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Early numeracy is one of the strongest predictors for later success in school mathematics (e.g., Duncan et al., 2007). The main goal of first grade mathematics teachers should therefore be to provide learning opportunities that enable all students to develop sound early numeracy skills. Developmental models, or learning progressions, can describe how early numerical understanding typically develops. Assessments that are aligned to empirically validated learning progressions can support teachers to understand their students learning better and target instruction accordingly. To date, there have been no progression-based instruments made available for German teachers to monitor their students’ progress in the domain of early numeracy. This dissertation contributes to the design of such an instrument. The first study analysed the suitability of early numeracy assessments currently used in German primary schools at school entry to identify students’ individual starting points for subsequent progress monitoring. The second study described the development of progression-based items and investigated the items in regards to main test quality criteria, such as reliability, validity, and test fairness, to find a suitable item pool to build targeted tests. The third study described the construction of the progress monitoring measure, referred to as the learning progress assessment (LPA). The study investigated the extent to which the LPA was able to monitor students’ individual learning progress in early numeracy over time. The results of the first study indicated that current school entry assessments were not able to provide meaningful information about the students’ initial learning status. Thus, the MARKO-D test (Ricken, Fritz, & Balzer, 2013) was used to determine the students’ initial numerical understanding in the other two studies, because it has been shown to be an effective measure of conceptual numerical understanding (Fritz, Ehlert, & Leutner, 2018). Both studies provided promising evidence for the quality of the LPA and its ability to detect changes in numerical understanding over the course of first grade. The studies of this dissertation can be considered an important step in the process of designing an empirically validated instrument that supports teachers to monitor their students’ early numeracy development and to adjust their teaching accordingly to enhance school achievement.
Academic Achievement in Math and Foreign Language: Individual Characteristics and Gender Stereotypes
(2019)
The study aims to investigate the contribution of individual characteristics and gender stereotypes of secondary school pupils in academic achievement in math and foreign language. A sample of pupils reported in 6th and 7th grades (three waves) their self-perceived ability and motivation for math and foreign language learning, math and foreign language gender stereotypes, implicit theories of intelligence; academic achievement (grades) in math in foreign language is also included in the analysis. Regression analysis and Mann Whitney U Test demonstrated that self-perceived ability in math and incremental theory of intelligence are significant predictors for academic achievement in maths. Boys are characterised by higher level of self-perceived abilities and motivation for learning math. However, academic achievement of girls in maths and foreign languages are higher as compared to boys. Pupils learning two foreign languages demonstrate higher level of self-perceived abilities for motivation and learning math and less expressed gender stereotypes about success in learning math and foreign languages. Study findings can be used for designing educational programmes for mathematics and foreign languages, professional development and finding solutions for individualized approach in school education.
The study investigates the effects of classroom composition (average ability, achievement, and socio-economic background, proportion of immigrant students) on the development in mathematics achievement, and reading literacy from grade 5 to 6. The study draws on a sample of N=1892 students in vocational track schools (Hauptschule) and intermediate track schools (Realschule) in Baden-Wuerttemberg, Germany. After controlling for school type, and between-school differences in student intake characteristics, none of the compositional characteristics showed a statistically significant effect on achievement development. School track was associated with the development of reading literacy even after controlling for individual differences; however, this relationship lost its statistical significance after the composition of the student body was additionally taken into account.
It is well-documented that academic achievement is associated with students' self-perceptions of their academic abilities, that is, their academic self-concepts. However, low-achieving students may apply self-protective strategies to maintain a favorable academic self-concept when evaluating their academic abilities. Consequently, the relation between achievement and academic self-concept might not be linear across the entire achievement continuum. Capitalizing on representative data from three large-scale assessments (i.e., TIMSS, PIRLS, PISA; N = 470,804), we conducted an integrative data analysis to address nonlinear trends in the relations between achievement and the corresponding self-concepts in mathematics and the verbal domain across 13 countries and 2 age groups (i.e., elementary and secondary school students). Polynomial and interrupted regression analyses showed nonlinear relations in secondary school students, demonstrating that the relations between achievement and the corresponding self-concepts were weaker for lower achieving students than for higher achieving students. Nonlinear effects were also present in younger students, but the pattern of results was rather heterogeneous. We discuss implications for theory as well as for the assessment and interpretation of self-concept.
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.
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.
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.
Four topics were investigated in this longitudinal person-centered study: (a) profiles of subjective task values and ability self-concepts of adolescents in the domain of mathematics, (b) the stability of and changes to the profiles of motivational beliefs from Grade 7 to 12, (c) the relation of changes to student-perceived classroom characteristics, and (d) the extent to which profile membership in early adolescence predicted mathematics achievement and career plans in late adolescence and the choice of math-related college majors and occupations in adulthood. Data were drawn from the Michigan Study of Adolescent and Adult Life Transitions Study. We focused on students who participated in the following 4 waves of data collection (N = 867): at the beginning of Grade 7 (Wave 3), at the end of Grade 7, in Grade 10 (Wave 5), and in Grade 12 (Wave 6). Four profiles that were stable across Grades 7 to 12 were identified using Latent Profile Analysis. Student-reported fairness and friendliness and competition in class predicted changes in profile membership. Profile membership in Grade 7 predicted math-related career plans in Grade 12. Profile membership in Grade 12 predicted the choice of math-related college major after finishing school and of math-related occupations in adulthood.
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.
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.