Fostering Mathematical Competences by Preparing for a Mathematical Competition

Mathematical competences are important for mastering the problems that are encoun-tered in a modern society that values knowledge. Such competences are relevant not only for mastering the mathematical problems encountered in school but also for managing everyday life. In practice, mathematical competences are required for finding solutions to society’s major problems (e.g., the prediction of global warming). Mathematical competences are thereby assumed to be individual cognitive abilities and skills as well as the outcomes of learning processes. An individual is ascribed with sophisticated mathematical competences if he or she is able to come up with new mathematical problems by applying previously existing mathematical competences meaningfully. Therewith, fostering mathematical competences is of major importance. Based on a cognitive-socio-constructive understanding of learning in mathematics, students need learn-ing possibilities that lock in their individual potential. Several mechanisms and factors have been shown to drive the acquisition of mathematical competences. To foster mathematical competences, challenging learning opportunities are necessary. Especially for students who are already able to solve curriculum-based tasks. One extracurricular enrichment approach that has been suggested to challenge students are (domain-specific, mathematical) academic competitions. But, to ensure that these students will be able to master the challenging prob-lems they will face in the competition, they must prepare appropriately to solve such prob-lems. Therefore, and to protect them from negative experiences such as failure, corresponding training programs have been suggested and implemented in practice. Such training programs prepare students to participate in a specific academic competition. Paper 1 reviews the appropriateness of academic competitions by summarizing the roles ascribed to academic competitions with regard to the promotion of gifted students. Using the example of the Mathematical Olympiad for elementary school students, a training program that considers the strengths and weaknesses of mathematically gifted elementary school stu-dents is introduced. The training was aimed at enhancing the performance in the Mathemati-cal Olympiad as well as (process-based) mathematical competences. The effectiveness of this particular training was examined in two empirical studies: In Paper 2, a quasi-experimental pre- and posttest design was used to investigate the effects of the training. Dependent variables were success in the Mathematical Olympiad, mathematical competences, and the motivation to do mathematics (i.e., math self-concept and value beliefs for mathematics). A total of 201 third- and fourth-grade students participated in this study. Positive effects were found for third and fourth graders’ performance in the Mathematical Olympiad, their mathematical competences, and the task-specific interest in mathematics of fourth-grade students. In Paper 3, the effects of a training that was aimed at fostering process-based mathe-matical competences on cognitive factors were investigated in detail. Dependent variables were success in the Mathematical Olympiad, content- and process-based mathematical com-petences, as well as domain-general cognitive abilities. Results of a randomized controlled field trial with 97 students indicated significant effects of the training on process-based com-petences but also transfer effects on domain-general abilities. In summary, this dissertation provides evidence for the positive influences of a training for an academic competition in mathematics on students’ performance in the competition and, additionally, their mathematical competences. Based on the results of the studies, questions for further educational research with regard to trainings and academic competitions can be deduced. The findings suggest that the effectiveness of separate core components should be investigated more detailed. Further, some implications for educational practice are summa-rized

