Students' instrumentalizations of hints and automated feedback in their task solution process when learning mathematics with a digital curriculum resource - Rezat, Sebastian (Proceedings of FAME 1 – Feedback & Assessment in Mathematics Education (ETC 14), 5-7 June 2024, Utrecht (The Netherlands))

How Do Advanced Pre-Service Teachers Develop Congruence Theorems for Quadrilaterals? - Hoffmann, Max; Schlüter, Sarah (Proceedings of the Fifth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2024, 10-14 June 2024))
In our paper, we present a study in which we investigate which strategies pre-service teachers (PSTs) use to find and, if necessary, reject possible candidates for congruence theorems for quadrilaterals. This study was conducted before the PTSs attended a university geometry course. In this way, statements about learning prerequisites can be made. For the study, we analyzed group discussions of PSTs to identify typical approaches and evaluate them from a mathematical perspective. The results can be considered for the further development of courses for PSTs and generate hypotheses for further research.
Keywords: Teachers’ and students’ practices at university level; Transition to; across and from university mathematics; Teaching and learning of specific topics in university mathematics; Congruence; Quadrilaterals

SRB Measures of Anosov Actions - Weich, Tobias; Guedes Bonthonneau, Yannick; Guillarmou, Colin (Journal of Differential Geometry)

Bedeutungsfacetten der Beziehungen von Differenzierbarkeit und Stetigkeit im Ein- und Mehrdimensionalen: Ein Blick auf die semantische Ebene - Lankeit, Elisa; Biehler, Rolf (Beiträge zum Mathematikunterricht 2024 - 57. Jahrestagung der Gesellschaft für Didaktik der Mathematik.)

Intuitiver Zugang zu datenbasierten Entscheidungsbäumen - Fleischer, Yannik; Biehler, Rolf (Beiträge zum Mathematikunterricht 2024 - 57. Jahrestagung der Gesellschaft für Didaktik der Mathematik.)

Transitionen zwischen Vektorobjekten in Schulbüchern - Mai, Tobias; Biehler, Rolf (Beiträge zum Mathematikunterricht 2024 - 57. Jahrestagung der Gesellschaft für Didaktik der Mathematik.)

Designing a Concept Inventory for Real Analysis - Bauer, Thomas; Biehler, Rolf; Lankeit, Elisa (INDRUM2024 PROCEEDINGS - Fifth conference of the International Network for Didactic Research in University Mathematics)

Algebraische Konzepte vertiefen und ihre Zusammenhänge im Schul- und Hoch-schulcurriculum verstehen lernen : Design-Prinzipien zur Anregung des Vereinheitlichens mathematischen Wissens im Mathematiklehramtsstudium - Wessel, Lena; Dellori, Anna (Mathematica Didactica)

Ressourcennutzung von Schüler:innen zum Lernen von Mathematik - Stallmeister, Lea; Rezat, Sebastian (Beiträge zum Mathematikunterricht 2024 - 57. Jahrestagung der Gesellschaft für Didaktik der Mathematik)

AnnoPy. Fachspezifische wissenschaftliche Textkompetenzen mit digitalen Medien in der Lehre fördern - Rezat, Sebastian; Rezat, Sara; Scholle, Oliver; Schulte, Carsten; Winkelnkemper, Felix (Lehrkräftebildung in der digitalen Welt. Zukunftsorientierte Forschungs- und Praxisperspektiven)
AnnoPy ist ein digitales Werkzeug, das an der Universität Paderborn in einer interdisziplinären Kooperation zwischen der Germanistischen Sprachdidaktik, Mathematikdidaktik und Informatikdidaktik entwickelt wurde, um wissenschaftliche Textkompetenzen zu fördern. Es kann in Präsenz- oder Blended-Learning-Szenarien eingesetzt werden, um eine Brücke zwischen individueller Auseinandersetzung mit dem Text und dessen sozial-diskursiver Aushandlung zu schlagen. Im Beitrag werden unterschiedliche Einsatzszenarien aus den drei beteiligten Disziplinen exemplarisch dargestellt, die jeweils unterschiedliche Facetten wissenschaftlicher Textkompetenz in den Mittelpunkt stellen. Im Fokus stehen dabei insbesondere die Förderung fachspezifischer Lesekompetenz im Rahmen einer Vorlesung mit großen Teilnehmendenzahlen sowie die Anwendung fachspezifischer Theorien und Konzepte in der Erschließung, Analyse und Beurteilung von Texten.
Keywords: digitale Medien; wissenschaftliche Textkompetenz; Lehrkonzept

