@article{44333, abstract = {{This work deals with an algebro–geometric theory of solutions of the classical Yang–Baxter equation based on torsion free coherent sheaves of Lie algebras on Weierstraß cubic curves.}}, author = {{Burban, Igor and Galinat, L.}}, journal = {{Communications in Mathematical Physics}}, number = {{1}}, pages = {{123–169}}, title = {{{Torsion free sheaves on Weierstraß cubic curves and the classical Yang-Baxter equation}}}, doi = {{10.1007/s00220-018-3172-2}}, volume = {{364}}, year = {{2018}}, } @unpublished{44538, author = {{Burban, Igor and Drozd, Yu.}}, title = {{{Non-commutative nodal curves and derived tame algebras}}}, year = {{2018}}, } @article{44332, author = {{Burban, Igor and Zheglov, A.}}, journal = {{International Journal of Mathematics}}, number = {{10}}, title = {{{Fourier-Mukai transform on Weierstraß cubics and commuting differential operators}}}, volume = {{29}}, year = {{2018}}, } @misc{45394, author = {{Dröse, Jennifer and Prediger, Susanne and Marcus, A.}}, title = {{{Strategien zum Verstehen von Textaufgaben – Fach- und sprachintegriertes Unterrichtsmaterial in Basis- und Regelfassung}}}, year = {{2018}}, } @article{6571, author = {{Jurgelucks, Benjamin and Claes, Leander and Walther, Andrea and Henning, Bernd}}, issn = {{1055-6788}}, journal = {{Optimization Methods and Software}}, number = {{4-6}}, pages = {{868----888}}, publisher = {{Taylor and Francis Ltd.}}, title = {{{Optimization of triple-ring electrodes on piezoceramic transducers using algorithmic differentiation}}}, doi = {{10.1080/10556788.2018.1435652}}, volume = {{33}}, year = {{2018}}, } @inproceedings{45680, author = {{Bruns, Julia and Unterhauser, E. and Gasteiger, H.}}, booktitle = {{Beiträge zum Mathematikunterricht}}, pages = {{377–380}}, publisher = {{WTM-Verlag}}, title = {{{Entwicklung des Begriffsverständnisses zu Vierecksfiguren in der Grundschule – Erste Ergebnisse aus dem Projekt BegriV}}}, year = {{2018}}, } @article{45690, author = {{Bruns, Julia and Gasteiger, H.}}, journal = {{mathematik lehren}}, pages = {{10–13}}, title = {{{Gemeinsame Arbeitsphasen produktiv nutzen – verschiedene Methoden kooperativen Lernens im Mathematikunterricht der Grundschule}}}, volume = {{205}}, year = {{2018}}, } @inbook{36485, abstract = {{This chapter presents an overview of the contributions in TSG 1: Early Childhood Mathematics Education at ICME-13 which focused on issues from the perspective of early childhood educators. A basic assumption of this chapter is that the opportunities for young children to develop mathematical understandings and skills are influenced by several conditions at a macro, meso and micro level. First, curricula provide a framework for early mathematics teaching and learning with varying expectations (by teachers) about what can occur in the pre-school environment—informal learning (such as through play), content to learn and activities to experience. Second, early childhood educators’ mathematical knowledge, pedagogical knowledge, understandings, beliefs, and perceptions influence how they enact these expectations. These competencies can be developed and supported by professional learning. Third, educational programs, resources and activities used in the pre-school environment impact on the mathematical opportunities children engage in at the micro level.}}, author = {{Cooke, Audrey and Bruns, Julia}}, booktitle = {{Contemporary Research and Perspectives on Early Childhood Mathematics Education}}, editor = {{Elia, Iliada and Mulligan, Joanne and Anderson, Ann and Baccaglini-Frank, Anna and Benz, Christiane}}, isbn = {{978-3-319-73432-3}}, pages = {{267–289}}, publisher = {{Springer International Publishing}}, title = {{{Early Childhood Educators’ Issues and Perspectives in Mathematics Education}}}, doi = {{10.1007/978-3-319-73432-3_14}}, year = {{2018}}, } @inbook{36480, abstract = {{Im vorangegangenen Kapitel wurde die Vorgeschichte beschrieben, wie es durch Initiative der Deutsche Telekom Stiftung zur Gründung des DZLM gekommen ist. In diesem zweiten Kapitel werden die Tätigkeitsfelder und Konzepte des DZLM in seiner ersten Förderphase vom 01.10.2011 bis 30.09.2016 beschrieben.