---
_id: '64625'
author:
- first_name: Anna
full_name: Fergusson, Anna
last_name: Fergusson
- first_name: Susanne
full_name: Podworny, Susanne
id: '30619'
last_name: Podworny
orcid: 0000-0002-6313-5987
- first_name: Yannik
full_name: Fleischer, Yannik
id: '42660'
last_name: Fleischer
orcid: https://orcid.org/0000-0003-0318-0329
- first_name: Sven
full_name: Hüsing, Sven
id: '58465'
last_name: Hüsing
- first_name: Malia S.
full_name: Puloka, Malia S.
last_name: Puloka
- first_name: Rolf
full_name: Biehler, Rolf
id: '16274'
last_name: Biehler
- first_name: Maxine
full_name: Pfannkuch, Maxine
last_name: Pfannkuch
- first_name: Stephanie
full_name: Budgett, Stephanie
last_name: Budgett
- first_name: Michelle
full_name: Dalrymple, Michelle
last_name: Dalrymple
citation:
ama: 'Fergusson A, Podworny S, Fleischer Y, et al. Branching out data science education:
Developing task and computational environment design principles for teaching data
science at the high school level through an international research collaboration.
In: Proceedings of the IASE 2025 Satellite Conference - Statistics and Data
Science Education in STEAM. International Association for Statistics Education;
2026. doi:10.52041/iase25.138'
apa: 'Fergusson, A., Podworny, S., Fleischer, Y., Hüsing, S., Puloka, M. S., Biehler,
R., Pfannkuch, M., Budgett, S., & Dalrymple, M. (2026). Branching out data
science education: Developing task and computational environment design principles
for teaching data science at the high school level through an international research
collaboration. Proceedings of the IASE 2025 Satellite Conference - Statistics
and Data Science Education in STEAM. https://doi.org/10.52041/iase25.138'
bibtex: '@inproceedings{Fergusson_Podworny_Fleischer_Hüsing_Puloka_Biehler_Pfannkuch_Budgett_Dalrymple_2026,
title={Branching out data science education: Developing task and computational
environment design principles for teaching data science at the high school level
through an international research collaboration}, DOI={10.52041/iase25.138},
booktitle={Proceedings of the IASE 2025 Satellite Conference - Statistics and
Data Science Education in STEAM}, publisher={International Association for Statistics
Education}, author={Fergusson, Anna and Podworny, Susanne and Fleischer, Yannik
and Hüsing, Sven and Puloka, Malia S. and Biehler, Rolf and Pfannkuch, Maxine
and Budgett, Stephanie and Dalrymple, Michelle}, year={2026} }'
chicago: 'Fergusson, Anna, Susanne Podworny, Yannik Fleischer, Sven Hüsing, Malia
S. Puloka, Rolf Biehler, Maxine Pfannkuch, Stephanie Budgett, and Michelle Dalrymple.
“Branching out Data Science Education: Developing Task and Computational Environment
Design Principles for Teaching Data Science at the High School Level through an
International Research Collaboration.” In Proceedings of the IASE 2025 Satellite
Conference - Statistics and Data Science Education in STEAM. International
Association for Statistics Education, 2026. https://doi.org/10.52041/iase25.138.'
ieee: 'A. Fergusson et al., “Branching out data science education: Developing
task and computational environment design principles for teaching data science
at the high school level through an international research collaboration,” 2026,
doi: 10.52041/iase25.138.'
mla: 'Fergusson, Anna, et al. “Branching out Data Science Education: Developing
Task and Computational Environment Design Principles for Teaching Data Science
at the High School Level through an International Research Collaboration.” Proceedings
of the IASE 2025 Satellite Conference - Statistics and Data Science Education
in STEAM, International Association for Statistics Education, 2026, doi:10.52041/iase25.138.'
short: 'A. Fergusson, S. Podworny, Y. Fleischer, S. Hüsing, M.S. Puloka, R. Biehler,
M. Pfannkuch, S. Budgett, M. Dalrymple, in: Proceedings of the IASE 2025 Satellite
Conference - Statistics and Data Science Education in STEAM, International Association
for Statistics Education, 2026.'
date_created: 2026-02-25T14:57:57Z
date_updated: 2026-02-25T14:58:49Z
department:
- _id: '67'
doi: 10.52041/iase25.138
language:
- iso: eng
publication: Proceedings of the IASE 2025 Satellite Conference - Statistics and Data
Science Education in STEAM
publication_status: published
publisher: International Association for Statistics Education
status: public
title: 'Branching out data science education: Developing task and computational environment
design principles for teaching data science at the high school level through an
international research collaboration'
type: conference
user_id: '58465'
year: '2026'
...
