---
_id: '61017'
abstract:
- lang: eng
text: Selecting tasks is a typical job in everyday teaching that requires teachers
to have content-specific expertise, including categories to think about and perceive
conceptual understanding. This contribution investigates the activation of prospective
teachers’ categories when solving tasks on the scalar product and evaluating their
relevance for teaching in upper secondary school. To further investigate, whether
input on content-related aspects could be helpful to promote a professional justification
for the selection of tasks, two groups with and without input are to be differentiated.
Different ways of dealing with underlying concept elements and evaluating the
relevance of tasks are discussed by examples.
author:
- first_name: Janine
full_name: Herrmann, Janine
id: '64060'
last_name: Herrmann
citation:
ama: 'Herrmann J. Which categories do prospective teachers apply when selecting
tasks for the scalar product? In: Cornejo C, Felmer P, Gómez DM, et al., eds.
Proceedings of the 48th Conference of the International Group for the Psychology
of Mathematics Education. Vol 1. ; 2025.'
apa: Herrmann, J. (2025). Which categories do prospective teachers apply when selecting
tasks for the scalar product? In C. Cornejo, P. Felmer, D. M. Gómez, P. Dartnell,
P. Araya, A. Peri, & V. Randolph (Eds.), Proceedings of the 48th Conference
of the International Group for the Psychology of Mathematics Education (Vol.
1).
bibtex: '@inproceedings{Herrmann_2025, title={Which categories do prospective teachers
apply when selecting tasks for the scalar product?}, volume={1}, booktitle={Proceedings
of the 48th Conference of the International Group for the Psychology of Mathematics
Education}, author={Herrmann, Janine}, editor={Cornejo, Claudia and Felmer, Patricio
and Gómez, David M. and Dartnell, Pablo and Araya, Paulina and Peri, Armando and
Randolph, Valeria }, year={2025} }'
chicago: Herrmann, Janine. “Which Categories Do Prospective Teachers Apply When
Selecting Tasks for the Scalar Product?” In Proceedings of the 48th Conference
of the International Group for the Psychology of Mathematics Education, edited
by Claudia Cornejo, Patricio Felmer, David M. Gómez, Pablo Dartnell, Paulina Araya,
Armando Peri, and Valeria Randolph, Vol. 1, 2025.
ieee: J. Herrmann, “Which categories do prospective teachers apply when selecting
tasks for the scalar product?,” in Proceedings of the 48th Conference of the
International Group for the Psychology of Mathematics Education, Santiago
de Chile, 2025, vol. 1.
mla: Herrmann, Janine. “Which Categories Do Prospective Teachers Apply When Selecting
Tasks for the Scalar Product?” Proceedings of the 48th Conference of the International
Group for the Psychology of Mathematics Education, edited by Claudia Cornejo
et al., vol. 1, 2025.
short: 'J. Herrmann, in: C. Cornejo, P. Felmer, D.M. Gómez, P. Dartnell, P. Araya,
A. Peri, V. Randolph (Eds.), Proceedings of the 48th Conference of the International
Group for the Psychology of Mathematics Education, 2025.'
conference:
end_date: 2025-08-02
location: Santiago de Chile
name: 48th PME Conference
start_date: 2025-07-28
date_created: 2025-08-26T08:35:10Z
date_updated: 2026-02-16T07:54:31Z
ddc:
- '510'
editor:
- first_name: Claudia
full_name: Cornejo, Claudia
last_name: Cornejo
- first_name: Patricio
full_name: Felmer, Patricio
last_name: Felmer
- first_name: David M.
full_name: Gómez, David M.
last_name: Gómez
- first_name: Pablo
full_name: Dartnell, Pablo
last_name: Dartnell
- first_name: Paulina
full_name: Araya, Paulina
last_name: Araya
- first_name: Armando
full_name: Peri, Armando
last_name: Peri
- first_name: 'Valeria '
full_name: 'Randolph, Valeria '
last_name: Randolph
file:
- access_level: closed
content_type: application/pdf
creator: herrmann
date_created: 2025-08-26T08:32:39Z
date_updated: 2025-08-26T08:32:39Z
file_id: '61018'
file_name: RR_Herrmann.pdf
file_size: 408502
relation: main_file
success: 1
file_date_updated: 2025-08-26T08:32:39Z
has_accepted_license: '1'
intvolume: ' 1'
keyword:
- Teacher expertise
- noticing
- analytical vectorial geometry
language:
- iso: eng
main_file_link:
- url: https://www.igpme.org/wp-content/uploads/2025/07/PME48_ResearchReports_E-ISSN_2790-3648.zip
publication: Proceedings of the 48th Conference of the International Group for the
Psychology of Mathematics Education
publication_identifier:
unknown:
- 2790-3648
quality_controlled: '1'
status: public
title: Which categories do prospective teachers apply when selecting tasks for the
scalar product?
type: conference
user_id: '64060'
volume: 1
year: '2025'
...
