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Die vorliegende Studie beschäftigt sich mit dem nach einer Strukturveränderung in der Sekundarstufe I entstandenen Schulmodell der Neuen Mittelschule. Untersucht wird, ob sich durch dieses Schulmodell und der damit intendierten neuen Lehr-, Lern- und Prüfungskultur Zusammenhänge zwischen gemessenen mathematischen Kompetenzen der Schüler und den durch Lehrer vergebenen Jahresnoten feststellen lassen.
Die Literaturrecherche macht deutlich, dass die Kritik an der Monokultur des leh-rerzentrierten Unterrichts zwar zu einer neuen Lehr-, Lern- und Prüfungskultur führt, deren Inhalte sind aber recht unterschiedlich, komplex und nicht eindeutig definiert. In der NMS soll die Leistungsbewertung als Lernhilfe fungieren, aber auch verlässliche Aussagen über die Leistung der Schüler treffen. Zur Wirkung der neuen Lernkultur in der NMS gibt es ebenso keine empirischen Befunde wie über die Wirkung der Leistungsbewertung.
An der empirischen Untersuchung nehmen 79 Schüler der sechsten Schulstufe aus drei Neuen Mittelschulen (dicht besiedelte, mittel besiedelte, dünn besiedelte Gemeinde) in Niederösterreich teil. In jeder Schule werden zwei Klassen untersucht. Dabei werden der Kompetenzstand in Mathematik, Schülerzentriertheit sowie Sozial- und Leistungsdruck aus Sicht der Schüler gemeinsam mit der Jah-resnote erhoben.
Für die Studie wird ein Pfadmodell entwickelt und mit einer Pfadanalyse ausge-wertet. Dabei zeigen sich zwar Zusammenhänge zwischen den gemessenen Kompetenzen in Mathematik und den Jahresnoten. Diese Jahresnoten besitzen über die Klasse bzw. die Schule hinaus aber nur eine bedingte Aussagekraft über die erbrachten Leistungen.
Spinal muscular atrophy (SMA) and Duchenne muscular dystrophy (DMD) both are rare genetic neuromuscular diseases with progressive loss of motor ability. The neuromotor developmental course of those diseases is well documented. In contrast, there is only little evidence about characteristics of general and specific cognitive development. In both conditions the final motor outcome is characterized by an inability to move autonomously: children with SMA never accomplish independent motoric exploration of their environment, while children with DMD do but later lose this ability again. These profound differences in developmental pathways might affect cognitive development of SMA vs. DMD children, as cognition is shaped by individual motor experiences. DMD patients show impaired executive functions, working memory, and verbal IQ, whereas only motor ability seems to be impaired in SMA. Advanced cognitive capacity in SMA may serve as a compensatory mechanism for achieving in education, career progression, and social satisfaction. This study aimed to relate differences in basic numerical concepts and arithmetic achievement in SMA and DMD patients to differences in their motor development and resulting sensorimotor and environmental experiences. Horizontal and vertical spatial-numerical associations were explored in SMA/DMD children ranging between 6 and 12 years through the random number generation task. Furthermore, arithmetic skills as well as general cognitive ability were assessed. Groups differed in spatial number processing as well as in arithmetic and domain-general cognitive functions. Children with SMA showed no horizontal and even reversed vertical spatial-numerical associations. Children with DMD on the other hand revealed patterns in spatial numerical associations comparable to healthy developing children. From the embodied Cognition perspective, early sensorimotor experience does play a role in development of mental number representations. However, it remains open whether and how this becomes relevant for the acquisition of higher order cognitive and arithmetic skills.