---
_id: '58353'
abstract:
- lang: eng
text: "Abstract\r\n Statistics and machine
learning are critical because they play an essential role in our everyday lives
and the careers we may pursue in the future. It may be beneficial to introduce
machine learning, such as decision trees (DTs), at an early stage of education.
The data-based construction of DTs is an example of a machine learning process,
which can be addressed in mathematics or statistics teaching because of relatively
low prior knowledge requirements. This paper focuses on investigating how sixth-grade
students create and evaluate data-based DTs. The basis is a teaching unit that
aims to lay the foundation for machine learning and enhance students’ understanding
of the process. We investigate students’ processes in detail while they build
DTs with data cards about food items to predict whether a new item is recommendable.
After the teaching unit, an interview study examines students’ strategies for
creating decision trees. The findings contribute to understanding students’ learning
processes and the challenges when working with decision trees."
author:
- first_name: Susanne
full_name: Podworny, Susanne
id: '30619'
last_name: Podworny
orcid: 0000-0002-6313-5987
- first_name: Rolf
full_name: Biehler, Rolf
id: '16274'
last_name: Biehler
- first_name: Yannik
full_name: Fleischer, Yannik
id: '42660'
last_name: Fleischer
orcid: https://orcid.org/0000-0003-0318-0329
citation:
ama: Podworny S, Biehler R, Fleischer Y. Young students’ engagement with data to
create decision trees. ZDM – Mathematics Education. Published online 2025.
doi:10.1007/s11858-024-01649-w
apa: Podworny, S., Biehler, R., & Fleischer, Y. (2025). Young students’ engagement
with data to create decision trees. ZDM – Mathematics Education. https://doi.org/10.1007/s11858-024-01649-w
bibtex: '@article{Podworny_Biehler_Fleischer_2025, title={Young students’ engagement
with data to create decision trees}, DOI={10.1007/s11858-024-01649-w},
journal={ZDM – Mathematics Education}, publisher={Springer Science and Business
Media LLC}, author={Podworny, Susanne and Biehler, Rolf and Fleischer, Yannik},
year={2025} }'
chicago: Podworny, Susanne, Rolf Biehler, and Yannik Fleischer. “Young Students’
Engagement with Data to Create Decision Trees.” ZDM – Mathematics Education,
2025. https://doi.org/10.1007/s11858-024-01649-w.
ieee: 'S. Podworny, R. Biehler, and Y. Fleischer, “Young students’ engagement with
data to create decision trees,” ZDM – Mathematics Education, 2025, doi:
10.1007/s11858-024-01649-w.'
mla: Podworny, Susanne, et al. “Young Students’ Engagement with Data to Create Decision
Trees.” ZDM – Mathematics Education, Springer Science and Business Media
LLC, 2025, doi:10.1007/s11858-024-01649-w.
short: S. Podworny, R. Biehler, Y. Fleischer, ZDM – Mathematics Education (2025).
date_created: 2025-01-24T07:55:53Z
date_updated: 2025-01-24T07:57:00Z
department:
- _id: '363'
doi: 10.1007/s11858-024-01649-w
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://link.springer.com/article/10.1007/s11858-024-01649-w
oa: '1'
publication: ZDM – Mathematics Education
publication_identifier:
issn:
- 1863-9690
- 1863-9704
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Young students’ engagement with data to create decision trees
type: journal_article
user_id: '37888'
year: '2025'
...
---
_id: '59622'
abstract:
- lang: eng
text: "Abstract\r\n This study explores
how high school students construct decision trees using data cards and the software
CODAP (codap.concord.org) in interviews after attending a teaching unit. We conceptualized
data-based decision tree construction using nine key aspects that we intended
to teach, tested variations of two design elements in teaching, and analyzed the
interviews qualitatively to compare student behavior to intended outcomes. We
found high alignment to intentions but also deviations in data activities and
informal or context-based rather than data-based reasoning. The design element
of context-free (blinded) data seems to enhance data-based reasoning, while the
design element of data card use showed diagnostic potential."
author:
- first_name: Yannik
full_name: Fleischer, Yannik
id: '42660'
last_name: Fleischer
orcid: https://orcid.org/0000-0003-0318-0329
- first_name: Rolf
full_name: Biehler, Rolf
id: '16274'
last_name: Biehler
citation:
ama: Fleischer Y, Biehler R. Exploring students’ constructions of data-based decision
trees after an introductory teaching unit on machine learning. ZDM – Mathematics
Education. 2025;57(1). doi:10.1007/s11858-025-01663-6
apa: Fleischer, Y., & Biehler, R. (2025). Exploring students’ constructions
of data-based decision trees after an introductory teaching unit on machine learning.
