--- _id: '19941' abstract: - lang: eng text: "In backward error analysis, an approximate solution to an equation is compared to the exact solution to a nearby ‘modified’ equation. In numerical ordinary differential equations, the two agree up to any power of the step size. If the differential equation has a geometric property then the modified equation may share it. In this way, known properties of differential equations can be applied to the approximation. But for partial differential equations, the known modified equations are of higher order, limiting applicability of the theory. Therefore, we study symmetric solutions of discretized\r\npartial differential equations that arise from a discrete variational principle. These symmetric solutions obey infinite-dimensional functional equations. We show that these equations admit second-order modified equations which are Hamiltonian and also possess first-order Lagrangians in modified coordinates. The modified equation and its associated structures are computed explicitly for the case of rotating travelling waves in the nonlinear wave equation." article_type: original author: - first_name: Robert I full_name: McLachlan, Robert I last_name: McLachlan - first_name: Christian full_name: Offen, Christian id: '85279' last_name: Offen orcid: https://orcid.org/0000-0002-5940-8057 citation: ama: McLachlan RI, Offen C. Backward error analysis for variational discretisations of partial  differential equations. Journal of Geometric Mechanics. 2022;14(3):447-471. doi:10.3934/jgm.2022014 apa: McLachlan, R. I., & Offen, C. (2022). Backward error analysis for variational discretisations of partial  differential equations. Journal of Geometric Mechanics, 14(3), 447–471. https://doi.org/10.3934/jgm.2022014 bibtex: '@article{McLachlan_Offen_2022, title={Backward error analysis for variational discretisations of partial  differential equations}, volume={14}, DOI={10.3934/jgm.2022014}, number={3}, journal={Journal of Geometric Mechanics}, publisher={AIMS}, author={McLachlan, Robert I and Offen, Christian}, year={2022}, pages={447–471} }' chicago: 'McLachlan, Robert I, and Christian Offen. “Backward Error Analysis for Variational Discretisations of Partial  Differential Equations.” Journal of Geometric Mechanics 14, no. 3 (2022): 447–71. https://doi.org/10.3934/jgm.2022014.' ieee: 'R. I. McLachlan and C. Offen, “Backward error analysis for variational discretisations of partial  differential equations,” Journal of Geometric Mechanics, vol. 14, no. 3, pp. 447–471, 2022, doi: 10.3934/jgm.2022014.' mla: McLachlan, Robert I., and Christian Offen. “Backward Error Analysis for Variational Discretisations of Partial  Differential Equations.” Journal of Geometric Mechanics, vol. 14, no. 3, AIMS, 2022, pp. 447–71, doi:10.3934/jgm.2022014. short: R.I. McLachlan, C. Offen, Journal of Geometric Mechanics 14 (2022) 447–471. date_created: 2020-10-06T16:33:19Z date_updated: 2023-08-10T08:44:55Z ddc: - '510' department: - _id: '636' doi: 10.3934/jgm.2022014 external_id: arxiv: - '2006.14172' file: - access_level: open_access content_type: application/pdf creator: coffen date_created: 2022-06-13T09:11:38Z date_updated: 2022-06-13T09:11:38Z description: |- In backward error analysis, an approximate solution to an equa- tion is compared to the exact solution to a nearby ‘modified’ equation. In numerical ordinary differential equations, the two agree up to any power of the step size. If the differential equation has a geometric property then the modified equation may share it. In this way, known properties of differential equations can be applied to the approximation. But for partial differential equations, the known modified equations are of higher order, limiting appli- cability of the theory. Therefore, we study symmetric solutions of discretized partial differential equations that arise from a discrete variational principle. These symmetric solutions obey infinite-dimensional functional equations. We show that these equations admit second-order modified equations which are Hamiltonian and also possess first-order Lagrangians in modified coordinates. The modified equation and its associated structures are computed explicitly for the case of rotating travelling waves in the nonlinear wave equation. file_id: '31859' file_name: 2_BlendedBEASymmPDE.pdf file_size: 1507248 relation: main_file title: Backward error analysis for variational discretisations of PDEs file_date_updated: 2022-06-13T09:11:38Z has_accepted_license: '1' intvolume: ' 14' issue: '3' language: - iso: eng oa: '1' page: 447 - 471 publication: Journal of Geometric Mechanics publication_status: published publisher: AIMS related_material: link: - relation: software url: https://github.com/Christian-Offen/multisymplectic status: public title: Backward error analysis for variational discretisations of partial differential equations type: journal_article user_id: '85279' volume: 14 year: '2022' ... --- _id: '23382' abstract: - lang: eng text: Hamiltonian systems are differential equations which describe systems in classical mechanics, plasma physics, and sampling problems. They exhibit many structural properties, such as a lack of attractors and the presence of conservation laws. To predict Hamiltonian dynamics based on discrete trajectory observations, incorporation of prior knowledge about Hamiltonian structure greatly improves predictions. This is typically done by learning the system's Hamiltonian and then integrating the Hamiltonian vector field with a symplectic integrator. For this, however, Hamiltonian data needs to be approximated based on the trajectory observations. Moreover, the numerical integrator introduces an additional discretisation error. In this paper, we show that an inverse modified Hamiltonian structure adapted to the geometric integrator can be learned directly from observations. A separate approximation step for the Hamiltonian data avoided. The inverse modified data compensates for the discretisation error such that the discretisation error is eliminated. The technique is developed for Gaussian Processes. article_type: original author: - first_name: Christian full_name: Offen, Christian id: '85279' last_name: Offen orcid: 0000-0002-5940-8057 - first_name: Sina full_name: Ober-Blöbaum, Sina id: '16494' last_name: Ober-Blöbaum citation: ama: 'Offen C, Ober-Blöbaum S. Symplectic integration of learned Hamiltonian systems. Chaos: An Interdisciplinary Journal of Nonlinear Science. 