}}, author = {{Barzel, Bärbel and Biehler, Rolf and Blömeke, Sigrid and Brandtner, Regine and Bruns, Julia and Dohrmann, Christian and Kortenkamp, Ulrich and Lange, Thomas and Leuders, Timo and Rösken-Winter, Bettina and Scherer, Petra and Selter, Christoph}}, booktitle = {{Mathematikfortbildungen professionalisieren: Konzepte, Beispiele und Erfahrungen des Deutschen Zentrums für Lehrerbildung Mathematik}}, editor = {{Biehler, Rolf and Lange, Thomas and Leuders, Timo and Rösken-Winter, Bettina and Scherer, Petra and Selter, Christoph}}, isbn = {{978-3-658-19028-6}}, pages = {{7–39}}, publisher = {{Springer Fachmedien Wiesbaden}}, title = {{{Das Deutsche Zentrum für Lehrerbildung Mathematik – DZLM}}}, doi = {{10.1007/978-3-658-19028-6_2}}, year = {{2018}}, } @inbook{36478, author = {{Bruns, Julia and Eichen, Lars}}, booktitle = {{Mathematikfortbildungen professionalisieren. Konzepte, Beispiele und Erfahrungen des Deutschen Zentrums für Lehrerbildung Mathematik}}, editor = {{Biehler, Rolf and Lange, Thomas and Leuders, Timo and Rösken-Winter, Bettina}}, pages = {{417--434}}, publisher = {{Springer}}, title = {{{EmMa - Fortbildung für elementarpädagogische Fachpersonen zur frühen mathematischen Bildung}}}, doi = {{10.1007/978-3-658-19028-6_21}}, year = {{2018}}, } @book{36475, editor = {{Gasteiger, Hedwig and Bruns, Julia}}, title = {{{Methoden empirischer Bildungsforschung im Kontext Frühkindliche Bildung und Entwicklung}}}, year = {{2018}}, } @unpublished{19940, abstract = {{Two smooth map germs are right-equivalent if and only if they generate two Lagrangian submanifolds in a cotangent bundle which have the same contact with the zero-section. In this paper we provide a reverse direction to this classical result of Golubitsky and Guillemin. Two Lagrangian submanifolds of a symplectic manifold have the same contact with a third Lagrangian submanifold if and only if the intersection problems correspond to stably right equivalent map germs. We, therefore, obtain a correspondence between local Lagrangian intersection problems and catastrophe theory while the classical version only captures tangential intersections. The correspondence is defined independently of any Lagrangian fibration of the ambient symplectic manifold, in contrast to other classical results. Moreover, we provide an extension of the correspondence to families of local Lagrangian intersection problems. This gives rise to a framework which allows a natural transportation of the notions of catastrophe theory such as stability, unfolding and (uni-)versality to the geometric setting such that we obtain a classification of families of local Lagrangian intersection problems. An application is the classification of Lagrangian boundary value problems for symplectic maps.}}, author = {{Offen, Christian}}, booktitle = {{arXiv:1811.10165}}, title = {{{Local intersections of Lagrangian manifolds correspond to catastrophe theory}}}, year = {{2018}}, } @article{19943, abstract = {{In this paper we continue our study of bifurcations of solutions of boundary-value problems for symplectic maps arising as Hamiltonian diffeomorphisms. These have been shown to be connected to catastrophe theory via generating functions and ordinary and reversal phase space symmetries have been considered. Here we present a convenient, coordinate free framework to analyse separated Lagrangian boundary value problems which include classical Dirichlet, Neumann and Robin boundary value problems. The framework is then used to prove the existence of obstructions arising from conformal symplectic symmetries on the bifurcation behaviour of solutions to Hamiltonian boundary value problems. Under non-degeneracy conditions, a group action by conformal symplectic symmetries has the effect that the flow map cannot degenerate in a direction which is tangential