TY - JOUR AU - Prediger, S. AU - Dröse, Jennifer AU - Stahnke, R. AU - Ademmer, C. ID - 45374 JF - Journal of Mathematics Teacher Education TI - Teacher expertise for fostering at-risk students’ understanding of basic concepts: conceptual model and evidence for growth ER - TY - CONF AU - Dröse, Jennifer AU - Griese, B. AU - Wessel, Lena ID - 45379 T2 - Twelfth Congress of the European Society for Research in Mathematics Education (CERME12) TI - Prosepctive teachers‘ diagnostic judgements on students’ under- standing of conditional probabilities ER - TY - CONF AB - Hamilton-Jacobi reachability methods for safety-critical control have been well studied, but the safety guarantees derived rely on the accuracy of the numerical computation. Thus, it is crucial to understand and account for any inaccuracies that occur due to uncertainty in the underlying dynamics and environment as well as the induced numerical errors. To this end, we propose a framework for modeling the error of the value function inherent in Hamilton-Jacobi reachability using a Gaussian process. The derived safety controller can be used in conjuncture with arbitrary controllers to provide a safe hybrid control law. The marginal likelihood of the Gaussian process then provides a confidence metric used to determine switches between a least restrictive controller and a safety controller. We test both the prediction as well as the correction capabilities of the presented method in a classical pursuit-evasion example. AU - Vertovec, Nikolaus AU - Ober-Blöbaum, Sina AU - Margellos, Kostas ID - 30733 TI - Verification of safety critical control policies using kernel methods ER - TY - CHAP AU - Dellori, Anna AU - Wessel, Lena ED - Trigueros, M. ED - Barquero, B. ED - Hochmuth, R. ED - Peters, J. ID - 48385 T2 - Proceedings of INDRUM2022 TI - Design principles for intertwining local and nonlocal mathematics - The case of relating registers and representations in abstract algebra ER - TY - JOUR AB - AbstractTeachers’ in-depth diagnostic thinking has been shown to be crucial for student-centered teaching as they need to perceive and interpret students’ understanding for well-informed decision-making on adaptive teaching practices. The paper presents a content-related approach to analyzing diagnostic thinking processes with respect to the mathematical knowledge elements that prospective teachers identify as students’ resources and obstacles. Prospective teachers’ challenge is that some relevant knowledge elements first have to be unpacked, because compact concepts (such as the place value concept) or procedures (such as for multi-digit multiplication) comprise several smaller knowledge elements (such as the positional property) that have to be made explicit for students to foster their learning processes adequately. Our study examines what knowledge elements prospective teachers perceive and interpret in a transcript vignettes on multi-digit multiplication (of decimal and natural numbers) and its underlying basic arithmetic concepts (place value understanding and meaning of multiplication) in written diagnostic judgments on students’ resources and obstacles (N = 196). A comparative design within the vignette is used to investigate how far the process of perceiving can be supported by thematic cues. The analysis reveals that those knowledge elements cued in the vignette by being already unpacked and explicitly addressed are perceived and interpreted more often (but with lower correctness) than those that are uncued and therefore have to be unpacked by the prospective teachers themselves. This confirms the need to prepare prospective teachers for unpacking mathematical concepts themselves. AU - Dröse, Jennifer AU - Prediger, Susanne ID - 40607 JF - Journal für Mathematik-Didaktik KW - Education KW - General Mathematics SN - 0173-5322 TI - Prospective Teachers’ Diagnostic Thinking on Students’ Understanding of Multi-Digit Multiplication: A Content-Related Analysis on Unpacking of Knowledge Elements ER - TY - CONF AU - Dröse, Jennifer AU - Griese, Birgit AU - Wessel, Lena ID - 48389 T2 - Twelfth Congress of the European Society for Research in Mathematics Education (CERME12) TI - Prospective teachers’ diagnostic judgments on students’ understanding of conditional probabilities ER - TY - CONF AU - Dröse, Jennifer AU - Wessel, Lena ED - Fernandez, C. ED - Llinares, S. ED - Gutiérrez, A. ED - Planas, N. ID - 45378 T2 - Proceedings of the 45th Conference of the International Group for the Psychology of Mathematics Education. PME TI - Prospective Teachers‘ Competence of Fostering Students’ Understanding in Script Writing Task ER - TY - JOUR AB - In this paper we give an overview over some aspects of the modern mathematical theory of Ruelle resonances for chaotic, i.e. uniformly hyperbolic, dynamical systems and their implications in physics. First we recall recent developments in the mathematical theory of resonances, in particular how invariant Ruelle distributions arise as residues of weighted zeta functions. Then we derive a correspondence between weighted and semiclassical zeta functions in the setting of negatively curved surfaces. Combining this with results of Hilgert, Guillarmou and Weich yields a high frequency interpretation of invariant Ruelle distributions as quantum mechanical matrix coefficients in constant negative curvature. We finish by presenting numerical calculations of phase space distributions in the more physical setting of 3-disk scattering systems. AU - Barkhofen, Sonja AU - Schütte, Philipp AU - Weich, Tobias ID - 31057 IS - 24 JF - Journal of Physics A: Mathematical and Theoretical TI - Semiclassical formulae For Wigner distributions VL - 55 ER - TY - THES AB - Vorgestellt wird ein Entwicklungsforschungsprojekt zur Konzeption und Durchführung einer Veranstaltung "Geometrie für Lehramtsstudierende". Die Schwerpunkte des Projekts sind zum einen die inhaltliche Gestaltung der Veranstaltung und zum anderen die Umsetzung von Professionsorientierung. Bezogen auf den inhaltlichen Aufbau wird das auf metrischen Räumen aufbauende Axiomensystem der "Saccheri-Ebene" vorgestellt und mit alternativen axiomatischen Zugängen zur ebenen Geometrie verglichen. Die Frage nach der Umsetzung von Professionsorientierung in Fachveranstaltungen ist eng mit der Problematik der zweiten Diskontinuität verbunden. In der Arbeit wird dieses Problem auf Grundlage der Synthese von theoretischen Hintergründen zur Bedeutung von mathematischem Wissen und Können für professionelle Handlungskompetenz von Mathematiklehrkräften diskutiert und darauf aufbauend werden theoriebasierte Entwurfsprinzipien für professionsorientierte Fachveranstaltungen entworfen. Zentrale Elemente der methodischen Gestaltung sind die sogenannten "Schnittstellenwochen" zu den Themen Kongruenz und Symmetrie sowie das begleitende Schnittstellen-ePortfolio. Das zentrale Ergebnis der Arbeit ist ein theoretisch fundiertes und empirisch evaluiertes ganzheitliches Veranstaltungskonzept für eine professionsorientierte Geometrie-Veranstaltung für Lehramtsstudierende, dessen Konzeption auf andere Fachveranstaltungen übertragbar ist. Darüber hinaus ergeben sich im Rahmen der durchgeführten Entwicklungsforschung verschiedene neue Beiträge zur Geometriedidaktik in Schule- und Hochschule. AU - Hoffmann, Max ID - 31363 TI - Von der Axiomatik bis zur Schnittstellenaufgabe: Entwicklung und Erforschung eines ganzheitlichen Lehrkonzepts für eine Veranstaltung Geometrie für Lehramtsstudierende ER - TY - JOUR AU - Bux, Kai-Uwe AU - Hilgert, Joachim AU - Weich, Tobias ID - 35322 IS - 2 JF - Journal of Spectral Theory KW - Geometry and Topology KW - Mathematical Physics KW - Statistical and Nonlinear Physics SN - 1664-039X TI - Poisson transforms for trees of bounded degree VL - 12 ER -