The Big Five personality traits play a major role in student achievement. As such, there is consistent evidence that students that are more conscientious receive better teacher-assigned grades in secondary school. However, research often does not support the claim that students that are more conscientious similarly achieve higher scores in domain-specific standardized achievement tests. Based on the Invest-and-Accrue Model, we argue that conscientiousness explains to some extent why certain students receive better grades despite similar academic accomplishments (i.e., achieving similar scores in domain-specific standardized achievement tests). Therefore, the present study examines to what extent the relationship between student personality and teacher-assigned grades consists of direct as opposed to indirect associations (via subject-specific standardized test scores). We used a representative sample of 14,710 ninth-grade students to estimate these direct and indirect pathways in mathematics and German. Structural equation models showed that test scores explained between 8 and 11% of the variance in teacher-assigned grades in mathematics and German. The Big Five personality traits in students additionally explained between 8 and 10% of the variance in grades. Finally, the personality-grade relationship consisted of direct (0.02 | β| ≤ 0.27) and indirect associations via test scores (0.01 | β| ≤ 0.07). Conscientiousness explained discrepancies between teacher-assigned grades and students’ scores in domain-specific standardized tests to a greater extent than any of the other Big Five personality traits. Our findings suggest that students that are more conscientious may invest more effort to accomplish classroom goals, but fall short of mastery.
Many children show negative emotions related to mathematics and some even develop mathematics anxiety. The present study focused on the relation between negative emotions and arithmetical performance in children with and without developmental dyscalculia (DD) using an affective priming task. Previous findings suggested that arithmetic performance is influenced if an affective prime precedes the presentation of an arithmetic problem. In children with DD specifically, responses to arithmetic operations are supposed to be facilitated by both negative and mathematics-related primes (= negative math priming effect). We investigated mathematical performance, math anxiety, and the domain-general abilities of 172 primary school children (76 with DD and 96 controls). All participants also underwent an affective priming task which consisted of the decision whether a simple arithmetic operation (addition or subtraction) that was preceded by a prime (positive/negative/neutral or mathematics-related) was true or false. Our findings did not reveal a negative math priming effect in children with DD. Furthermore, when considering accuracy levels, gender, or math anxiety, the negative math priming effect could not be replicated. However, children with DD showed more math anxiety when explicitly assessed by a specific math anxiety interview and showed lower mathematical performance compared to controls. Moreover, math anxiety was equally present in boys and girls, even in the earliest stages of schooling, and interfered negatively with performance. In conclusion, mathematics is often associated with negative emotions that can be manifested in specific math anxiety, particularly in children with DD. Importantly, present findings suggest that in the assessed age group, it is more reliable to judge math anxiety and investigate its effects on mathematical performance explicitly by adequate questionnaires than by an affective math priming task.
Women are often underrepresented in math-intensive fields like the physical sciences, technology, engineering and mathematics. By comparison, boys relative to girls are less likely to strive for jobs in social and human-services domains. Relatively few studies have considered that intra-individual comparisons across domains may contribute to gendered occupational choices. This study examines whether girls’ and boys’ motivational beliefs in mathematics and language arts are predictive of their career plans in these fields. The study focusses on same domain and cross-domain effects and investigates bidirectional relations between motivational beliefs and career plans. Data for this study stem from 1,117 ninth and tenth graders (53.2% girls) from secondary schools in Berlin, Germany. Findings show systematic gender differences in samedomain effects in mathematics: girls’ comparatively lower mathematics self-concept and intrinsic value predicted a lower likelihood of striving for a math-related career. Crossdomain effects were not related to gender-specific career plans, with only one exception. Girls’ lower levels of intrinsic value in mathematics corresponded to a higher likelihood of striving for a career in language-related fields, which subsequently predicted lower levels of intrinsic value in mathematics. This finding points to a need to address both genderspecific motivational beliefs and gender-specific career plans in school when aiming to enhance more gender equality in girls’ and boys’ occupational choices.
Semiclassical asymptotics for the scattering amplitude in the presence of focal points at infinity
(2006)
We consider scattering in $\R^n$, $n\ge 2$, described by the Schr\"odinger operator $P(h)=-h^2\Delta+V$, where $V$ is a short-range potential. With the aid of Maslov theory, we give a geometrical formula for the semiclassical asymptotics as $h\to 0$ of the scattering amplitude $f(\omega_-,\omega_+;\lambda,h)$ $\omega_+\neq\omega_-$) which remains valid in the presence of focal points at infinity (caustics). Crucial for this analysis are precise estimates on the asymptotics of the classical phase trajectories and the relationship between caustics in euclidean phase space and caustics at infinity.