to the action. This imposes restrictions on which singularities can occur in boundary value problems. Our results generalise classical results about conjugate loci on Riemannian manifolds to a large class of Hamiltonian boundary value problems with, for example, scaling symmetries. }}, author = {{McLachlan, Robert I and Offen, Christian}}, journal = {{New Zealand Journal of Mathematics}}, keywords = {{Hamiltonian boundary value problems, singularities, conformal symplectic geometry, catastrophe theory, conjugate loci}}, pages = {{83--99}}, title = {{{Hamiltonian boundary value problems, conformal symplectic symmetries, and conjugate loci}}}, doi = {{10.53733/34 }}, volume = {{48}}, year = {{2018}}, } @inproceedings{56249, author = {{Fleischmann, Yael and Kempen, Leander and Mai, Tobias and Biehler, Rolf}}, booktitle = {{Hanse-Kolloquium zur Hochschuldidaktik der Mathematik}}, editor = {{Klinger, M. and Schüler-Meyer, A. and Wessel, L.}}, pages = {{101–116}}, publisher = {{WTM-Verlag}}, title = {{{Die online Lernmaterialien von studiVEMINT: Einsatzszenarien im Blended Learning Format in mathematischen Vorkursen}}}, year = {{2018}}, } @article{56254, author = {{Kempen, Leander and Biehler, Rolf}}, issn = {{2198-9745}}, journal = {{International Journal of Research in Undergraduate Mathematics Education}}, number = {{1}}, pages = {{27--55}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{Pre-Service Teachers’ Benefits from an Inquiry-Based Transition-to-Proof Course with a Focus on Generic Proofs}}}, doi = {{10.1007/s40753-018-0082-9}}, volume = {{5}}, year = {{2018}}, } @book{56253, author = {{Hochmuth, Reinhard and Biehler, Rolf and Schaper, Niclas and Kuklinski, Christiane and Lankeit, Elisa and Leis, Elena and Liebendörfer, Michael and Schürmann, Mirko}}, publisher = {{Leibniz Universität Hannover}}, title = {{{Wirkung und Gelingensbedingungen von Unterstützungsmaßnahmen für mathmatikbezogenes Lernen in der Studieneingangsphase: Schlussbericht: Teilprojekt A der Leibniz Universität Hannover, Teilprojekte B und C der Universität Paderborn: Berichtszeitraum: 01.03. 2015-31.08. 2018}}}, year = {{2018}}, } @inbook{56349, author = {{Barzel, Bärbel and Biehler, Rolf and Blömeke, Sigrid and Brandtner, Regine and Bruns, Julia and Dohrmann, Christian and Kortenkamp, Ulrich and Lange, Thomas and Leuders, Timo and Rösken-Winter, Bettina and Scherer, Petra and Selter, Christoph}}, booktitle = {{Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik}}, isbn = {{9783658190279}}, issn = {{2197-8751}}, pages = {{7--40}}, publisher = {{Springer Fachmedien Wiesbaden}}, title = {{{Das Deutsche Zentrum für Lehrerbildung Mathematik – DZLM}}}, doi = {{10.1007/978-3-658-19028-6_2}}, year = {{2018}}, } @book{56354, editor = {{Biehler, Rolf and Budde, Lea and Frischemeier, Daniel and Heinemann, B. and Podworny, Susanne and Schulte, Carsten and Wassong, Thomas}}, publisher = {{Universitätsbibliothek Paderborn}}, title = {{{Paderborn symposium on data science education at school level 2017: The collected extended abstracts. Universitätsbibliothek Paderborn}}}, year = {{2018}}, } @article{56361, author = {{Biehler, Rolf and Frischemeier, Daniel and Podworny, Susanne}}, issn = {{1863-9690}}, journal = {{ZDM}}, number = {{7}}, pages = {{1237--1251}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{Elementary preservice teachers’ reasoning about statistical modeling in a civic statistics context}}}, doi = {{10.1007/s11858-018-1001-x}}, volume = {{50}}, year = {{2018}}, } @article{56360, author = {{Biehler, Rolf and Frischemeier, Daniel and Podworny, Susanne}}, journal = {{Zeitschrift für Hochschulentwicklung}}, number = {{2}}, pages = {{169--182}}, title = {{{ Civic Engagement in Higher Education: A university course in civic statistics for mathematics preservice teachers - Civic Engagement in Higher Education: A university course in civic statistics for mathematics preservice teachers}}}, doi = {{10.3217/ZFHE-13-02/11}}, volume = {{13}}, year = {{2018}}, }