---
_id: '64149'
author:
- first_name: Janine
full_name: Herrmann, Janine
id: '64060'
last_name: Herrmann
- first_name: Lena
full_name: Wessel, Lena
last_name: Wessel
citation:
ama: 'Herrmann J, Wessel L. Verstehenstypen von Lehrkräften zum Konzept Skalarprodukt
und ihre Vorstellungen von Verstehensprozessen. In: Schick L, Platz M, Lambert
A, eds. Beiträge Zum Mathematikunterricht. ; 2025:483-486. doi:https://doi.org/10.37626/GA9783959872782.0'
apa: Herrmann, J., & Wessel, L. (2025). Verstehenstypen von Lehrkräften zum
Konzept Skalarprodukt und ihre Vorstellungen von Verstehensprozessen. In L. Schick,
M. Platz, & A. Lambert (Eds.), Beiträge zum Mathematikunterricht (pp.
483–486). https://doi.org/10.37626/GA9783959872782.0
bibtex: '@inproceedings{Herrmann_Wessel_2025, title={Verstehenstypen von Lehrkräften
zum Konzept Skalarprodukt und ihre Vorstellungen von Verstehensprozessen}, DOI={https://doi.org/10.37626/GA9783959872782.0},
booktitle={Beiträge zum Mathematikunterricht}, author={Herrmann, Janine and Wessel,
Lena}, editor={Schick, Lisa and Platz, Melanie and Lambert, Anselm}, year={2025},
pages={483–486} }'
chicago: Herrmann, Janine, and Lena Wessel. “Verstehenstypen von Lehrkräften Zum
Konzept Skalarprodukt Und Ihre Vorstellungen von Verstehensprozessen.” In Beiträge
Zum Mathematikunterricht, edited by Lisa Schick, Melanie Platz, and Anselm
Lambert, 483–86, 2025. https://doi.org/10.37626/GA9783959872782.0.
ieee: 'J. Herrmann and L. Wessel, “Verstehenstypen von Lehrkräften zum Konzept Skalarprodukt
und ihre Vorstellungen von Verstehensprozessen,” in Beiträge zum Mathematikunterricht,
Saarbrücken, 2025, pp. 483–486, doi: https://doi.org/10.37626/GA9783959872782.0.'
mla: Herrmann, Janine, and Lena Wessel. “Verstehenstypen von Lehrkräften Zum Konzept
Skalarprodukt Und Ihre Vorstellungen von Verstehensprozessen.” Beiträge Zum
Mathematikunterricht, edited by Lisa Schick et al., 2025, pp. 483–86, doi:https://doi.org/10.37626/GA9783959872782.0.
short: 'J. Herrmann, L. Wessel, in: L. Schick, M. Platz, A. Lambert (Eds.), Beiträge
Zum Mathematikunterricht, 2025, pp. 483–486.'
conference:
end_date: 2025-0307
location: Saarbrücken
name: Gesellschaft der Mathematik
start_date: 2025-03-03
date_created: 2026-02-13T09:35:26Z
date_updated: 2026-02-16T07:49:49Z
ddc:
- '370'
- '510'
doi: https://doi.org/10.37626/GA9783959872782.0
editor:
- first_name: Lisa
full_name: Schick, Lisa
last_name: Schick
- first_name: Melanie
full_name: Platz, Melanie
last_name: Platz
- first_name: Anselm
full_name: Lambert, Anselm
last_name: Lambert
file:
- access_level: closed
content_type: application/pdf
creator: herrmann
date_created: 2026-02-13T09:34:08Z
date_updated: 2026-02-13T09:34:08Z
file_id: '64150'
file_name: BzMU25_HERRMANN_Verstehenstypen.pdf
file_size: 536533
relation: main_file
success: 1
file_date_updated: 2026-02-13T09:34:08Z
has_accepted_license: '1'
language:
- iso: eng
page: 483-486
publication: Beiträge zum Mathematikunterricht
status: public
title: Verstehenstypen von Lehrkräften zum Konzept Skalarprodukt und ihre Vorstellungen
von Verstehensprozessen
type: conference
user_id: '64060'
year: '2025'
...