2022;32(1). doi:10.1063/5.0065913' apa: 'Offen, C., & Ober-Blöbaum, S. (2022). Symplectic integration of learned Hamiltonian systems. Chaos: An Interdisciplinary Journal of Nonlinear Science, 32(1). https://doi.org/10.1063/5.0065913' bibtex: '@article{Offen_Ober-Blöbaum_2022, title={Symplectic integration of learned Hamiltonian systems}, volume={32(1)}, DOI={10.1063/5.0065913}, journal={Chaos: An Interdisciplinary Journal of Nonlinear Science}, publisher={AIP}, author={Offen, Christian and Ober-Blöbaum, Sina}, year={2022} }' chicago: 'Offen, Christian, and Sina Ober-Blöbaum. “Symplectic Integration of Learned Hamiltonian Systems.” Chaos: An Interdisciplinary Journal of Nonlinear Science 32(1) (2022). https://doi.org/10.1063/5.0065913.' ieee: 'C. Offen and S. Ober-Blöbaum, “Symplectic integration of learned Hamiltonian systems,” Chaos: An Interdisciplinary Journal of Nonlinear Science, vol. 32(1), 2022, doi: 10.1063/5.0065913.' mla: 'Offen, Christian, and Sina Ober-Blöbaum. “Symplectic Integration of Learned Hamiltonian Systems.” Chaos: An Interdisciplinary Journal of Nonlinear Science, vol. 32(1), AIP, 2022, doi:10.1063/5.0065913.' short: 'C. Offen, S. Ober-Blöbaum, Chaos: An Interdisciplinary Journal of Nonlinear Science 32(1) (2022).' date_created: 2021-08-11T08:24:02Z date_updated: 2023-08-10T08:48:14Z ddc: - '510' department: - _id: '636' doi: 10.1063/5.0065913 external_id: arxiv: - '2108.02492' file: - access_level: open_access content_type: application/pdf creator: coffen date_created: 2021-12-13T14:56:15Z date_updated: 2021-12-13T14:56:15Z file_id: '28734' file_name: SymplecticShadowIntegration_AIP.pdf file_size: 2285059 relation: main_file file_date_updated: 2021-12-13T14:56:15Z has_accepted_license: '1' language: - iso: eng main_file_link: - open_access: '1' url: https://aip.scitation.org/doi/abs/10.1063/5.0065913 oa: '1' publication: 'Chaos: An Interdisciplinary Journal of Nonlinear Science' publication_status: published publisher: AIP quality_controlled: '1' related_material: link: - description: GitHub relation: software url: https://github.com/Christian-Offen/symplectic-shadow-integration status: public title: Symplectic integration of learned Hamiltonian systems type: journal_article user_id: '85279' volume: 32(1) year: '2022' ... --- _id: '40613' author: - first_name: Jennifer full_name: Dröse, Jennifer id: '85820' last_name: Dröse citation: ama: 'Dröse J. Verstehensgrundlagen diagnostizieren - Diagnostisches Denken von drei Professionalisierungsgruppen. In: Beiträge Zum Mathematikunterricht. ; 2022.' apa: Dröse, J. (2022). Verstehensgrundlagen diagnostizieren - Diagnostisches Denken von drei Professionalisierungsgruppen. Beiträge Zum Mathematikunterricht. bibtex: '@inproceedings{Dröse_2022, title={Verstehensgrundlagen diagnostizieren - Diagnostisches Denken von drei Professionalisierungsgruppen}, booktitle={Beiträge zum Mathematikunterricht}, author={Dröse, Jennifer}, year={2022} }' chicago: Dröse, Jennifer. “Verstehensgrundlagen Diagnostizieren - Diagnostisches Denken von Drei Professionalisierungsgruppen.” In Beiträge Zum Mathematikunterricht, 2022. ieee: J. Dröse, “Verstehensgrundlagen diagnostizieren - Diagnostisches Denken von drei Professionalisierungsgruppen,” 2022. mla: Dröse, Jennifer. “Verstehensgrundlagen Diagnostizieren - Diagnostisches Denken von Drei Professionalisierungsgruppen.” Beiträge Zum Mathematikunterricht, 2022. short: 'J. Dröse, in: Beiträge Zum Mathematikunterricht, 2022.' date_created: 2023-01-27T19:00:01Z date_updated: 2023-08-15T06:04:03Z department: - _id: '98' language: - iso: eng publication: Beiträge zum Mathematikunterricht status: public title: Verstehensgrundlagen diagnostizieren - Diagnostisches Denken von drei Professionalisierungsgruppen type: conference user_id: '85820' year: '2022' ... --- _id: '47520' author: - first_name: Lara Marie full_name: Graf, Lara Marie id: '89837' last_name: Graf - first_name: Uta full_name: Häsel-Weide, Uta id: '60267' last_name: Häsel-Weide - first_name: Marcus full_name: Nührenbörger, Marcus last_name: Nührenbörger - first_name: Karina full_name: Höveler, Karina last_name: Höveler citation: ama: 'Graf LM, Häsel-Weide U, Nührenbörger M, Höveler K. Lernwege von fachfremd unterrichtenden Lehrkräften zur Ablösung vom zählenden Rechnen. In: IDMI-Primar Goethe-Universität Frankfurt, ed. Beiträge Zum Mathematikunterricht 2022 - 56. Jahrestagung Der Gesellschaft Für Didaktik Der Mathematik. ; 2022:773-776.' apa: Graf, L. M., Häsel-Weide, U., Nührenbörger, M., & Höveler, K. (2022). Lernwege von fachfremd unterrichtenden Lehrkräften zur Ablösung vom zählenden Rechnen. In IDMI-Primar Goethe-Universität Frankfurt (Ed.), Beiträge zum Mathematikunterricht 2022 - 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik (pp. 773–776). bibtex: '@inproceedings{Graf_Häsel-Weide_Nührenbörger_Höveler_2022, title={Lernwege von fachfremd unterrichtenden Lehrkräften zur Ablösung vom zählenden Rechnen}, booktitle={Beiträge zum Mathematikunterricht 2022 - 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik}, author={Graf, Lara Marie and Häsel-Weide, Uta and Nührenbörger, Marcus and Höveler, Karina}, editor={IDMI-Primar Goethe-Universität Frankfurt}, year={2022}, pages={773–776} }' chicago: Graf, Lara Marie, Uta Häsel-Weide, Marcus Nührenbörger, and Karina Höveler. “Lernwege von Fachfremd Unterrichtenden Lehrkräften Zur Ablösung Vom Zählenden Rechnen.” In Beiträge Zum Mathematikunterricht 2022 - 56. Jahrestagung Der Gesellschaft Für Didaktik Der Mathematik, edited by IDMI-Primar Goethe-Universität Frankfurt, 773–76, 2022. ieee: L. M. Graf, U. Häsel-Weide, M. Nührenbörger, and K. Höveler, “Lernwege von fachfremd unterrichtenden Lehrkräften zur Ablösung vom zählenden Rechnen,” in Beiträge zum Mathematikunterricht 2022 - 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik, Frankfurt am Main, 2022, pp. 773–776. mla: Graf, Lara Marie, et al. “Lernwege von Fachfremd Unterrichtenden Lehrkräften Zur Ablösung Vom Zählenden Rechnen.” Beiträge Zum Mathematikunterricht 2022 - 56. Jahrestagung Der Gesellschaft Für Didaktik Der Mathematik, edited by IDMI-Primar Goethe-Universität Frankfurt, 2022, pp. 773–76. short: 'L.M. Graf, U. Häsel-Weide, M. Nührenbörger, K. Höveler, in: IDMI-Primar Goethe-Universität Frankfurt (Ed.), Beiträge Zum Mathematikunterricht 2022 - 56. Jahrestagung Der Gesellschaft Für Didaktik Der Mathematik, 2022, pp. 773–776.' conference: end_date: 02.09.2022 location: Frankfurt am Main name: 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik start_date: 29.08.2022 corporate_editor: - IDMI-Primar Goethe-Universität Frankfurt date_created: 2023-09-27T10:01:52Z date_updated: 2023-09-27T10:02:12Z department: - _id: '543' language: - iso: eng page: 773-776 publication: Beiträge zum Mathematikunterricht 2022 - 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik status: public title: Lernwege von fachfremd unterrichtenden Lehrkräften zur Ablösung vom zählenden Rechnen type: conference user_id: '44184' year: '2022' ... --- _id: '47519' author: - first_name: Imke full_name: Schwerin, Imke id: '48912' last_name: Schwerin citation: ama: 'Schwerin I. Verdoppeln und Halbieren im 2. Schuljahr - Vorgehensweisen und Verständnis. In: IDMI-Primar Goethe-Universität Frankfurt, ed. Beiträge Zum Mathematikunterricht 2022 - 56. Jahrestagung Der Gesellschaft Für Didaktik Der Mathematik. ; 2022:401-404.' apa: Schwerin, I. (2022). Verdoppeln und Halbieren im 2. Schuljahr - Vorgehensweisen und Verständnis. In IDMI-Primar Goethe-Universität Frankfurt (Ed.), Beiträge zum Mathematikunterricht 2022 - 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik (pp. 401–404). bibtex: '@inproceedings{Schwerin_2022, title={Verdoppeln und Halbieren im 