Higher-order interactions lead to ‘reluctant’ synchrony breaking - von der Gracht, Sören; Nijholt, Eddie; Rink, Bob (Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences)
To model dynamical systems on networks with higher-order (non-pairwise) interactions, we recently introduced a new class of ordinary differential equations (ODEs) on hypernetworks. Here, we consider one-parameter synchrony breaking bifurcations in such ODEs. We call a synchrony breaking steady-state branch ‘reluctant’ if it is tangent to a synchrony space, but does not lie inside it. We prove that reluctant synchrony breaking is ubiquitous in hypernetwork systems, by constructing a large class of examples that support it. We also give an explicit formula for the order of tangency to the synchrony space of a reluctant steady-state branch.
Keywords: higher-order interactions; synchrony breaking; network dynamics; coupled cell systems

Praktiken der Förderung im inklusiven Mathematikunterricht - Häsel-Weide, Uta; Nührenbörger, M. (Beiträge zum Mathematikuntericht 2024. 57. Jahrestagung der Gesellschaft für Didaktik der Mathematik)

Patterson-Sullivan and Wigner distributions of convex-cocompact hyperbolic surfaces - Delarue, Benjamin; Palmirotta, Guendalina (arXiv:2411.19782)
We prove that the Patterson-Sullivan and Wigner distributions on the unit sphere bundle of a convex-cocompact hyperbolic surface are asymptotically identical. This generalizes results in the compact case by Anantharaman-Zelditch and Hansen-Hilgert-Schr\"oder.

Asymptotic behavior of solutions to the extension problem for the fractional Laplacian on noncompact symmetric spaces - Papageorgiou, Efthymia (Journal of Evolution Equations)
Abstract This work deals with the extension problem for the fractional Laplacian on Riemannian symmetric spaces G / K of noncompact type and of general rank, which gives rise to a family of convolution operators, including the Poisson operator. More precisely, motivated by Euclidean results for the Poisson semigroup, we study the long-time asymptotic behavior of solutions to the extension problem for $$L^1$$ L 1 initial data. In the case of the Laplace–Beltrami operator, we show that if the initial data are bi- K -invariant, then the solution to the extension problem behaves asymptotically as the mass times the fundamental solution, but this convergence may break down in the non-bi- K -invariant case. In the second part, we investigate the long-time asymptotic behavior of the extension problem associated with the so-called distinguished Laplacian on G / K . In this case, we observe phenomena which are similar to the Euclidean setting for the Poisson semigroup, such as $$L^1$$ L 1 asymptotic convergence without the assumption of bi- K -invariance.
Keywords: Mathematics (miscellaneous)

