Children's performance estimation in mathematics and science tests over a school year: A pilot study

The metacognitve ability to accurately estimate ones performance in a test, is assumed to be of central importance for initializing task-oriented effort. In addition activating adequate problem-solving strategies, and engaging in efficient error detection and correction. Although school children's' ability to estimate their own performance has been widely investigated, this was mostly done under highly-controlled, experimental set-ups including only one single test occasion. Method: The aim of this study was to investigate this metacognitive ability in the context of real achievement tests in mathematics. Developed and applied by a teacher of a 5th grade class over the course of a school year these tests allowed the exploration of the variability of performance estimation accuracy as a function of test difficulty. Results: Mean performance estimations were generally close to actual performance with somewhat less variability compared to test performance. When grouping the children into three achievement levels, results revealed higher accuracy of performance estimations in the high achievers compared to the low and average achievers. In order to explore the generalization of these findings, analyses were also conducted for the same children's tests in their science classes revealing a very similar pattern of results compared to the domain of mathematics. Discussion and Conclusion: By and large, the present study, in a natural environment, confirmed previous laboratory findings but also offered additional insights into the generalisation and the test dependency of students' performances estimations.

How gender fair are German schoolbooks in the twenty-first century? An analysis of language and illustrations in schoolbooks for mathematics and German

Schoolbooks convey not only school-relevant knowledge; they also influence the development of stereotypes about different social groups. Particularly during the 1970s and 1980s, many studies analysed schoolbooks and criticised the overall predominance of male persons and of traditional role allocations. Since that time, women’s and men’s occupations and social functions have changed considerably. The present research investigated gender portrayals in schoolbooks for German and mathematics that were recently published in Germany. We examined the proportions of female and male persons in pictures and texts and categorized their activities, occupational and parental roles. Going beyond previous studies, we added two criteria: the use of gender-fair language and the spatial arrangements of persons in pictures. Our results show that schoolbooks for German contained almost balanced depictions of girls and boys, whereas women were less frequently shown than men. In mathematics books, males outnumbered females in general. Across both types of books, female and male persons were engaged in many different activities, not only gendertyped ones; however, male persons were more often described via their profession than females. Use of gender-fair language has found its way into schoolbooks but is not used consistently. Books for German were more gender fair in terms of linguistic forms than books for mathematics. For spatial arrangements, we found no indication for gender biases. The results are discussed with a focus on how schoolbooks can be optimized to contribute to gender equality.

The Impact of Language Opacity and Proficiency on Reading Strategies in Bilinguals: An Eye Movement Study

Reading strategies vary across languages according to orthographic depth - the complexity of the grapheme in relation to phoneme conversion rules - notably at the level of eye movement patterns. We recently demonstrated that a group of early bilinguals, who learned both languages equally under the age of seven, presented a first fixation location (FFL) closer to the beginning of words when reading in German as compared with French. Since German is known to be orthographically more transparent than French, this suggested that different strategies were being engaged depending on the orthographic depth of the used language. Opaque languages induce a global reading strategy, and transparent languages force a local/serial strategy. Thus, pseudo-words were processed using a local strategy in both languages, suggesting that the link between word forms and their lexical representation may also play a role in selecting a specific strategy. In order to test whether corresponding effects appear in late bilinguals with low proficiency in their second language (L2), we present a new study in which we recorded eye movements while two groups of late German-French and French-German bilinguals read aloud isolated French and German words and pseudo-words. Since, a transparent reading strategy is local and serial, with a high number of fixations per stimuli, and the level of the bilingual participants' L2 is low, the impact of language opacity should be observed in L1. We therefore predicted a global reading strategy if the bilinguals' L1 was French (FFL close to the middle of the stimuli with fewer fixations per stimuli) and a local and serial reading strategy if it was German. Thus, the L2 of each group, as well as pseudo-words, should also require a local and serial reading strategy. Our results confirmed these hypotheses, suggesting that global word processing is only achieved by bilinguals with an opaque L1 when reading in an opaque language; the low level in the L2 gives way to a local and serial reading strategy. These findings stress the fact that reading behavior is influenced not only by the linguistic mode but also by top-down factors, such as readers' proficiency.

Executive functioning, metacognition, and self-perceived competence in elementary school children: An explorative study on their interrelations and their role for school achievement

In the present study, associations between executive functioning, metacognition, and self-perceived competence in the context of early academic outcomes were examined. A total of 209 children attending first grade were initially assessed in terms of their executive functioning and academic self-concept. One year later, children’s executive functioning, academic self-concept, metacognitive monitoring and control, as well as their achievement in mathematics and literacy were evaluated. Structural equation modeling revealed that executive functioning was significantly related to metacognitive control, both cross-sectionally and longitudinally, and that self-concept was substantially associated with metacognitive monitoring, both cross-sectionally and longitudinally. Individual differences in executive functioning and metacognitive control were significantly related to academic outcomes, with metacognitive control appearing to yield a more circumscribed influence on academic outcomes (only literacy) compared to executive functioning (literacy and mathematics).

