---
_id: '57895'
abstract:
- lang: eng
  text: "In our paper, we present a study in which we investigate which strategies
    pre-service teachers (PSTs) use to find and, if necessary, reject possible candidates
    for congruence theorems for quadrilaterals. This study was conducted before the
    PTSs attended a university geometry course. In this way, statements about learning
    prerequisites can be made. For the study, we analyzed group discussions of PSTs
    to identify typical approaches and evaluate them from a mathematical perspective.
    The results can be considered for the further development of courses for PSTs
    and generate hypotheses\r\nfor further research."
author:
- first_name: Max
  full_name: Hoffmann, Max
  id: '32202'
  last_name: Hoffmann
  orcid: 0000-0002-6964-7123
- first_name: Sarah
  full_name: Schlüter, Sarah
  last_name: Schlüter
citation:
  ama: 'Hoffmann M, Schlüter S. How Do Advanced Pre-Service Teachers Develop Congruence
    Theorems for Quadrilaterals? In: González-Martín AS, Gueudet G, Florensa I, Lombard
    N, eds. <i>Proceedings of the Fifth Conference of the International Network for
    Didactic Research in University Mathematics (INDRUM 2024, 10-14 June 2024)</i>.
    Escola Univerist`aria Salesiana de Sarri`a – Univ. Aut`onoma de Barcelona and
    INDRUM; 2024.'
  apa: Hoffmann, M., &#38; Schlüter, S. (2024). How Do Advanced Pre-Service Teachers
    Develop Congruence Theorems for Quadrilaterals? In A. S. González-Martín, G. Gueudet,
    I. Florensa, &#38; N. Lombard (Eds.), <i>Proceedings of the Fifth Conference of
    the International Network for Didactic Research in University Mathematics (INDRUM
    2024, 10-14 June 2024)</i>. Escola Univerist`aria Salesiana de Sarri`a – Univ.
    Aut`onoma de Barcelona and INDRUM.
  bibtex: '@inproceedings{Hoffmann_Schlüter_2024, place={Barcelona}, title={How Do
    Advanced Pre-Service Teachers Develop Congruence Theorems for Quadrilaterals?},
    booktitle={Proceedings of the Fifth Conference of the International Network for
    Didactic Research in University Mathematics (INDRUM 2024, 10-14 June 2024)}, publisher={Escola
    Univerist`aria Salesiana de Sarri`a – Univ. Aut`onoma de Barcelona and INDRUM},
    author={Hoffmann, Max and Schlüter, Sarah}, editor={González-Martín, Alejandro
    S. and Gueudet, Ghislaine and Florensa, Ignasi and Lombard, Nathan}, year={2024}
    }'
  chicago: 'Hoffmann, Max, and Sarah Schlüter. “How Do Advanced Pre-Service Teachers
    Develop Congruence Theorems for Quadrilaterals?” In <i>Proceedings of the Fifth
    Conference of the International Network for Didactic Research in University Mathematics
    (INDRUM 2024, 10-14 June 2024)</i>, edited by Alejandro S. González-Martín, Ghislaine
    Gueudet, Ignasi Florensa, and Nathan Lombard. Barcelona: Escola Univerist`aria
    Salesiana de Sarri`a – Univ. Aut`onoma de Barcelona and INDRUM, 2024.'
  ieee: M. Hoffmann and S. Schlüter, “How Do Advanced Pre-Service Teachers Develop
    Congruence Theorems for Quadrilaterals?,” in <i>Proceedings of the Fifth Conference
    of the International Network for Didactic Research in University Mathematics (INDRUM
    2024, 10-14 June 2024)</i>, 2024.
  mla: Hoffmann, Max, and Sarah Schlüter. “How Do Advanced Pre-Service Teachers Develop
    Congruence Theorems for Quadrilaterals?” <i>Proceedings of the Fifth Conference
    of the International Network for Didactic Research in University Mathematics (INDRUM
    2024, 10-14 June 2024)</i>, edited by Alejandro S. González-Martín et al., Escola
    Univerist`aria Salesiana de Sarri`a – Univ. Aut`onoma de Barcelona and INDRUM,
    2024.
  short: 'M. Hoffmann, S. Schlüter, in: A.S. González-Martín, G. Gueudet, I. Florensa,
    N. Lombard (Eds.), Proceedings of the Fifth Conference of the International Network
    for Didactic Research in University Mathematics (INDRUM 2024, 10-14 June 2024),
    Escola Univerist`aria Salesiana de Sarri`a – Univ. Aut`onoma de Barcelona and
    INDRUM, Barcelona, 2024.'
date_created: 2025-01-02T10:45:53Z
date_updated: 2025-01-02T10:45:59Z
ddc:
- '370'
- '510'
department:
- _id: '97'
- _id: '643'
editor:
- first_name: Alejandro S.
  full_name: González-Martín, Alejandro S.