2. Schuljahr - Vorgehensweisen und Verständnis}, booktitle={Beiträge zum Mathematikunterricht 2022 - 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik}, author={Schwerin, Imke}, editor={IDMI-Primar Goethe-Universität Frankfurt}, year={2022}, pages={401–404} }' chicago: Schwerin, Imke. “Verdoppeln Und Halbieren Im 2. Schuljahr - Vorgehensweisen Und Verständnis.” In Beiträge Zum Mathematikunterricht 2022 - 56. Jahrestagung Der Gesellschaft Für Didaktik Der Mathematik, edited by IDMI-Primar Goethe-Universität Frankfurt, 401–4, 2022. ieee: I. Schwerin, “Verdoppeln und Halbieren im 2. Schuljahr - Vorgehensweisen und Verständnis,” in Beiträge zum Mathematikunterricht 2022 - 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik, Frankfurt am Main, 2022, pp. 401–404. mla: Schwerin, Imke. “Verdoppeln Und Halbieren Im 2. Schuljahr - Vorgehensweisen Und Verständnis.” Beiträge Zum Mathematikunterricht 2022 - 56. Jahrestagung Der Gesellschaft Für Didaktik Der Mathematik, edited by IDMI-Primar Goethe-Universität Frankfurt, 2022, pp. 401–04. short: 'I. Schwerin, in: IDMI-Primar Goethe-Universität Frankfurt (Ed.), Beiträge Zum Mathematikunterricht 2022 - 56. Jahrestagung Der Gesellschaft Für Didaktik Der Mathematik, 2022, pp. 401–404.' conference: end_date: 02.09.2022 location: Frankfurt am Main name: 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik start_date: 29.08.2022 corporate_editor: - IDMI-Primar Goethe-Universität Frankfurt date_created: 2023-09-27T09:53:36Z date_updated: 2023-09-27T09:54:00Z department: - _id: '543' language: - iso: eng page: 401-404 publication: Beiträge zum Mathematikunterricht 2022 - 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik status: public title: Verdoppeln und Halbieren im 2. Schuljahr - Vorgehensweisen und Verständnis type: conference user_id: '44184' year: '2022' ... --- _id: '48407' author: - first_name: Anna full_name: Dellori, Anna last_name: Dellori - first_name: Lena full_name: Wessel, Lena id: '85190' last_name: Wessel citation: ama: 'Dellori A, Wessel L. Pre-service Teachers’ Professional Development: Relating Abstract Algebra and School Algebra. In: Karunakaran SS, Higgins A, eds. Proceedings of the 24th Annual Conference on Research in Undergraduate Mathematics Education. MA; 2022:1177.' apa: 'Dellori, A., & Wessel, L. (2022). Pre-service Teachers’ Professional Development: Relating Abstract Algebra and School Algebra. In S. S. Karunakaran & A. Higgins (Eds.), Proceedings of the 24th Annual Conference on Research in Undergraduate Mathematics Education (p. 1177). MA.' bibtex: '@inbook{Dellori_Wessel_2022, place={Boston}, title={Pre-service Teachers’ Professional Development: Relating Abstract Algebra and School Algebra}, booktitle={Proceedings of the 24th Annual Conference on Research in Undergraduate Mathematics Education}, publisher={MA}, author={Dellori, Anna and Wessel, Lena}, editor={Karunakaran, S.S. and Higgins, A.}, year={2022}, pages={1177} }' chicago: 'Dellori, Anna, and Lena Wessel. “Pre-Service Teachers’ Professional Development: Relating Abstract Algebra and School Algebra.” In Proceedings of the 24th Annual Conference on Research in Undergraduate Mathematics Education, edited by S.S. Karunakaran and A. Higgins, 1177. Boston: MA, 2022.' ieee: 'A. Dellori and L. Wessel, “Pre-service Teachers’ Professional Development: Relating Abstract Algebra and School Algebra,” in Proceedings of the 24th Annual Conference on Research in Undergraduate Mathematics Education, S. S. Karunakaran and A. Higgins, Eds. Boston: MA, 2022, p. 1177.' mla: 'Dellori, Anna, and Lena Wessel. “Pre-Service Teachers’ Professional Development: Relating Abstract Algebra and School Algebra.” Proceedings of the 24th Annual Conference on Research in Undergraduate Mathematics Education, edited by S.S. Karunakaran and A. Higgins, MA, 2022, p. 1177.' short: 'A. Dellori, L. Wessel, in: S.S. Karunakaran, A. Higgins (Eds.), Proceedings of the 24th Annual Conference on Research in Undergraduate Mathematics Education, MA, Boston, 2022, p. 1177.' date_created: 2023-10-24T07:28:19Z date_updated: 2023-10-24T07:28:22Z department: - _id: '34' - _id: '10' - _id: '97' - _id: '643' editor: - first_name: S.S. full_name: Karunakaran, S.S. last_name: Karunakaran - first_name: A. full_name: Higgins, A. last_name: Higgins language: - iso: eng page: '1177' place: Boston publication: Proceedings of the 24th Annual Conference on Research in Undergraduate Mathematics Education publisher: MA status: public title: 'Pre-service Teachers'' Professional Development: Relating Abstract Algebra and School Algebra' type: book_chapter user_id: '37888' year: '2022' ... --- _id: '48408' author: - first_name: Lena full_name: Wessel, Lena id: '85190' last_name: Wessel - first_name: Jennifer full_name: Dröse, Jennifer id: '85820' last_name: Dröse citation: ama: 'Wessel L, Dröse J. Schreiben will gelernt sein: Schreiblerngelegenheiten adaptiv gestalten. mathematik lehren. 2022;233:33-36.' apa: 'Wessel, L., & Dröse, J. (2022). Schreiben will gelernt sein: Schreiblerngelegenheiten adaptiv gestalten. mathematik lehren, 233, 33–36.' bibtex: '@article{Wessel_Dröse_2022, title={Schreiben will gelernt sein: Schreiblerngelegenheiten adaptiv gestalten}, volume={233}, journal={mathematik lehren}, author={Wessel, Lena and Dröse, Jennifer}, year={2022}, pages={33–36} }' chicago: 'Wessel, Lena, and Jennifer Dröse. “Schreiben will gelernt sein: Schreiblerngelegenheiten adaptiv gestalten.” mathematik lehren 233 (2022): 33–36.' ieee: 'L. Wessel and J. Dröse, “Schreiben will gelernt sein: Schreiblerngelegenheiten adaptiv gestalten,” mathematik lehren, vol. 233, pp. 33–36, 2022.' mla: 'Wessel, Lena, and Jennifer Dröse. “Schreiben will gelernt sein: Schreiblerngelegenheiten adaptiv gestalten.” mathematik lehren, vol. 233, 2022, pp. 33–36.' short: L. Wessel, J. Dröse, mathematik lehren 233 (2022) 33–36. date_created: 2023-10-24T07:33:17Z date_updated: 2023-10-24T07:33:22Z department: - _id: '34' - _id: '10' - _id: '97' - _id: '643' intvolume: ' 233' language: - iso: ger page: 33-36 publication: mathematik lehren status: public title: 'Schreiben will gelernt sein: Schreiblerngelegenheiten adaptiv gestalten' type: journal_article user_id: '37888' volume: 233 year: '2022' ... --- _id: '46160' author: - first_name: Lena full_name: Wessel, Lena id: '85190' last_name: Wessel - first_name: Timo full_name: Leuders, Timo last_name: Leuders citation: ama: 'Wessel L, Leuders T. Profession-Specific Curriculum Design in Mathematics Teacher Education: Connecting Disciplinary Practice to the Learning of Group Theory. In: Biehler R, Liebendörfer M, Gueudet G, Rasmussen C, Winslow C, eds. Practice-Oriented Research in Tertiary Mathematics Education. Springer International Publishing; 2022:349-368. doi:10.1007/978-3-031-14175-1_17' apa: 'Wessel, L., & Leuders, T. (2022). Profession-Specific Curriculum Design in Mathematics Teacher Education: Connecting Disciplinary Practice to the Learning of Group Theory. In R. Biehler, M. Liebendörfer, G. Gueudet, C. Rasmussen, & C. Winslow (Eds.), Practice-Oriented Research in Tertiary Mathematics Education (pp. 349–368). Springer International Publishing. https://doi.org/10.1007/978-3-031-14175-1_17' bibtex: '@inbook{Wessel_Leuders_2022, place={Cham}, title={Profession-Specific Curriculum Design in Mathematics Teacher Education: Connecting Disciplinary Practice to the Learning of Group Theory}, DOI={10.1007/978-3-031-14175-1_17}, booktitle={Practice-Oriented Research in Tertiary Mathematics Education}, publisher={Springer International Publishing}, author={Wessel, Lena and Leuders, Timo}, editor={Biehler, Rolf and Liebendörfer, Michael and Gueudet, G. and Rasmussen, C. and Winslow, C.