---
_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'
...
---
_id: '32560'
abstract:
- lang: eng
  text: "Several methods are available to answer questions regarding similarity and
    accuracy,\r\neach of which has specific properties and limitations. This study
    focuses on the\r\nLatent Congruence Model (LCM; Cheung, 2009), because of its
    capacity to deal\r\nwith cross-informant measurement invariance issues. Until
    now, no cross-national\r\napplications of LCM are present in the literature, perhaps
    because of the difficulty\r\nto deal with both cross-national and cross-informant
    measurement issues implied by\r\nthose models. This study presents a step-by-step
    procedure to apply LCM to dyadic\r\ncross-national research designs controlling
    for both cross-national and cross-informant\r\nmeasurement invariance. An illustrative
    example on parent–child support exchanges in\r\nItaly and Germany is provided.
    Findings help to show the different possible scenarios\r\nof partial invariance,
    and a discussion related to how to deal with those scenarios is\r\nprovided. Future
    perspectives in the study of parent–child similarity and accuracy in\r\ncross-national
    research will be discussed."
article_number: '672383'
author:
- first_name: Semira
  full_name: Tagliabue, Semira
  last_name: Tagliabue
- first_name: Michela
  full_name: Zambelli, Michela
  last_name: Zambelli
- first_name: Angela
  full_name: Sorgente, Angela
  last_name: Sorgente
- first_name: Sabrina
  full_name: Sommer, Sabrina
  last_name: Sommer
- first_name: Christian
  full_name: Hoellger, Christian
  last_name: Hoellger
- first_name: Heike M.
  full_name: Buhl, Heike M.
  id: '27152'
  last_name: Buhl
- first_name: Margherita
  full_name: Lanz, Margherita
  last_name: Lanz
citation:
  ama: 'Tagliabue S, Zambelli M, Sorgente A, et al. Latent Congruence Model to Investigate
    Similarity and Accuracy in Family Members’ Perception: The Challenge of Cross-National
    and Cross-Informant Measurement (Non)Invariance. <i>Frontiers in Psychology</i>.
    2021;12. doi:<a href="https://doi.org/10.3389/fpsyg.2021.672383">10.3389/fpsyg.2021.672383</a>'
  apa: 'Tagliabue, S., Zambelli, M., Sorgente, A., Sommer, S., Hoellger, C., Buhl,
    H. M., &#38; Lanz, M. (2021). Latent Congruence Model to Investigate Similarity
    and Accuracy in Family Members’ Perception: The Challenge of Cross-National and
    Cross-Informant Measurement (Non)Invariance. <i>Frontiers in Psychology</i>, <i>12</i>,
    Article 672383. <a href="https://doi.org/10.3389/fpsyg.2021.672383">https://doi.org/10.3389/fpsyg.2021.672383</a>'
  bibtex: '@article{Tagliabue_Zambelli_Sorgente_Sommer_Hoellger_Buhl_Lanz_2021, title={Latent
    Congruence Model to Investigate Similarity and Accuracy in Family Members’ Perception:
    The Challenge of Cross-National and Cross-Informant Measurement (Non)Invariance},
    volume={12}, DOI={<a href="https://doi.org/10.3389/fpsyg.2021.672383">10.3389/fpsyg.2021.672383</a>},
    number={672383}, journal={Frontiers in Psychology}, publisher={Frontiers Media
    SA}, author={Tagliabue, Semira and Zambelli, Michela and Sorgente, Angela and
    Sommer, Sabrina and Hoellger, Christian and Buhl, Heike M. and Lanz, Margherita},
    year={2021} }'
  chicago: 'Tagliabue, Semira, Michela Zambelli, Angela Sorgente, Sabrina Sommer,
    Christian Hoellger, Heike M. Buhl, and Margherita Lanz. “Latent Congruence Model
    to Investigate Similarity and Accuracy in Family Members’ Perception: The Challenge
    of Cross-National and Cross-Informant Measurement (Non)Invariance.” <i>Frontiers
    in Psychology</i> 12 (2021). <a href="https://doi.org/10.3389/fpsyg.2021.672383">https://doi.org/10.3389/fpsyg.2021.672383</a>.'
  ieee: 'S. Tagliabue <i>et al.</i>, “Latent Congruence Model to Investigate Similarity
    and Accuracy in Family Members’ Perception: The Challenge of Cross-National and
    Cross-Informant Measurement (Non)Invariance,” <i>Frontiers in Psychology</i>,
    vol. 12, Art. no. 672383, 2021, doi: <a href="https://doi.org/10.3389/fpsyg.2021.672383">10.3389/fpsyg.2021.672383</a>.'
  mla: 'Tagliabue, Semira, et al. “Latent Congruence Model to Investigate Similarity
    and Accuracy in Family Members’ Perception: The Challenge of Cross-National and
    Cross-Informant Measurement (Non)Invariance.” <i>Frontiers in Psychology</i>,
    vol. 12, 672383, Frontiers Media SA, 2021, doi:<a href="https://doi.org/10.3389/fpsyg.2021.672383">10.3389/fpsyg.2021.672383</a>.'
  short: S. Tagliabue, M. Zambelli, A. Sorgente, S. Sommer, C. Hoellger, H.M. Buhl,
    M. Lanz, Frontiers in Psychology 12 (2021).
date_created: 2022-08-03T05:59:20Z
date_updated: 2022-08-29T06:38:34Z
department:
- _id: '427'
doi: 10.3389/fpsyg.2021.672383
intvolume: '        12'
keyword:
- latent congruence model
- measurement invariance
- similarity
- accuracy
- cross-national
- cross-informant
- parent-child relationship
- support exchanges
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://www.frontiersin.org/articles/10.3389/fpsyg.2021.672383/pdf
oa: '1'
publication: Frontiers in Psychology
publication_identifier:
  issn:
  - 1664-1078
publication_status: published
publisher: Frontiers Media SA
status: public
title: 'Latent Congruence Model to Investigate Similarity and Accuracy in Family Members''
  Perception: The Challenge of Cross-National and Cross-Informant Measurement (Non)Invariance'
type: journal_article
user_id: '42165'
volume: 12
year: '2021'
...