On the Universal Transformation of Data-Driven Models to Control Systems - Peitz, Sebastian; Bieker, Katharina (Automatica)
As in almost every other branch of science, the major advances in data science and machine learning have also resulted in significant improvements regarding the modeling and simulation of nonlinear dynamical systems. It is nowadays possible to make accurate medium to long-term predictions of highly complex systems such as the weather, the dynamics within a nuclear fusion reactor, of disease models or the stock market in a very efficient manner. In many cases, predictive methods are advertised to ultimately be useful for control, as the control of high-dimensional nonlinear systems is an engineering grand challenge with huge potential in areas such as clean and efficient energy production, or the development of advanced medical devices. However, the question of how to use a predictive model for control is often left unanswered due to the associated challenges, namely a significantly higher system complexity, the requirement of much larger data sets and an increased and often problem-specific modeling effort. To solve these issues, we present a universal framework (which we call QuaSiModO: Quantization-Simulation-Modeling-Optimization) to transform arbitrary predictive models into control systems and use them for feedback control. The advantages of our approach are a linear increase in data requirements with respect to the control dimension, performance guarantees that rely exclusively on the accuracy of the predictive model, and only little prior knowledge requirements in control theory to solve complex control problems. In particular the latter point is of key importance to enable a large number of researchers and practitioners to exploit the ever increasing capabilities of predictive models for control in a straight-forward and systematic fashion.

Conceptual understanding of third grades for axial symmetry - Wallner, Melina; Häsel-Weide, Uta (International Symposium in Elementary Mathematics Teaching. Proceedings: New Directions in Elementary Mathematics Education)

Hypernetworks: Cluster Synchronization Is a Higher-Order Effect - von der Gracht, Sören; Nijholt, Eddie; Rink, Bob (SIAM Journal on Applied Mathematics)
Many networked systems are governed by non-pairwise interactions between nodes. The resulting higher-order interaction structure can then be encoded by means of a hypernetwork. In this paper we consider dynamical systems on hypernetworks by defining a class of admissible maps for every such hypernetwork. We explain how to classify robust cluster synchronization patterns on hypernetworks by finding balanced partitions, and we generalize the concept of a graph fibration to the hypernetwork context. We also show that robust synchronization patterns are only fully determined by polynomial admissible maps of high order. This means that, unlike in dyadic networks, cluster synchronization on hypernetworks is a higher-order, i.e., nonlinear, effect. We give a formula, in terms of the order of the hypernetwork, for the degree of the polynomial admissible maps that determine robust synchronization patterns. We also demonstrate that this degree is optimal by investigating a class of examples. We conclude by demonstrating how this effect may cause remarkable synchrony breaking bifurcations that occur at high polynomial degree.
Keywords: Applied Mathematics

Idélic Approach in Enumerating Heisenberg Extensions - Klüners, Jürgen; Wang, Jiuya (La Matematica)

Expertise and professionalism for inclusive (mathematics) teaching and learning: reflections on findings from interdisciplinary professionalisation research - Seitz, Simone; Häsel-Weide, Uta; Wilke, Yannik; Wallner, Melina (Teachers and Teaching)

Discrete Lagrangian Neural Networks with Automatic Symmetry Discovery - Lishkova, Yana; Scherer, Paul; Ridderbusch, Steffen; Jamnik, Mateja; Liò, Pietro; Ober-Blöbaum, Sina; Offen, Christian (IFAC-PapersOnLine)
By one of the most fundamental principles in physics, a dynamical system will exhibit those motions which extremise an action functional. This leads to the formation of the Euler-Lagrange equations, which serve as a model of how the system will behave in time. If the dynamics exhibit additional symmetries, then the motion fulfils additional conservation laws, such as conservation of energy (time invariance), momentum (translation invariance), or angular momentum (rotational invariance). To learn a system representation, one could learn the discrete Euler-Lagrange equations, or alternatively, learn the discrete Lagrangian function Ld which defines them. Based on ideas from Lie group theory, in this work we introduce a framework to learn a discrete Lagrangian along with its symmetry group from discrete observations of motions and, therefore, identify conserved quantities. The learning process does not restrict the form of the Lagrangian, does not require velocity or momentum observations or predictions and incorporates a cost term which safeguards against unwanted solutions and against potential numerical issues in forward simulations. The learnt discrete quantities are related to their continuous analogues using variational backward error analysis and numerical results demonstrate the improvement such models can have both qualitatively and quantitatively even in the presence of noise.