ZDM – Mathematics Education, 57(1). https://doi.org/10.1007/s11858-025-01663-6
bibtex: '@article{Fleischer_Biehler_2025, title={Exploring students’ constructions
of data-based decision trees after an introductory teaching unit on machine learning},
volume={57}, DOI={10.1007/s11858-025-01663-6},
number={1}, journal={ZDM – Mathematics Education}, publisher={Springer Science
and Business Media LLC}, author={Fleischer, Yannik and Biehler, Rolf}, year={2025}
}'
chicago: Fleischer, Yannik, and Rolf Biehler. “Exploring Students’ Constructions
of Data-Based Decision Trees after an Introductory Teaching Unit on Machine Learning.”
ZDM – Mathematics Education 57, no. 1 (2025). https://doi.org/10.1007/s11858-025-01663-6.
ieee: 'Y. Fleischer and R. Biehler, “Exploring students’ constructions of data-based
decision trees after an introductory teaching unit on machine learning,” ZDM
– Mathematics Education, vol. 57, no. 1, 2025, doi: 10.1007/s11858-025-01663-6.'
mla: Fleischer, Yannik, and Rolf Biehler. “Exploring Students’ Constructions of
Data-Based Decision Trees after an Introductory Teaching Unit on Machine Learning.”
ZDM – Mathematics Education, vol. 57, no. 1, Springer Science and Business
Media LLC, 2025, doi:10.1007/s11858-025-01663-6.
short: Y. Fleischer, R. Biehler, ZDM – Mathematics Education 57 (2025).
date_created: 2025-04-22T07:59:07Z
date_updated: 2025-04-22T08:00:59Z
department:
- _id: '363'
doi: 10.1007/s11858-025-01663-6
intvolume: ' 57'
issue: '1'
language:
- iso: eng
main_file_link:
- url: https://link.springer.com/article/10.1007/s11858-025-01663-6
publication: ZDM – Mathematics Education
publication_identifier:
issn:
- 1863-9690
- 1863-9704
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Exploring students’ constructions of data-based decision trees after an introductory
teaching unit on machine learning
type: journal_article
user_id: '37888'
volume: 57
year: '2025'
...
---
_id: '59053'
author:
- first_name: Daniel
full_name: Frischemeier, Daniel
last_name: Frischemeier
- first_name: Rolf
full_name: Biehler, Rolf
id: '16274'
last_name: Biehler
citation:
ama: 'Frischemeier D, Biehler R. Förderung von statistischem Denken im Mathematikunterricht
der Primarstufe: Bedeutsame Ideen und Förderungsmöglichkeiten. Stochastik in
der Schule. 2025;45(1):22-33.'
apa: 'Frischemeier, D., & Biehler, R. (2025). Förderung von statistischem Denken
im Mathematikunterricht der Primarstufe: Bedeutsame Ideen und Förderungsmöglichkeiten.
Stochastik in der Schule, 45(1), 22–33.'
bibtex: '@article{Frischemeier_Biehler_2025, title={Förderung von statistischem
Denken im Mathematikunterricht der Primarstufe: Bedeutsame Ideen und Förderungsmöglichkeiten},
volume={45}, number={1}, journal={Stochastik in der Schule}, author={Frischemeier,
Daniel and Biehler, Rolf}, year={2025}, pages={22–33} }'
chicago: 'Frischemeier, Daniel, and Rolf Biehler. “Förderung von statistischem Denken
im Mathematikunterricht der Primarstufe: Bedeutsame Ideen und Förderungsmöglichkeiten.”
Stochastik in der Schule 45, no. 1 (2025): 22–33.'
ieee: 'D. Frischemeier and R. Biehler, “Förderung von statistischem Denken im Mathematikunterricht
der Primarstufe: Bedeutsame Ideen und Förderungsmöglichkeiten,” Stochastik
in der Schule, vol. 45, no. 1, pp. 22–33, 2025.'
mla: 'Frischemeier, Daniel, and Rolf Biehler. “Förderung von statistischem Denken
im Mathematikunterricht der Primarstufe: Bedeutsame Ideen und Förderungsmöglichkeiten.”