  last_name: González-Martín
- first_name: Ghislaine
  full_name: Gueudet, Ghislaine
  last_name: Gueudet
- first_name: Ignasi
  full_name: Florensa, Ignasi
  last_name: Florensa
- first_name: Nathan
  full_name: Lombard, Nathan
  last_name: Lombard
file:
- access_level: closed
  content_type: application/pdf
  creator: maxh
  date_created: 2025-01-02T10:42:21Z
  date_updated: 2025-01-02T10:42:21Z
  file_id: '57896'
  file_name: 2024_Hoffmann_Schlueter_CongruenceQuadrilaterals.pdf
  file_size: 315111
  relation: main_file
  success: 1
file_date_updated: 2025-01-02T10:42:21Z
has_accepted_license: '1'
keyword:
- Teachers’ and students’ practices at university level
- Transition to
- across and from university mathematics
- Teaching and learning of specific topics in university mathematics
- Congruence
- Quadrilaterals
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://indrum2024.sciencesconf.org/data/pages/Proceedings_INDRUM2024.pdf
oa: '1'
place: Barcelona
publication: Proceedings of the Fifth Conference of the International Network for
  Didactic Research in University Mathematics (INDRUM 2024, 10-14 June 2024)
publication_status: published
publisher: Escola Univerist`aria Salesiana de Sarri`a – Univ. Aut`onoma de Barcelona
  and INDRUM
quality_controlled: '1'
status: public
title: How Do Advanced Pre-Service Teachers Develop Congruence Theorems for Quadrilaterals?
type: conference
user_id: '32202'
year: '2024'
...
---
_id: '31849'
author:
- first_name: Max
  full_name: Hoffmann, Max
  id: '32202'
  last_name: Hoffmann
  orcid: 0000-0002-6964-7123
- first_name: Rolf
  full_name: Biehler, Rolf
  id: '16274'
  last_name: Biehler
citation:
  ama: 'Hoffmann M, Biehler R. Student Teachers ’ Knowledge of Congruence before a
    University Course on Geometry. In: Trigueros M, Barquero B, Hochmuth R, Peters
    J, eds. <i>Proceedings of the Fourth Conference of the International Network for
    Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022)</i>.
    University of Hannover and INDRUM.; 2023.'
  apa: Hoffmann, M., &#38; Biehler, R. (2023). Student Teachers ’ Knowledge of Congruence
    before a University Course on Geometry. In M. Trigueros, B. Barquero, R. Hochmuth,
    &#38; J. Peters (Eds.), <i>Proceedings of the Fourth Conference of the International
    Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October
    2022)</i>. University of Hannover and INDRUM.
  bibtex: '@inproceedings{Hoffmann_Biehler_2023, place={Hannover}, title={Student
    Teachers ’ Knowledge of Congruence before a University Course on Geometry}, booktitle={Proceedings
    of the Fourth Conference of the International Network for Didactic Research in
    University Mathematics (INDRUM 2022, 19-22 October 2022)}, publisher={University
    of Hannover and INDRUM.}, author={Hoffmann, Max and Biehler, Rolf}, editor={Trigueros,
    Marı́a and Barquero, Berta and Hochmuth, Reinhard and Peters, Jana}, year={2023}
    }'
  chicago: 'Hoffmann, Max, and Rolf Biehler. “Student Teachers ’ Knowledge of Congruence
    before a University Course on Geometry.” In <i>Proceedings of the Fourth Conference
    of the International Network for Didactic Research in University Mathematics (INDRUM
    2022, 19-22 October 2022)</i>, edited by Marı́a Trigueros, Berta Barquero, Reinhard
    Hochmuth, and Jana Peters. Hannover: University of Hannover and INDRUM., 2023.'
  ieee: M. Hoffmann and R. Biehler, “Student Teachers ’ Knowledge of Congruence before
    a University Course on Geometry,” in <i>Proceedings of the Fourth Conference of
    the International Network for Didactic Research in University Mathematics (INDRUM
    2022, 19-22 October 2022)</i>, 2023.
  mla: Hoffmann, Max, and Rolf Biehler. “Student Teachers ’ Knowledge of Congruence
    before a University Course on Geometry.” <i>Proceedings of the Fourth Conference
    of the International Network for Didactic Research in University Mathematics (INDRUM
    2022, 19-22 October 2022)</i>, edited by Marı́a Trigueros et al., University of
    Hannover and INDRUM., 2023.
  short: 'M. Hoffmann, R. Biehler, in: M. Trigueros, B. Barquero, R. Hochmuth, J.
    Peters (Eds.), Proceedings of the Fourth Conference of the International Network
    for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022),
    University of Hannover and INDRUM., Hannover, 2023.'
date_created: 2022-06-12T11:07:34Z
date_updated: 2023-03-25T10:11:35Z
ddc:
- '370'
- '510'
department:
- _id: '97'
editor:
- first_name: Marı́a
  full_name: Trigueros, Marı́a
  last_name: Trigueros
- first_name: Berta
  full_name: Barquero, Berta
  last_name: Barquero
- first_name: Reinhard
  full_name: Hochmuth, Reinhard
  last_name: Hochmuth
- first_name: Jana
  full_name: Peters, Jana
  last_name: Peters
file:
- access_level: closed
  content_type: application/pdf
  creator: maxh
  date_created: 2023-03-25T10:01:03Z
  date_updated: 2023-03-25T10:01:03Z
  file_id: '43096'
  file_name: HoffmannBiehler2022_indrum_congruence.pdf
  file_size: 201942
  relation: main_file
  success: 1
file_date_updated: 2023-03-25T10:01:03Z
has_accepted_license: '1'
keyword:
- Teaching and learning of specific topics in university mathematics
- Transition to
- across and from university mathematics
- Student Teachers
- Geometry
- Congruence
- Double Discontinuity.
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://hal.univ-reims.fr/INDRUM2022/
oa: '1'
place: Hannover
publication: Proceedings of the Fourth Conference of the International Network for
  Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022)
publication_status: published
publisher: University of Hannover and INDRUM.
quality_controlled: '1'
status: public
title: Student Teachers ’ Knowledge of Congruence before a University Course on Geometry
type: conference
user_id: '32202'
year: '2023'
...