NFDI4Microbiota – national research data infrastructure for microbiota research

Microbes – bacteria, archaea, unicellular eukaryotes, and viruses – play an important role in human and environmental health. Growing awareness of this fact has led to a huge increase in microbiological research and applications in a variety of fields. Driven by technological advances that allow high-throughput molecular characterization of microbial species and communities, microbiological research now offers unparalleled opportunities to address current and emerging needs. As well as helping to address global health threats such as antimicrobial resistance and viral pandemics, it also has a key role to play in areas such as agriculture, waste management, water treatment, ecosystems remediation, and the diagnosis, treatment and prevention of various diseases. Reflecting this broad potential, billions of euros have been invested in microbiota research programs worldwide. Though run independently, many of these projects are closely related. However, Germany currently has no infrastructure to connect such projects or even compare their results. Thus, the potential synergy of data and expertise is being squandered. The goal of the NFDI4Microbiota consortium is to serve and connect this broad and heterogeneous research community by elevating the availability and quality of research results through dedicated training, and by facilitating the generation, management, interpretation, sharing, and reuse of microbial data. In doing so, we will also foster interdisciplinary interactions between researchers. NFDI4Microbiota will achieve this by creating a German microbial research network through training and community-building activities, and by creating a cloud-based system that will make the storage, integration and analysis of microbial data, especially omics data, consistent, reproducible, and accessible across all areas of life sciences. In addition to increasing the quality of microbial research in Germany, our training program will support widespread and proper usage of these services. Through this dual emphasis on education and services, NFDI4Microbiota will ensure that microbial research in Germany is synergistic and efficient, and thus excellent. By creating a central resource for German microbial research, NDFDI4Microbiota will establish a connecting hub for all NFDI consortia that work with microbiological data, including GHGA, NFDI4Biodiversity, NFDI4Agri and several others. NFDI4Microbiota will provide non-microbial specialists from these consortia with direct and easy access to the necessary expertise and infrastructure in microbial research in order to facilitate their daily work and enhance their research. The links forged through NFDI4Microbiota will not only increase the synergy between NFDI consortia, but also elevate the overall quality and relevance of microbial research in Germany

The association of basic numerical abilities and math achievement: The mediating role of visuospatial and arithmetical abilities

Basic numerical abilities such as number line estimation have been observed repeatedly to be associated with mathematical achievement. Recently, it was argued that the association between basic numerical abilities and mathematical achievement is fully mediated by visuospatial abilities. However, arithmetical abilities have not yet been considered as influencing this association, even though solution strategies in number line estimation as well as mathematical achievement often involve arithmetical procedures. Therefore, we investigated the mediating role of arithmetical and visuospatial abilities on the association between number line estimation and mathematical achievement in a sample of n = 599 German elementary school students. Results indicated that arithmetical abilities as well as visuospatial abilities mediated the association between number line estimation and mathematical achievement. However, neither visuospatial nor arithmetical abilities fully mediated the association between number line estimation and mathematical achievement when considered in isolation. This substantiates the relevance of the intertwined development of visuospatial and arithemtical abilities as well as basic numerical abilities such as number line estimation (i.e. the combination of domain-specific numerical and domain-general abilities) driving mathematical achievement

Supplementary Information files for: The association of basic numerical abilities and math achievement: The mediating role of visuospatial and arithmetical abilities

Supplementary Information files for: The association of basic numerical abilities and math achievement: The mediating role of visuospatial and arithmetical abilitiesBasic numerical abilities such as number line estimation have been observed repeatedly to be associated with mathematical achievement. Recently, it was argued that the association between basic numerical abilities and mathematical achievement is fully mediated by visuospatial abilities. However, arithmetical abilities have not yet been considered as influencing this association, even though solution strategies in number line estimation as well as mathematical achievement often involve arithmetical procedures. Therefore, we investigated the mediating role of arithmetical and visuospatial abilities on the association between number line estimation and mathematical achievement in a sample of n = 599 German elementary school students. Results indicated that arithmetical abilities as well as visuospatial abilities mediated the association between number line estimation and mathematical achievement. However, neither visuospatial nor arithmetical abilities fully mediated the association between number line estimation and mathematical achievement when considered in isolation. This substantiates the relevance of the intertwined development of visuospatial and arithemtical abilities as well as basic numerical abilities such as number line estimation (i.e. the combination of domain-specific numerical and domain-general abilities) driving mathematical achievement<br

Getting fit for the mathematical olympiad: positive effects on achievement and motivation?

