---
_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'
...