}, year={2022}, pages={349–368} }' chicago: 'Wessel, Lena, and Timo Leuders. “Profession-Specific Curriculum Design in Mathematics Teacher Education: Connecting Disciplinary Practice to the Learning of Group Theory.” In Practice-Oriented Research in Tertiary Mathematics Education, edited by Rolf Biehler, Michael Liebendörfer, G. Gueudet, C. Rasmussen, and C. Winslow, 349–68. Cham: Springer International Publishing, 2022. https://doi.org/10.1007/978-3-031-14175-1_17.' ieee: 'L. Wessel and T. Leuders, “Profession-Specific Curriculum Design in Mathematics Teacher Education: Connecting Disciplinary Practice to the Learning of Group Theory,” in Practice-Oriented Research in Tertiary Mathematics Education, R. Biehler, M. Liebendörfer, G. Gueudet, C. Rasmussen, and C. Winslow, Eds. Cham: Springer International Publishing, 2022, pp. 349–368.' mla: 'Wessel, Lena, and Timo Leuders. “Profession-Specific Curriculum Design in Mathematics Teacher Education: Connecting Disciplinary Practice to the Learning of Group Theory.” Practice-Oriented Research in Tertiary Mathematics Education, edited by Rolf Biehler et al., Springer International Publishing, 2022, pp. 349–68, doi:10.1007/978-3-031-14175-1_17.' short: 'L. Wessel, T. Leuders, in: R. Biehler, M. Liebendörfer, G. Gueudet, C. Rasmussen, C. Winslow (Eds.), Practice-Oriented Research in Tertiary Mathematics Education, Springer International Publishing, Cham, 2022, pp. 349–368.' date_created: 2023-07-26T10:34:02Z date_updated: 2023-10-30T09:00:53Z department: - _id: '34' - _id: '10' - _id: '97' - _id: '643' doi: 10.1007/978-3-031-14175-1_17 editor: - first_name: Rolf full_name: Biehler, Rolf last_name: Biehler - first_name: Michael full_name: Liebendörfer, Michael last_name: Liebendörfer - first_name: G. full_name: Gueudet, G. last_name: Gueudet - first_name: C. full_name: Rasmussen, C. last_name: Rasmussen - first_name: C. full_name: Winslow, C. last_name: Winslow language: - iso: eng page: 349-368 place: Cham publication: Practice-Oriented Research in Tertiary Mathematics Education publication_identifier: isbn: - '9783031141744' - '9783031141751' issn: - 1869-4918 - 1869-4926 publication_status: published publisher: Springer International Publishing status: public title: 'Profession-Specific Curriculum Design in Mathematics Teacher Education: Connecting Disciplinary Practice to the Learning of Group Theory' type: book_chapter user_id: '37888' year: '2022' ... --- _id: '48325' author: - first_name: Anna full_name: Dellori, Anna last_name: Dellori - first_name: Lena full_name: Wessel, Lena id: '85190' last_name: Wessel citation: ama: Dellori A, Wessel L. Entwicklung und Erprobung von professionsorientierten Lernumgebungen zur Wissensvernetzung in der Algebra. Beiträge zum Mathematikunterricht 2022. Published online 2022:665-668. doi:10.17877/DE290R-23598 apa: Dellori, A., & Wessel, L. (2022). Entwicklung und Erprobung von professionsorientierten Lernumgebungen zur Wissensvernetzung in der Algebra. Beiträge zum Mathematikunterricht 2022, 665–668. https://doi.org/10.17877/DE290R-23598 bibtex: '@article{Dellori_Wessel_2022, title={Entwicklung und Erprobung von professionsorientierten Lernumgebungen zur Wissensvernetzung in der Algebra}, DOI={10.17877/DE290R-23598}, journal={Beiträge zum Mathematikunterricht 2022}, publisher={LibreCat University}, author={Dellori, Anna and Wessel, Lena}, year={2022}, pages={665–668} }' chicago: Dellori, Anna, and Lena Wessel. “Entwicklung und Erprobung von professionsorientierten Lernumgebungen zur Wissensvernetzung in der Algebra.” Beiträge zum Mathematikunterricht 2022, 2022, 665–68. https://doi.org/10.17877/DE290R-23598. ieee: 'A. Dellori and L. Wessel, “Entwicklung und Erprobung von professionsorientierten Lernumgebungen zur Wissensvernetzung in der Algebra,” Beiträge zum Mathematikunterricht 2022, pp. 665–668, 2022, doi: 10.17877/DE290R-23598.' mla: Dellori, Anna, and Lena Wessel. “Entwicklung und Erprobung von professionsorientierten Lernumgebungen zur Wissensvernetzung in der Algebra.” Beiträge zum Mathematikunterricht 2022, LibreCat University, 2022, pp. 665–68, doi:10.17877/DE290R-23598. short: A. Dellori, L. Wessel, Beiträge zum Mathematikunterricht 2022 (2022) 665–668. date_created: 2023-10-19T09:37:24Z date_updated: 2023-10-31T09:32:18Z department: - _id: '34' - _id: '10' - _id: '97' - _id: '643' doi: 10.17877/DE290R-23598 language: - iso: ger main_file_link: - url: http://dx.doi.org/10.17877/DE290R-23598 page: 665-668 publication: Beiträge zum Mathematikunterricht 2022 publisher: LibreCat University status: public title: Entwicklung und Erprobung von professionsorientierten Lernumgebungen zur Wissensvernetzung in der Algebra type: journal_article user_id: '37888' year: '2022' ... --- _id: '45373' author: - first_name: Jennifer full_name: Dröse, Jennifer id: '85820' last_name: Dröse - first_name: P. full_name: Neugebauer, P. last_name: Neugebauer - first_name: R. full_name: Delucchi Danhier, R. last_name: Delucchi Danhier - first_name: B. full_name: Mertins, B. last_name: Mertins citation: ama: 'Dröse J, Neugebauer P, Delucchi Danhier R, Mertins B. Eye-Tracking Studie zu Textaufgaben in Klasse 5: Bemerken und Interpretieren syntaktischer Strukturen. In: Kleine P, Graulich N, Kuhn J, Schindler M, eds. Eye-Tracking in der Mathematik- und Naturwissenschaftsdidaktik. Forschung und Praxis. ; 2022:209-225. doi:https://doi.org/10.1007/978-3-662-63214-7' apa: 'Dröse, J., Neugebauer, P., Delucchi Danhier, R., & Mertins, B. (2022). Eye-Tracking Studie zu Textaufgaben in Klasse 5: Bemerken und Interpretieren syntaktischer Strukturen. In P. Kleine, N. Graulich, J. Kuhn, & M. Schindler (Eds.), Eye-Tracking in der Mathematik- und Naturwissenschaftsdidaktik. Forschung und Praxis (pp. 209–225). https://doi.org/10.1007/978-3-662-63214-7' bibtex: '@inbook{Dröse_Neugebauer_Delucchi Danhier_Mertins_2022, title={Eye-Tracking Studie zu Textaufgaben in Klasse 5: Bemerken und Interpretieren syntaktischer Strukturen}, DOI={https://doi.org/10.1007/978-3-662-63214-7}, booktitle={Eye-Tracking in der Mathematik- und Naturwissenschaftsdidaktik. Forschung und Praxis}, author={Dröse, Jennifer and Neugebauer, P. and Delucchi Danhier, R. and Mertins, B.}, editor={Kleine, P. and Graulich, N. and Kuhn, J. and Schindler, M.