All around the world, there are numerous academic competitions (e.g., “Academic Olympiads”) and corresponding training courses to foster students’ competences and motivation. But do students’ competences and motivation really benefit from such courses? We developed and evaluated a course that was designed to prepare third and fourth graders to participate in the German Mathematical Olympiad. Its effectiveness was evaluated in a quasi-experimental pre- and posttest design (N = 201 students). Significant positive effects of the training were found for performance in the academic competition (for both third and fourth graders) as well as mathematical competences as measured with a curriculum-oriented test (for fourth graders only). Differential effects across grade levels (with more pronounced positive effects in fourth-grade students) were observed for students’ math self-concept and task-specific interest in mathematics, pointing to possible social comparison effects.Weltweit gibt es eine Vielzahl akademischer Wettbewerbe (z.B. „Akademische Olympiaden“) sowie entsprechende Begleitangebote, in denen Leistung und Motivation der Teilnehmenden gefördert werden sollen. Aber profitieren Teilnehmende wirklich von solchen Kursen? Wir haben ein solches Begleitangebot, das Lernende der dritten und vierten Klasse auf die Teilnahme an der Deutschen Mathematik-Olympiade vorbereiten soll, entwickelt und dessen Wirksamkeit in einem quasi-experimentellen Prä- and Posttest-Design evaluiert (N=201 SchülerInnen). Die Ergebnisse zeigten positive Effekte auf die Leistungen in der Mathe-Olympiade für Schülerinnen und Schüler beider Klassenstufen sowie auf die mathematischen Kompetenzen der ViertklässlerInnen gemessen mit einem Curriculums-orientierten Test. Darüber hinaus wurden für das mathematische Selbstkonzept und das aufgabenspezifische Interesse der SchülerInnen in Mathematik stärkere positive Effekte bei den Viertklässlern beobachtet, was darauf hindeutet, dass soziale Vergleichsprozesse stattgefunden haben

Individuelle Förderung mit den LemaS-Boxen : Evidenzbasierte Materialien für den Mathematik-, Deutsch- und Sachunterricht in der Grundschule

Die Gestaltung von Lernumgebungen, die unterschiedliche Lernpotenziale fordern und fördern, ist eine Kernaufgabe schulischer Bildungsprozesse. Die Frage, welche Gestaltungselemente einer Lernumgebung sich für welche Lernenden unter welchen Bedingungen als wirksam erwiesen und wie eine Implementation dieser Elemente in die Praxis gelingen kann, ist dabei von hoher Bedeutung. Ausgehend von Enrichment-Konzepten und -Materialien, die sich bisher im Rahmen eines Begabtenförderungsprogramms für Dritt- und Viertklässler als wirksam erwiesen haben, entstehen in LemaS-Teilprojekt 7 „ENRICHMINT“ Unterrichtsmaterialien, die auch im Regelweise des Teilprojekts nach dem sogenannten Design-Based Implementation Research vorgestellt und ein erstes Fazit gezogen. Außerdem werden die grundlegenden Konzepte der Unterrichtsmaterialien für den Mathematik-, Sach-, und Deutschunterricht vorgestellt und die nächsten Schritte der Arbeit des Teilprojekts skizziert.Providing learning environments that demand and promote different learning potentials is a principal task of school education. The questions which single design elements of a learning environment prove to be effective for which learners under which conditions and how these elements can be implemented in practice are of paramount importance. Based on enrichment concepts and materials that were found to be effective within the framework of an extracurricular promotion program for third and fourth graders, teaching materials are created in LemaS-sub-project 7 “ENRICHMINT” to be used in regular lessons. In this chapter, the working procedure of the sub-project based on the so-called Design-Based Implementation Research is described and first preliminary conclusions are presented. Additionally, the basic concepts of the teaching materials for mathematics, science and German lessons are presented and the next steps on the agenda of the sub-project are outlined

Getting fit for the Mathematical Olympiad: positive effects on achievement and motivation?

All around the world, there are numerous academic competitions (e.g., “Academic Olympiads”) and corresponding training courses to foster students’ competences and motivation. But do students’ competences and motivation really benefit from such courses? We developed and evaluated a course that was designed to prepare third and fourth graders to participate in the German Mathematical Olympiad. Its effectiveness was evaluated in a quasi-experimental pre- and posttest design (N = 201 students). Significant positive effects of the training were found for performance in the academic competition (for both third and fourth graders) as well as mathematical competences as measured with a curriculum-oriented test (for fourth graders only). Differential effects across grade levels (with more pronounced positive effects in fourth-grade students) were observed for students’ math self-concept and task-specific interest in mathematics, pointing to possible social comparison effects.</p