Stochastik in der Schule, vol. 45, no. 1, 2025, pp. 22–33.'
short: D. Frischemeier, R. Biehler, Stochastik in der Schule 45 (2025) 22–33.
date_created: 2025-03-17T09:02:59Z
date_updated: 2025-03-17T09:03:05Z
department:
- _id: '363'
intvolume: ' 45'
issue: '1'
language:
- iso: ger
page: 22-33
publication: Stochastik in der Schule
status: public
title: 'Förderung von statistischem Denken im Mathematikunterricht der Primarstufe:
Bedeutsame Ideen und Förderungsmöglichkeiten'
type: journal_article
user_id: '37888'
volume: 45
year: '2025'
...
---
_id: '60351'
abstract:
- lang: eng
text: This article is a short summary of the report of survey team 3, presented
to the 15th International Congress on Mathematical Education (ICME-15) in Sydney
in July 2024.
author:
- first_name: Rolf
full_name: Biehler, Rolf
id: '16274'
last_name: Biehler
- first_name: Takashi
full_name: Kawakami, Takashi
last_name: Kawakami
- first_name: Erna
full_name: Lampen, Erna
last_name: Lampen
- first_name: Travis
full_name: Weiland, Travis
last_name: Weiland
- first_name: Lucía
full_name: Zapata-Cardona, Lucía
last_name: Zapata-Cardona
citation:
ama: Biehler R, Kawakami T, Lampen E, Weiland T, Zapata-Cardona L. Statistics and
data science education as a vehicle for empowering citizens – short summary of
a survey. European Mathematical Society Magazine. Published online 2025.
doi:10.4171/mag/257
apa: Biehler, R., Kawakami, T., Lampen, E., Weiland, T., & Zapata-Cardona, L.
(2025). Statistics and data science education as a vehicle for empowering citizens
– short summary of a survey. European Mathematical Society Magazine. https://doi.org/10.4171/mag/257
bibtex: '@article{Biehler_Kawakami_Lampen_Weiland_Zapata-Cardona_2025, title={Statistics
and data science education as a vehicle for empowering citizens – short summary
of a survey}, DOI={10.4171/mag/257},
journal={European Mathematical Society Magazine}, publisher={European Mathematical
Society - EMS - Publishing House GmbH}, author={Biehler, Rolf and Kawakami, Takashi
and Lampen, Erna and Weiland, Travis and Zapata-Cardona, Lucía}, year={2025} }'
chicago: Biehler, Rolf, Takashi Kawakami, Erna Lampen, Travis Weiland, and Lucía
Zapata-Cardona. “Statistics and Data Science Education as a Vehicle for Empowering
Citizens – Short Summary of a Survey.” European Mathematical Society Magazine,
2025. https://doi.org/10.4171/mag/257.
ieee: 'R. Biehler, T. Kawakami, E. Lampen, T. Weiland, and L. Zapata-Cardona, “Statistics
and data science education as a vehicle for empowering citizens – short summary
of a survey,” European Mathematical Society Magazine, 2025, doi: 10.4171/mag/257.'
mla: Biehler, Rolf, et al. “Statistics and Data Science Education as a Vehicle for
Empowering Citizens – Short Summary of a Survey.” European Mathematical Society
Magazine, European Mathematical Society - EMS - Publishing House GmbH, 2025,
doi:10.4171/mag/257.
short: R. Biehler, T. Kawakami, E. Lampen, T. Weiland, L. Zapata-Cardona, European
Mathematical Society Magazine (2025).
date_created: 2025-06-24T06:58:17Z
date_updated: 2025-06-24T06:59:42Z
department:
- _id: '363'
doi: 10.4171/mag/257
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.4171/MAG/257
oa: '1'
publication: European Mathematical Society Magazine
publication_identifier:
issn:
- 2747-7894
- 2747-7908
publication_status: published
publisher: European Mathematical Society - EMS - Publishing House GmbH
status: public
title: Statistics and data science education as a vehicle for empowering citizens
– short summary of a survey
type: journal_article
user_id: '37888'
year: '2025'
...