}, year={2022}, pages={209–225} }' chicago: 'Dröse, Jennifer, P. Neugebauer, R. Delucchi Danhier, and B. Mertins. “Eye-Tracking Studie zu Textaufgaben in Klasse 5: Bemerken und Interpretieren syntaktischer Strukturen.” In Eye-Tracking in der Mathematik- und Naturwissenschaftsdidaktik. Forschung und Praxis, edited by P. Kleine, N. Graulich, J. Kuhn, and M. Schindler, 209–25, 2022. https://doi.org/10.1007/978-3-662-63214-7.' ieee: 'J. Dröse, P. Neugebauer, R. Delucchi Danhier, and B. Mertins, “Eye-Tracking Studie zu Textaufgaben in Klasse 5: Bemerken und Interpretieren syntaktischer Strukturen,” in Eye-Tracking in der Mathematik- und Naturwissenschaftsdidaktik. Forschung und Praxis, P. Kleine, N. Graulich, J. Kuhn, and M. Schindler, Eds. 2022, pp. 209–225.' mla: 'Dröse, Jennifer, et al. “Eye-Tracking Studie zu Textaufgaben in Klasse 5: Bemerken und Interpretieren syntaktischer Strukturen.” Eye-Tracking in der Mathematik- und Naturwissenschaftsdidaktik. Forschung und Praxis, edited by P. Kleine et al., 2022, pp. 209–25, doi:https://doi.org/10.1007/978-3-662-63214-7.' short: 'J. Dröse, P. Neugebauer, R. Delucchi Danhier, B. Mertins, in: P. Kleine, N. Graulich, J. Kuhn, M. Schindler (Eds.), Eye-Tracking in der Mathematik- und Naturwissenschaftsdidaktik. Forschung und Praxis, 2022, pp. 209–225.' date_created: 2023-05-31T06:22:21Z date_updated: 2023-11-02T08:07:31Z department: - _id: '98' doi: https://doi.org/10.1007/978-3-662-63214-7 editor: - first_name: P. full_name: Kleine, P. last_name: Kleine - first_name: N. full_name: Graulich, N. last_name: Graulich - first_name: J. full_name: Kuhn, J. last_name: Kuhn - first_name: M. full_name: Schindler, M. last_name: Schindler language: - iso: ger page: 209-225 publication: Eye-Tracking in der Mathematik- und Naturwissenschaftsdidaktik. Forschung und Praxis quality_controlled: '1' status: public title: 'Eye-Tracking Studie zu Textaufgaben in Klasse 5: Bemerken und Interpretieren syntaktischer Strukturen' type: book_chapter user_id: '85820' year: '2022' ... --- _id: '45374' author: - first_name: S. full_name: Prediger, S. last_name: Prediger - first_name: Jennifer full_name: Dröse, Jennifer id: '85820' last_name: Dröse - first_name: R. full_name: Stahnke, R. last_name: Stahnke - first_name: C. full_name: Ademmer, C. last_name: Ademmer citation: ama: 'Prediger S, Dröse J, Stahnke R, Ademmer C. Teacher expertise for fostering at-risk students’ understanding of basic concepts: conceptual model and evidence for growth. Journal of Mathematics Teacher Education. Published online 2022. doi:https://doi.org/10.1007/s10857-022-09538-3' apa: 'Prediger, S., Dröse, J., Stahnke, R., & Ademmer, C. (2022). Teacher expertise for fostering at-risk students’ understanding of basic concepts: conceptual model and evidence for growth. Journal of Mathematics Teacher Education. https://doi.org/10.1007/s10857-022-09538-3' bibtex: '@article{Prediger_Dröse_Stahnke_Ademmer_2022, title={Teacher expertise for fostering at-risk students’ understanding of basic concepts: conceptual model and evidence for growth}, DOI={https://doi.org/10.1007/s10857-022-09538-3}, journal={Journal of Mathematics Teacher Education}, author={Prediger, S. and Dröse, Jennifer and Stahnke, R. and Ademmer, C.}, year={2022} }' chicago: 'Prediger, S., Jennifer Dröse, R. Stahnke, and C. Ademmer. “Teacher Expertise for Fostering At-Risk Students’ Understanding of Basic Concepts: Conceptual Model and Evidence for Growth.” Journal of Mathematics Teacher Education, 2022. https://doi.org/10.1007/s10857-022-09538-3.' ieee: 'S. Prediger, J. Dröse, R. Stahnke, and C. Ademmer, “Teacher expertise for fostering at-risk students’ understanding of basic concepts: conceptual model and evidence for growth,” Journal of Mathematics Teacher Education, 2022, doi: https://doi.org/10.1007/s10857-022-09538-3.' mla: 'Prediger, S., et al. “Teacher Expertise for Fostering At-Risk Students’ Understanding of Basic Concepts: Conceptual Model and Evidence for Growth.” Journal of Mathematics Teacher Education, 2022, doi:https://doi.org/10.1007/s10857-022-09538-3.' short: S. Prediger, J. Dröse, R. Stahnke, C. Ademmer, Journal of Mathematics Teacher Education (2022). date_created: 2023-05-31T06:27:51Z date_updated: 2023-11-02T08:07:42Z department: - _id: '98' doi: https://doi.org/10.1007/s10857-022-09538-3 language: - iso: eng publication: Journal of Mathematics Teacher Education quality_controlled: '1' status: public title: 'Teacher expertise for fostering at-risk students’ understanding of basic concepts: conceptual model and evidence for growth' type: journal_article user_id: '85820' year: '2022' ... --- _id: '45379' author: - first_name: Jennifer full_name: Dröse, Jennifer id: '85820' last_name: Dröse - first_name: B. full_name: Griese, B. last_name: Griese - first_name: Lena full_name: Wessel, Lena id: '85190' last_name: Wessel citation: ama: 'Dröse J, Griese B, Wessel L. Prosepctive teachers‘ diagnostic judgements on students’ under- standing of conditional probabilities. In: Twelfth Congress of the European Society for Research in Mathematics Education (CERME12). ; 2022.' apa: Dröse, J., Griese, B., & Wessel, L. (2022). Prosepctive teachers‘ diagnostic judgements on students’ under- standing of conditional probabilities. Twelfth Congress of the European Society for Research in Mathematics Education (CERME12). bibtex: '@inproceedings{Dröse_Griese_Wessel_2022, place={Bozen-Bolzano, Italy}, title={Prosepctive teachers‘ diagnostic judgements on students’ under- standing of conditional probabilities}, booktitle={Twelfth Congress of the European Society for Research in Mathematics Education (CERME12)}, author={Dröse, Jennifer and Griese, B. and Wessel, Lena}, year={2022} }' chicago: Dröse, Jennifer, B. Griese, and Lena Wessel. “Prosepctive Teachers‘ Diagnostic Judgements on Students’ under- Standing of Conditional Probabilities.” In Twelfth Congress of the European Society for Research in Mathematics Education (CERME12). Bozen-Bolzano, Italy, 2022. ieee: J. Dröse, B. Griese, and L. Wessel, “Prosepctive teachers‘ diagnostic judgements on students’ under- standing of conditional probabilities,” 2022. mla: Dröse, Jennifer, et al. “Prosepctive Teachers‘ Diagnostic Judgements on Students’ under- Standing of Conditional Probabilities.” Twelfth Congress of the European Society for Research in Mathematics Education (CERME12), 2022. short: 'J. Dröse, B. Griese, L. Wessel, in: Twelfth Congress of the European Society for Research in Mathematics Education (CERME12), Bozen-Bolzano, Italy, 2022.' date_created: 2023-05-31T06:59:15Z date_updated: 2023-11-02T08:05:43Z department: - _id: '98' language: - iso: eng place: Bozen-Bolzano, Italy publication: Twelfth Congress of the European Society for Research in Mathematics Education (CERME12) quality_controlled: '1' status: public title: Prosepctive teachers‘ diagnostic judgements on students’ under- standing of conditional probabilities type: conference user_id: '85820' year: '2022' ... --- _id: '30733' abstract: - lang: eng text: 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. author: - first_name: Nikolaus full_name: Vertovec, Nikolaus id: '93930' last_name: Vertovec - first_name: Sina full_name: Ober-Blöbaum, Sina id: '16494' last_name: Ober-Blöbaum - first_name: Kostas full_name: Margellos, Kostas last_name: Margellos citation: ama: 'Vertovec N, Ober-Blöbaum S, Margellos K. Verification of safety critical control policies using kernel methods. In: ; 2022:1870-1875.' apa: Vertovec, N., Ober-Blöbaum, S., & Margellos, K. (2022). Verification of safety critical control policies using kernel methods. 