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Mathematical arguments are central components of mathematics and play a role in certain types of modelling of potential mathematical giftedness. However, particular characteristics of arguments are interpreted differently in the context of mathematical giftedness. Some models of giftedness see no connection, whereas other models consider the formulation of complete and plausible arguments as a partial aspect of giftedness. Furthermore, longitudinal changes in argumentation characteristics remain open. This leads to the research focus of this article, which is to identify and describe the changes of argumentation products in potentially mathematically gifted children over a longer period. For this purpose, the argumentation products of children from third to sixth grade are collected throughout a longitudinal study and examined with respect to the use of examples and generalizations. The analysis of all products results in six different types of changes in the characteristics of the argumentation products identified over the survey period and case studies are used to illustrate student use of examples and generalizations of these types. This not only reveals the general importance of the use of examples in arguments. For one type, an increase in generalized arguments can be observed over the survey period. The article will conclude with a discussion of the role of argument characteristics in describing potential mathematical giftedness.
Identification of the intermediates and determination of their structures in the reduction of dioxygen to water by cytochrome c oxidase (CcO) are particularly important to understanding both O2 activation and proton pumping by the enzyme. In this work, we report the products of the rapid reaction of O2 with the mixed valence form (CuA(2+), heme a(3+), heme a3(2+)-CuB(1+)) of the enzyme. The resonance Raman results show the formation of two ferryl-oxo species with characteristic Fe(IV)=O stretching modes at 790 and 804 cm(-1) at the peroxy oxidation level (PM). Density functional theory calculations show that the protein environment of the proximal H-bonded His-411 determines the strength of the distal Fe(IV)=O bond. In contrast to previous proposals, the PM intermediate is also formed in the reaction of Y167F with O2. These results suggest that in the fully reduced enzyme, the proton pumping ν(Fe(IV)=O) = 804 cm(-1) to ν(Fe(IV)=O) = 790 cm(-1) transition (P→F, where P is peroxy and F is ferryl) is triggered not only by electron transfer from heme a to heme a3 but also by the formation of the H-bonded form of the His-411-Fe(IV)=O conformer in the proximal site of heme a3. The implications of these results with respect to the role of an O=Fe(IV)-His-411-H-bonded form to the ring A propionate of heme a3-Asp-399-H2O site and, thus, to the exit/output proton channel (H2O) pool during the proton pumping P→F transition are discussed. We propose that the environment proximal to the heme a3 controls the spectroscopic properties of the ferryl intermediates in cytochrome oxidases.
Background: Understanding the coupling of O2 reduction to proton pumping by CcO requires detection of reaction intermediates.
Results: We have detected two oxoferryl intermediates at the PM oxidation state.
Conclusion: The H-bonding properties of the proximal heme a3 His ligand control the strength of the oxoferryl species.
Significance: The role of His-411, Thr-389, Gly-386, and Asp-399 residues in the proton pumping P→F transition is outlined.
Hintergrund: Ab Frühjahr 2020 kam es zur weltweiten Verbreitung von SARS-CoV‑2 mit der heute als erste Welle der Pandemie bezeichneten Phase ab März 2020. Diese resultierte an vielen Kliniken in Umstrukturierungen und Ressourcenverschiebungen. Ziel unserer Arbeit war die Erfassung der Auswirkungen der Pandemie auf die universitäre Hals-Nasen-Ohren(HNO)-Heilkunde für die Forschung, Lehre und Weiterbildung. Material und Methoden: Die Direktorinnen und Direktoren der 39 Universitäts-HNO-Kliniken in Deutschland wurden mithilfe einer strukturierten Online-Befragung zu den Auswirkungen der Pandemie im Zeitraum von März bis April 2020 auf die Forschung, Lehre und die Weiterbildung befragt. Ergebnisse: Alle 39 Direktorinnen und Direktoren beteiligten sich an der Umfrage. Hiervon gaben 74,4 % (29/39) an, dass es zu einer Verschlechterung ihrer Forschungstätigkeit infolge der Pandemie gekommen sei. Von 61,5 % (24/39) wurde berichtet, dass pandemiebezogene Forschungsaspekte aufgegriffen wurden. Von allen Kliniken wurde eine Einschränkung der Präsenzlehre berichtet und 97,5 % (38/39) führten neue digitale Lehrformate ein. Im Beobachtungszeitraum sahen 74,4 % der Klinikdirektoren die Weiterbildung der Assistenten nicht gefährdet. Schlussfolgerung: Die Ergebnisse geben einen Einblick in die heterogenen Auswirkungen der Pandemie. Die kurzfristige Bearbeitung pandemiebezogener Forschungsthemen und die Einführung innovativer digitaler Konzepte für die studentische Lehre belegt eindrücklich das große innovative Potenzial und die schnelle Reaktionsfähigkeit der HNO-Universitätskliniken, um auch während der Pandemie ihre Aufgaben in der Forschung, Lehre und Weiterbildung bestmöglich zu erfüllen.
Adaptive, synchronous, and mobile online education: developing the ASYMPTOTE learning environment
(2022)
The COVID-19-induced distance education was perceived as highly challenging by teachers and students. A cross-national comparison of five European countries identified several challenges occurred during the distance learning period. On this basis, the article aims to develop a theoretical framework and design requirements for distance and online learning tools. As one example for online learning in mathematics education, the ASYMPTOTE system is introduced. It will be freely available by May 2022. ASYMPTOTE is aimed at the adaptive and synchronous delivery of online education by taking a mobile learning approach. Its core is the so-called digital classroom, which not only allows students to interact with each other or with the teacher but also enables teachers to monitor their students’ work progress in real time. With respect to the theoretical framework, this article analyses to what extent the ASYMPTOTE system meets the requirements of online learning. Overall, the digital classroom can be seen as a promising tool for teachers to carry out appropriate formative assessment and—partly—to maintain personal and content-related interaction at a distance. Moreover, we highlight the availability of this tool. Due to its mobile learning approach, almost all students will be able to participate in lessons conducted with ASYMPTOTE.
Geometry is part of the core of mathematics. It has been relevant ever since people have interacted with nature and its phenomena. Geometry’s relevance to the teaching and learning of mathematics can be emphasized, too. Nevertheless, a current potential shift in the topics of mathematics education to the detriment of geometry might be emerging. That is, other topics related to mathematics are seeming to grow in importance in comparison to geometry. Despite this, or perhaps because of it, geometry is an important component of current research in mathematics education. In the literature review, we elaborate relevant foci on the basis of current conference proceedings. By means of about 50 journal articles, five main topics are elaborated in more detail: geometric thinking and practices, geometric contents and topics, teacher education in geometry, argumentation and proof in geometry, as well as the use of digital tools for the teaching and learning of geometry. Conclusions and limitations for current and future research on geometry are formulated at the end of the article. In particular, the transfer to the practices of geometric teaching is explored on the basis of the elaborated research findings in order to combine both aspects of the teaching and learning of geometry.