Flexibility Properties in Complex Analysis and Affine Algebraic Geometry

In the last decades affine algebraic varieties and Stein manifolds with big (infinite-dimensional) automorphism groups have been intensively studied. Several notions expressing that the automorphisms group is big have been proposed. All of them imply that the manifold in question is an Oka–Forstnerič manifold. This important notion has also recently merged from the intensive studies around the homotopy principle in Complex Analysis. This homotopy principle, which goes back to the 1930s, has had an enormous impact on the development of the area of Several Complex Variables and the number of its applications is constantly growing. In this overview chapter we present three classes of properties: (1) density property, (2) flexibility, and (3) Oka–Forstnerič. For each class we give the relevant definitions, its most significant features and explain the known implications between all these properties. Many difficult mathematical problems could be solved by applying the developed theory, we indicate some of the most spectacular ones.

Foundations of stochastic geometry and theory of random sets

The first section of this chapter starts with the Buffon problem, which is one of the oldest in stochastic geometry, and then continues with the definition of measures on the space of lines. The second section defines random closed sets and related measurability issues, explains how to characterize distributions of random closed sets by means of capacity functionals and introduces the concept of a selection. Based on this concept, the third section starts with the definition of the expectation and proves its convexifying effect that is related to the Lyapunov theorem for ranges of vector-valued measures. Finally, the strong law of large numbers for Minkowski sums of random sets is proved and the corresponding limit theorem is formulated. The chapter is concluded by a discussion of the union-scheme for random closed sets and a characterization of the corresponding stable laws.

Gender Stereotypes and Gendered Vocational Aspirations among Secondary School Students

Research Topic/Aim: Horizontal gender inequalities appear to be rather stable, with girls more often choosing ‘female' service professions, and boys choosing career paths related to science, technology, engineering or mathematics, since measures to bring more women into typical ‘male' jobs and more men into typical ‘female' jobs did not turn out to be sustainable. This paper focuses on gender stereotypes, namely non-egalitarian patriarchal gender-role orientations and gender associations of the school subjects German and mathematics. Dealing with and abolishing such gender stereotypes may be key strategy to reach sustainability regarding more equal vocational choices. Thus, gender stereotypes will be theorised and empirically analysed as a major predictor of gender-typical vocational perspectives considering interest in these school subjects as a mediating factor. Furthermore, we focus on structural patriarchy as a root of gender-role orientations, and teacher gender regarding its impact on gendered images of subjects. Theoretical and methodology framework: Our analyses of gender segregation in vocational aspirations and vocational choice center on Gottfredson's (2002; Gottfredson and Becker, 1981) Theory of Circumscription, Compromise and Self-Creation. One of the main assumptions of this theory is that people associate jobs with particular sexes and those jobs that do not fit particular gender roles are not considered. Empirical analyses are based on survey data of eighth-graders in the Swiss canton of Bern (N = 672). Structural Equation Models (SEM) for male and female students are estimated. Conclusions/Findings: Results reveal different patterns for boys and girls; for boys, gender-typical (male) vocational perspective could be explained via gender role orientations, interest in mathematics and gender associations of the school subjects, for girls, the factors under consideration could be empirically linked to ‘atypical vocational perspective'. Relevance to Nordic educational research: The study focuses on gender relations in society and how they are reproduced. Gender segregation in vocational choice and at the labour market is a universal issue - affecting both egalitarian and non-egalitarian gender regimes in similar ways. Although in general Northern countries appear to be more equal regarding gender inequality, gender segregation is rather persistent (Jarman, Blackburn and Brooks, 2012) and therefore remains a relevant topic.

How need for cognition affects the processing of achievement-related information

The present article analyzed, how need for cognition (NFC) influences the formation of performance expectancies. When processing information, individuals with lower NFC often rely on salient information and shortcuts compared to individuals higher in NFC. We assume that these preferences of processing will also make individuals low in NFC more responsive to salient achievement-related cues because the processing of salient cues is cognitively less demanding than the processing of non-salient cues. Therefore, individuals lower in NFC should tend to draw wider ranging inferences from salient achievement-related information. In a sample of N = 197 secondary school students, achievement-related feedback (grade on an English examination) affected changes in expectancies in non-corresponding academic subjects (e.g., expectation of final grade in mathematics or history) when NFC was lower, whereas for students with higher NFC, changes in expectancies in non-corresponding academic subjects were not affected.

Rasmussen's spectral sequences and the \germslN-concordance invariants

Combining known spectral sequences with a new spectral sequence relating reduced and unreduced slN-homology yields a relations hip between the Homflypt-homology of a knot and its slN-concordance invariants. As an application, some of the slN-concordance invariants are shown to be linearly independent.