1870–1875. bibtex: '@inproceedings{Vertovec_Ober-Blöbaum_Margellos_2022, title={Verification of safety critical control policies using kernel methods}, author={Vertovec, Nikolaus and Ober-Blöbaum, Sina and Margellos, Kostas}, year={2022}, pages={1870–1875} }' chicago: Vertovec, Nikolaus, Sina Ober-Blöbaum, and Kostas Margellos. “Verification of Safety Critical Control Policies Using Kernel Methods,” 1870–75, 2022. ieee: N. Vertovec, S. Ober-Blöbaum, and K. Margellos, “Verification of safety critical control policies using kernel methods,” London, 2022, pp. 1870–1875. mla: Vertovec, Nikolaus, et al. Verification of Safety Critical Control Policies Using Kernel Methods. 2022, pp. 1870–75. short: 'N. Vertovec, S. Ober-Blöbaum, K. Margellos, in: 2022, pp. 1870–1875.' conference: end_date: 2022-07-15 location: London name: 2022 European Control Conference (ECC) start_date: 2022-07-12 date_created: 2022-03-31T11:14:13Z date_updated: 2023-11-29T10:00:18Z ddc: - '510' department: - _id: '636' has_accepted_license: '1' language: - iso: eng page: 1870-1875 status: public title: Verification of safety critical control policies using kernel methods type: conference user_id: '15694' year: '2022' ... --- _id: '48385' author: - first_name: Anna full_name: Dellori, Anna last_name: Dellori - first_name: Lena full_name: Wessel, Lena id: '85190' last_name: Wessel citation: ama: 'Dellori A, Wessel L. Design principles for intertwining local and nonlocal mathematics - The case of relating registers and representations in abstract algebra. In: Trigueros M, Barquero B, Hochmuth R, Peters J, eds. Proceedings of INDRUM2022. ; 2022:572-573.' apa: Dellori, A., & Wessel, L. (2022). Design principles for intertwining local and nonlocal mathematics - The case of relating registers and representations in abstract algebra. In M. Trigueros, B. Barquero, R. Hochmuth, & J. Peters (Eds.), Proceedings of INDRUM2022 (pp. 572–573). bibtex: '@inbook{Dellori_Wessel_2022, title={Design principles for intertwining local and nonlocal mathematics - The case of relating registers and representations in abstract algebra}, booktitle={Proceedings of INDRUM2022}, author={Dellori, Anna and Wessel, Lena}, editor={Trigueros, M. and Barquero, B. and Hochmuth, R. and Peters, J.}, year={2022}, pages={572–573} }' chicago: Dellori, Anna, and Lena Wessel. “Design Principles for Intertwining Local and Nonlocal Mathematics - The Case of Relating Registers and Representations in Abstract Algebra.” In Proceedings of INDRUM2022, edited by M. Trigueros, B. Barquero, R. Hochmuth, and J. Peters, 572–73, 2022. ieee: A. Dellori and L. Wessel, “Design principles for intertwining local and nonlocal mathematics - The case of relating registers and representations in abstract algebra,” in Proceedings of INDRUM2022, M. Trigueros, B. Barquero, R. Hochmuth, and J. Peters, Eds. 2022, pp. 572–573. mla: Dellori, Anna, and Lena Wessel. “Design Principles for Intertwining Local and Nonlocal Mathematics - The Case of Relating Registers and Representations in Abstract Algebra.” Proceedings of INDRUM2022, edited by M. Trigueros et al., 2022, pp. 572–73. short: 'A. Dellori, L. Wessel, in: M. Trigueros, B. Barquero, R. Hochmuth, J. Peters (Eds.), Proceedings of INDRUM2022, 2022, pp. 572–573.' date_created: 2023-10-23T09:40:30Z date_updated: 2023-10-23T09:43:48Z department: - _id: '34' - _id: '10' - _id: '97' - _id: '643' editor: - first_name: M. full_name: Trigueros, M. last_name: Trigueros - first_name: B. full_name: Barquero, B. last_name: Barquero - first_name: R. full_name: Hochmuth, R. last_name: Hochmuth - first_name: J. full_name: Peters, J. last_name: Peters language: - iso: eng page: 572-573 publication: Proceedings of INDRUM2022 status: public title: Design principles for intertwining local and nonlocal mathematics - The case of relating registers and representations in abstract algebra type: book_chapter user_id: '37888' year: '2022' ... --- _id: '40607' abstract: - lang: eng text: 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. author: - first_name: Jennifer full_name: Dröse, Jennifer last_name: Dröse - first_name: Susanne full_name: Prediger, Susanne last_name: Prediger citation: ama: 'Dröse J, Prediger S. Prospective Teachers’ Diagnostic Thinking on Students’ Understanding of Multi-Digit Multiplication: A Content-Related Analysis on Unpacking of Knowledge Elements. Journal für Mathematik-Didaktik. Published online 2022. doi:10.1007/s13138-022-00214-w' apa: 'Dröse, J., & Prediger, S. (2022). Prospective Teachers’ Diagnostic Thinking on Students’ Understanding of Multi-Digit Multiplication: A Content-Related Analysis on Unpacking of Knowledge Elements. Journal Für Mathematik-Didaktik. https://doi.org/10.1007/s13138-022-00214-w' bibtex: '@article{Dröse_Prediger_2022, title={Prospective Teachers’ Diagnostic Thinking on Students’ Understanding of Multi-Digit Multiplication: A Content-Related Analysis on Unpacking of Knowledge Elements}, DOI={10.1007/s13138-022-00214-w}, journal={Journal für Mathematik-Didaktik}, publisher={Springer Science and Business Media LLC}, author={Dröse, Jennifer and Prediger, Susanne}, year={2022} }' chicago: 'Dröse, Jennifer, and Susanne Prediger. “Prospective Teachers’ Diagnostic Thinking on Students’ Understanding of Multi-Digit Multiplication: A Content-Related Analysis on Unpacking of Knowledge Elements.” Journal Für Mathematik-Didaktik, 2022. https://doi.org/10.1007/s13138-022-00214-w.' ieee: 'J. Dröse and S. Prediger, “Prospective Teachers’ Diagnostic Thinking on Students’ Understanding of Multi-Digit Multiplication: A Content-Related Analysis on Unpacking of Knowledge Elements,” Journal für Mathematik-Didaktik, 2022, doi: 10.1007/s13138-022-00214-w.' mla: 'Dröse, Jennifer, and Susanne Prediger. “Prospective Teachers’ Diagnostic Thinking on Students’ Understanding of Multi-Digit Multiplication: A Content-Related Analysis on Unpacking of Knowledge Elements.” Journal Für Mathematik-Didaktik, Springer Science and Business Media LLC, 2022, doi:10.1007/s13138-022-00214-w.' short: J. Dröse, S. Prediger, Journal Für Mathematik-Didaktik (2022). date_created: 2023-01-27T18:47:24Z date_updated: 2023-11-02T08:05:14Z department: - _id: '98' doi: 10.1007/s13138-022-00214-w keyword: - Education - General Mathematics language: - iso: eng publication: Journal für Mathematik-Didaktik publication_identifier: issn: - 0173-5322 - 1869-2699 publication_status: published publisher: Springer Science and Business Media LLC quality_controlled: '1' status: public title: 'Prospective Teachers’ Diagnostic Thinking on Students’ Understanding of Multi-Digit Multiplication: A Content-Related Analysis on Unpacking of Knowledge Elements' type: journal_article user_id: '85820' year: '2022' ... --- _id: '48389' author: - first_name: Jennifer full_name: Dröse, Jennifer