---
_id: '61051'
author:
- first_name: Janine
full_name: Herrmann, Janine
id: '64060'
last_name: Herrmann
citation:
ama: 'Herrmann J. Ansprüche an eine Fortbildung zur analytischen Geometrie. In:
Ebers P, Rösken F, Barzel B, Büchter A, Schacht F, Scherer P, eds. Beiträge
zum Mathematikunterricht 2024. ; :1666. doi:http://dx.doi.org/10.17877/DE290R-25188'
apa: Herrmann, J. (n.d.). Ansprüche an eine Fortbildung zur analytischen Geometrie.
In P. Ebers, F. Rösken, B. Barzel, A. Büchter, F. Schacht, & P. Scherer (Eds.),
Beiträge zum Mathematikunterricht 2024 (p. 1666). http://dx.doi.org/10.17877/DE290R-25188
bibtex: '@inproceedings{Herrmann, title={Ansprüche an eine Fortbildung zur analytischen
Geometrie}, DOI={http://dx.doi.org/10.17877/DE290R-25188},
booktitle={Beiträge zum Mathematikunterricht 2024}, author={Herrmann, Janine},
editor={Ebers, Patrick and Rösken, Fabian and Barzel, Bärbel and Büchter, Andreas
and Schacht, Florian and Scherer, Petra }, pages={1666} }'
chicago: Herrmann, Janine. “Ansprüche an eine Fortbildung zur analytischen Geometrie.”
In Beiträge zum Mathematikunterricht 2024, edited by Patrick Ebers, Fabian Rösken,
Bärbel Barzel, Andreas Büchter, Florian Schacht, and Petra Scherer, 1666, n.d.
http://dx.doi.org/10.17877/DE290R-25188.
ieee: 'J. Herrmann, “Ansprüche an eine Fortbildung zur analytischen Geometrie,”
in Beiträge zum Mathematikunterricht 2024, Duisburg-Essen, p. 1666, doi:
http://dx.doi.org/10.17877/DE290R-25188.'
mla: Herrmann, Janine. “Ansprüche an eine Fortbildung zur analytischen Geometrie.”
Beiträge zum Mathematikunterricht 2024, edited by Patrick Ebers et al.,
p. 1666, doi:http://dx.doi.org/10.17877/DE290R-25188.
short: 'J. Herrmann, in: P. Ebers, F. Rösken, B. Barzel, A. Büchter, F. Schacht,
P. Scherer (Eds.), Beiträge zum Mathematikunterricht 2024, n.d., p. 1666.'
conference:
end_date: 2024-03-08
location: Duisburg-Essen
name: GdM 2024
start_date: 2024-03-04
date_created: 2025-08-28T10:01:14Z
date_updated: 2025-08-28T10:01:26Z
ddc:
- '510'
doi: http://dx.doi.org/10.17877/DE290R-25188
editor:
- first_name: Patrick
full_name: Ebers, Patrick
last_name: Ebers
- first_name: 'Fabian '
full_name: 'Rösken, Fabian '
last_name: Rösken
- first_name: Bärbel
full_name: Barzel, Bärbel
last_name: Barzel
- first_name: Andreas
full_name: Büchter, Andreas
last_name: Büchter
- first_name: 'Florian '
full_name: 'Schacht, Florian '
last_name: Schacht
- first_name: 'Petra '
full_name: 'Scherer, Petra '
last_name: Scherer
file:
- access_level: closed
content_type: application/pdf
creator: herrmann
date_created: 2025-08-28T10:00:24Z
date_updated: 2025-08-28T10:00:24Z
file_id: '61054'
file_name: BzMU24_HERRMANN_Geometriefortbildungen.pdf
file_size: 57284
relation: main_file
success: 1
file_date_updated: 2025-08-28T10:00:24Z
has_accepted_license: '1'
language:
- iso: ger
page: '1666'
publication: Beiträge zum Mathematikunterricht 2024
publication_status: accepted
status: public
title: Ansprüche an eine Fortbildung zur analytischen Geometrie
type: conference
user_id: '64060'
year: '2025'
...