively influenced by the achievement of others in his or her school (a frame of reference effect) and that this negative frame of reference effect is not or only slightly reduced by the quality, standing, or prestige of the track or school attended (a 'reflected glory' effect). Going beyond prior studies, the present research used both between-school and within-school approaches to investigate frame of reference and reflected glory effects in education, incorporating students' own perceptions of the standing of their school and class. Multilevel analyses were performed with data from 3 large-scale assessments with 4,810, 1,502, and 4,247 students, respectively. Findings from all 3 studies showed that, given comparable individual achievement, placement in high-achieving learning groups was associated with comparatively low academic self-concepts. However, students' academic self-concept was not merely a reflection of their relative position within the class but also substantively associated with their individual and shared perceptions of the class's standing. Moreover, the negative effects of being placed in high-achieving learning groups were weaker for high-achieving students. Overall, the studies support both educational and social psychology theorizing on social comparison. Keywords: social comparison, achievement, frame of reference effect, reflected glory effect DOI: 10.1037/a0016306