id: '85820' last_name: Dröse - first_name: Birgit full_name: Griese, Birgit last_name: Griese - first_name: Lena full_name: Wessel, Lena id: '85190' last_name: Wessel citation: ama: 'Dröse J, Griese B, Wessel L. Prospective teachers’ diagnostic judgments on students’ understanding of conditional probabilities. In: Twelfth Congress of the European Society for Research in Mathematics Education (CERME12). ; 2022.' apa: Dröse, J., Griese, B., & Wessel, L. (2022). Prospective teachers’ diagnostic judgments on students’ understanding of conditional probabilities. Twelfth Congress of the European Society for Research in Mathematics Education (CERME12). TwelfthCongressoftheEuropeanSocietyforResearchin Mathematics Education(CERME12), Bozen-Bolzano,Italy. bibtex: '@inproceedings{Dröse_Griese_Wessel_2022, title={Prospective teachers’ diagnostic judgments on students’ understanding of conditional probabilities}, booktitle={Twelfth Congress of the European Society for Research in Mathematics Education (CERME12)}, author={Dröse, Jennifer and Griese, Birgit and Wessel, Lena}, year={2022} }' chicago: Dröse, Jennifer, Birgit Griese, and Lena Wessel. “Prospective Teachers’ Diagnostic Judgments on Students’ Understanding of Conditional Probabilities.” In Twelfth Congress of the European Society for Research in Mathematics Education (CERME12), 2022. ieee: J. Dröse, B. Griese, and L. Wessel, “Prospective teachers’ diagnostic judgments on students’ understanding of conditional probabilities,” presented at the TwelfthCongressoftheEuropeanSocietyforResearchin Mathematics Education(CERME12), Bozen-Bolzano,Italy, 2022. mla: Dröse, Jennifer, et al. “Prospective Teachers’ Diagnostic Judgments on Students’ Understanding of Conditional Probabilities.” Twelfth Congress of the European Society for Research in Mathematics Education (CERME12), 2022. short: 'J. Dröse, B. Griese, L. Wessel, in: Twelfth Congress of the European Society for Research in Mathematics Education (CERME12), 2022.' conference: location: Bozen-Bolzano,Italy name: TwelfthCongressoftheEuropeanSocietyforResearchin Mathematics Education(CERME12) start_date: Feb2022 date_created: 2023-10-23T10:56:02Z date_updated: 2023-11-02T08:04:55Z department: - _id: '34' - _id: '10' - _id: '97' - _id: '643' language: - iso: eng main_file_link: - url: https://hal.science/hal-03744585/ publication: Twelfth Congress of the European Society for Research in Mathematics Education (CERME12) quality_controlled: '1' status: public title: Prospective teachers’ diagnostic judgments on students’ understanding of conditional probabilities type: conference user_id: '85820' year: '2022' ... --- _id: '45378' author: - first_name: Jennifer full_name: Dröse, Jennifer id: '85820' last_name: Dröse - first_name: Lena full_name: Wessel, Lena id: '85190' last_name: Wessel citation: ama: 'Dröse J, Wessel L. Prospective Teachers‘ Competence of Fostering Students’ Understanding in Script Writing Task. In: Fernandez C, Llinares S, Gutiérrez A, Planas N, eds. Proceedings of the 45th Conference of the International Group for the Psychology of Mathematics Education. PME. ; 2022.' apa: Dröse, J., & Wessel, L. (2022). Prospective Teachers‘ Competence of Fostering Students’ Understanding in Script Writing Task. In C. Fernandez, S. Llinares, A. Gutiérrez, & N. Planas (Eds.), Proceedings of the 45th Conference of the International Group for the Psychology of Mathematics Education. PME. bibtex: '@inproceedings{Dröse_Wessel_2022, title={Prospective Teachers‘ Competence of Fostering Students’ Understanding in Script Writing Task}, booktitle={Proceedings of the 45th Conference of the International Group for the Psychology of Mathematics Education. PME}, author={Dröse, Jennifer and Wessel, Lena}, editor={Fernandez, C. and Llinares, S. and Gutiérrez, A. and Planas, N.}, year={2022} }' chicago: Dröse, Jennifer, and Lena Wessel. “Prospective Teachers‘ Competence of Fostering Students’ Understanding in Script Writing Task.” In Proceedings of the 45th Conference of the International Group for the Psychology of Mathematics Education. PME, edited by C. Fernandez, S. Llinares, A. Gutiérrez, and N. Planas, 2022. ieee: J. Dröse and L. Wessel, “Prospective Teachers‘ Competence of Fostering Students’ Understanding in Script Writing Task,” in Proceedings of the 45th Conference of the International Group for the Psychology of Mathematics Education. PME, 2022. mla: Dröse, Jennifer, and Lena Wessel. “Prospective Teachers‘ Competence of Fostering Students’ Understanding in Script Writing Task.” Proceedings of the 45th Conference of the International Group for the Psychology of Mathematics Education. PME, edited by C. Fernandez et al., 2022. short: 'J. Dröse, L. Wessel, in: C. Fernandez, S. Llinares, A. Gutiérrez, N. Planas (Eds.), Proceedings of the 45th Conference of the International Group for the Psychology of Mathematics Education. PME, 2022.' date_created: 2023-05-31T06:54:24Z date_updated: 2023-11-02T08:05:31Z department: - _id: '98' editor: - first_name: C. full_name: Fernandez, C. last_name: Fernandez - first_name: S. full_name: Llinares, S. last_name: Llinares - first_name: A. full_name: Gutiérrez, A. last_name: Gutiérrez - first_name: N. full_name: Planas, N. last_name: Planas language: - iso: eng publication: Proceedings of the 45th Conference of the International Group for the Psychology of Mathematics Education. PME quality_controlled: '1' status: public title: Prospective Teachers‘ Competence of Fostering Students’ Understanding in Script Writing Task type: conference user_id: '85820' year: '2022' ... --- _id: '31057' abstract: - lang: eng text: 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. article_number: '244007' article_type: review author: - first_name: Sonja full_name: Barkhofen, Sonja id: '48188' last_name: Barkhofen - first_name: Philipp full_name: Schütte, Philipp id: '50168' last_name: Schütte - first_name: Tobias full_name: Weich, Tobias id: '49178' last_name: Weich orcid: 0000-0002-9648-6919 citation: ama: 'Barkhofen S, Schütte P, Weich T. Semiclassical formulae For Wigner distributions. Journal of Physics A: Mathematical and Theoretical. 2022;55(24). doi:10.1088/1751-8121/ac6d2b' apa: 'Barkhofen, S., Schütte, P., & Weich, T. (2022). Semiclassical formulae For Wigner distributions. Journal of Physics A: Mathematical and Theoretical, 55(24), Article 244007. https://doi.org/10.1088/1751-8121/ac6d2b' bibtex: '@article{Barkhofen_Schütte_Weich_2022, title={Semiclassical formulae For Wigner distributions}, volume={55}, DOI={10.1088/1751-8121/ac6d2b}, number={24244007}, journal={Journal of Physics A: Mathematical and Theoretical}, publisher={IOP Publishing Ltd}, author={Barkhofen, Sonja and Schütte, Philipp and Weich, Tobias}, year={2022} }' chicago: 'Barkhofen, Sonja, Philipp Schütte, and Tobias Weich. “Semiclassical Formulae For Wigner Distributions.” Journal of Physics A: Mathematical and Theoretical 55, no. 24 (2022). https://doi.org/10.1088/1751-8121/ac6d2b.' ieee: 'S. Barkhofen, P. Schütte, and T. Weich, “Semiclassical formulae For Wigner distributions,” Journal of Physics A: Mathematical and Theoretical, vol. 55, no. 24, Art. no. 244007, 2022, doi: 10.1088/1751-8121/ac6d2b.' mla: 'Barkhofen, Sonja, et al. “Semiclassical Formulae For Wigner Distributions.” Journal of Physics A: Mathematical and Theoretical, vol. 55, no. 24, 244007, IOP Publishing Ltd, 2022, doi:10.1088/1751-8121/ac6d2b.' short: 'S. Barkhofen, P. Schütte, T. Weich, Journal of Physics A: Mathematical and Theoretical 55 (2022).' date_created: 2022-05-04T12:23:11Z date_updated: 2024-02-06T20:40:45Z department: - _id: '623' - _id: '548' - _id: '10' doi: 10.1088/1751-8121/ac6d2b external_id: arxiv: - '2201.04892' intvolume: ' 55' issue: '24' language: - iso: eng publication: 'Journal of Physics A: Mathematical and Theoretical' publisher: IOP Publishing Ltd status: public title: Semiclassical formulae For Wigner distributions type: journal_article user_id: '49178' volume: 55 year: '2022' ... --- _id: '31363' abstract: - lang: eng text: 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. - lang: eng text: This thesis presents a design research project on the conception and implementation of a course "Geometry for Student Teachers". The focal points of the project are, on the one hand, the content structure of the course and, on the other hand, the implementation of professional orientation. With regard to the content structure, the axiom system of the "Saccheri plane", which is based on metric spaces, is presented and compared with alternative axiomatic approaches to plane geometry. The question of implementing professional orientation in mathematics courses is closely connected to the problem of the second discontinuity. In the paper, this problem is discussed on the basis of the synthesis of theoretical backgrounds on the importance of mathematical knowledge and skills for professional competence of mathematics teachers. Building on this, theory-based design principles for profession-oriented subject courses are developed. Central elements of the methodological design are the so-called "interface weeks" on the topics of congruence and symmetry and an accompanying interface ePortfolio. The central result of the thesis is a theoretically founded and empirically evaluated holistic course concept for a profession-oriented geometry course for student teachers, the conception of which is transferable to other subject events. In addition, various new contributions to the didactics of geometry in schools and universities result from the desing research. author: - first_name: Max full_name: Hoffmann, Max id: '32202' last_name: Hoffmann orcid: 0000-0002-6964-7123 citation: ama: 'Hoffmann M. Von Der Axiomatik Bis Zur Schnittstellenaufgabe: Entwicklung Und Erforschung Eines Ganzheitlichen Lehrkonzepts Für Eine Veranstaltung Geometrie Für Lehramtsstudierende.; 2022. doi:10.17619/UNIPB/1-1313' apa: 'Hoffmann, M. (2022). Von der Axiomatik bis zur Schnittstellenaufgabe: Entwicklung und Erforschung eines ganzheitlichen Lehrkonzepts für eine Veranstaltung Geometrie für Lehramtsstudierende. https://doi.org/10.17619/UNIPB/1-1313' bibtex: '@book{Hoffmann_2022, title={Von der Axiomatik bis zur Schnittstellenaufgabe: Entwicklung und Erforschung eines ganzheitlichen Lehrkonzepts für eine Veranstaltung Geometrie für Lehramtsstudierende}, DOI={10.17619/UNIPB/1-1313}, author={Hoffmann, Max}, year={2022} }' chicago: 'Hoffmann, Max. Von Der Axiomatik Bis Zur Schnittstellenaufgabe: Entwicklung Und Erforschung Eines Ganzheitlichen Lehrkonzepts Für Eine Veranstaltung Geometrie Für Lehramtsstudierende, 2022. https://doi.org/10.17619/UNIPB/1-1313.' ieee: 'M. Hoffmann, Von der Axiomatik bis zur Schnittstellenaufgabe: Entwicklung und Erforschung eines ganzheitlichen Lehrkonzepts für eine Veranstaltung Geometrie für Lehramtsstudierende. 2022.' mla: 'Hoffmann, Max. Von Der Axiomatik Bis Zur Schnittstellenaufgabe: Entwicklung Und Erforschung Eines Ganzheitlichen Lehrkonzepts Für Eine Veranstaltung Geometrie Für Lehramtsstudierende. 2022, doi:10.17619/UNIPB/1-1313.' short: 'M. Hoffmann, Von Der Axiomatik Bis Zur Schnittstellenaufgabe: Entwicklung Und Erforschung Eines Ganzheitlichen Lehrkonzepts Für Eine Veranstaltung Geometrie Für Lehramtsstudierende, 2022.' date_created: 2022-05-22T10:56:47Z date_updated: 2024-02-19T06:28:58Z department: - _id: '97' doi: 10.17619/UNIPB/1-1313 language: - iso: eng main_file_link: - open_access: '1' url: https://digital.ub.uni-paderborn.de/hs/content/titleinfo/6503170 oa: '1' page: '410' status: public supervisor: - first_name: Rolf full_name: Biehler, Rolf last_name: Biehler - first_name: Joachim full_name: Hilgert, Joachim id: '220' last_name: Hilgert title: 'Von der Axiomatik bis zur Schnittstellenaufgabe: Entwicklung und Erforschung eines ganzheitlichen Lehrkonzepts für eine Veranstaltung Geometrie für Lehramtsstudierende' type: dissertation user_id: '49063' year: '2022' ... --- _id: '35322' author: - first_name: Kai-Uwe full_name: Bux, Kai-Uwe last_name: Bux - first_name: Joachim full_name: Hilgert, Joachim id: '220' last_name: Hilgert - first_name: Tobias full_name: Weich, Tobias id: '49178' last_name: Weich orcid: 0000-0002-9648-6919 citation: ama: Bux K-U, Hilgert J, Weich T. Poisson transforms for trees of bounded degree. Journal of Spectral Theory. 2022;12(2):659-681. doi:10.4171/jst/414 apa: Bux, K.-U., Hilgert, J., & Weich, T. (2022). Poisson transforms for trees of bounded degree. Journal of Spectral Theory, 12(2), 659–681. https://doi.org/10.4171/jst/414 bibtex: '@article{Bux_Hilgert_Weich_2022, title={Poisson transforms for trees of bounded degree}, volume={12}, DOI={10.4171/jst/414}, number={2}, journal={Journal of Spectral Theory}, publisher={European Mathematical Society - EMS - Publishing House GmbH}, author={Bux, Kai-Uwe and Hilgert, Joachim and Weich, Tobias}, year={2022}, pages={659–681} }' chicago: 'Bux, Kai-Uwe, Joachim Hilgert, and Tobias Weich. “Poisson Transforms for Trees of Bounded Degree.” Journal of Spectral Theory 12, no. 2 (2022): 659–81. https://doi.org/10.4171/jst/414.' ieee: 'K.-U. Bux, J. Hilgert, and T. Weich, “Poisson transforms for trees of bounded degree,” Journal of Spectral Theory, vol. 12, no. 2, pp. 659–681, 2022, doi: 10.4171/jst/414.' mla: Bux, Kai-Uwe, et al. “Poisson Transforms for Trees of Bounded Degree.” Journal of Spectral Theory, vol. 12, no. 2, European Mathematical Society - EMS - Publishing House GmbH, 2022, pp. 659–81, doi:10.4171/jst/414. short: K.-U. Bux, J. Hilgert, T. Weich, Journal of Spectral Theory 12 (2022) 659–681. date_created: 2023-01-06T08:49:06Z date_updated: 2024-02-19T06:28:12Z department: - _id: '10' - _id: '623' - _id: '548' - _id: '91' doi: 10.4171/jst/414 intvolume: ' 12' issue: '2' keyword: - Geometry and Topology - Mathematical Physics - Statistical and Nonlinear Physics language: - iso: eng page: 659-681 publication: Journal of Spectral Theory publication_identifier: issn: - 1664-039X publication_status: published publisher: European Mathematical Society - EMS - Publishing House GmbH status: public title: Poisson transforms for trees of bounded degree type: journal_article user_id: '49063' volume: 12 year: '2022' ...