---
_id: '60495'
author:
- first_name: Susanne
full_name: Podworny, Susanne
id: '30619'
last_name: Podworny
orcid: 0000-0002-6313-5987
- first_name: Yannik
full_name: Fleischer, Yannik
id: '42660'
last_name: Fleischer
orcid: https://orcid.org/0000-0003-0318-0329
- first_name: Rolf
full_name: Biehler, Rolf
id: '16274'
last_name: Biehler
citation:
ama: Podworny S, Fleischer Y, Biehler R. Explorative Datenanalyse in der Schule
– Analyse der Mediennutzung von Jugendlichen mit den YOU‑PB Daten. Stochastik
in der Schule. 2025;45(2):9-16.
apa: Podworny, S., Fleischer, Y., & Biehler, R. (2025). Explorative Datenanalyse
in der Schule – Analyse der Mediennutzung von Jugendlichen mit den YOU‑PB Daten.
Stochastik in der Schule, 45(2), 9–16.
bibtex: '@article{Podworny_Fleischer_Biehler_2025, title={Explorative Datenanalyse
in der Schule – Analyse der Mediennutzung von Jugendlichen mit den YOU‑PB Daten},
volume={45}, number={2}, journal={Stochastik in der Schule}, author={Podworny,
Susanne and Fleischer, Yannik and Biehler, Rolf}, year={2025}, pages={9–16} }'
chicago: 'Podworny, Susanne, Yannik Fleischer, and Rolf Biehler. “Explorative Datenanalyse
in der Schule – Analyse der Mediennutzung von Jugendlichen mit den YOU‑PB Daten.”
Stochastik in der Schule 45, no. 2 (2025): 9–16.'
ieee: S. Podworny, Y. Fleischer, and R. Biehler, “Explorative Datenanalyse in der
Schule – Analyse der Mediennutzung von Jugendlichen mit den YOU‑PB Daten,” Stochastik
in der Schule, vol. 45, no. 2, pp. 9–16, 2025.
mla: Podworny, Susanne, et al. “Explorative Datenanalyse in der Schule – Analyse
der Mediennutzung von Jugendlichen mit den YOU‑PB Daten.” Stochastik in der
Schule, vol. 45, no. 2, 2025, pp. 9–16.
short: S. Podworny, Y. Fleischer, R. Biehler, Stochastik in der Schule 45 (2025)
9–16.
date_created: 2025-07-02T09:45:14Z
date_updated: 2025-07-02T09:45:22Z
department:
- _id: '363'
intvolume: ' 45'
issue: '2'
language:
- iso: ger
page: 9-16
publication: Stochastik in der Schule
publication_status: published
status: public
title: Explorative Datenanalyse in der Schule – Analyse der Mediennutzung von Jugendlichen
mit den YOU‑PB Daten
type: journal_article
user_id: '37888'
volume: 45
year: '2025'
...
---
_id: '60532'
author:
- first_name: Rolf
full_name: Biehler, Rolf
id: '16274'
last_name: Biehler
- first_name: Carsten
full_name: Schulte, Carsten
id: '60311'
last_name: Schulte
citation:
ama: 'Biehler R, Schulte C. Lessons Learned from the ProDaBi Project: Shaping Perspectives
at the Intersection of Data, AI, and Education Towards Fostering AI and Data Science
Literacy in Schools Across Disciplines. In: Proceedings of the 1st Symposium
on Integrating AI and Data Science into School Education Across Disciplines (AIDEA
1 2025), Salzburg, Austria. ; 2025.'
apa: 'Biehler, R., & Schulte, C. (2025). Lessons Learned from the ProDaBi Project:
Shaping Perspectives at the Intersection of Data, AI, and Education Towards Fostering
AI and Data Science Literacy in Schools Across Disciplines. In Proceedings
of the 1st Symposium on Integrating AI and Data Science into School Education
Across Disciplines (AIDEA 1 2025), Salzburg, Austria.'
bibtex: '@inbook{Biehler_Schulte_2025, title={Lessons Learned from the ProDaBi Project:
Shaping Perspectives at the Intersection of Data, AI, and Education Towards Fostering
AI and Data Science Literacy in Schools Across Disciplines.}, booktitle={Proceedings
of the 1st Symposium on Integrating AI and Data Science into School Education
Across Disciplines (AIDEA 1 2025), Salzburg, Austria}, author={Biehler, Rolf and
Schulte, Carsten}, year={2025} }'
chicago: 'Biehler, Rolf, and Carsten Schulte. “Lessons Learned from the ProDaBi
Project: Shaping Perspectives at the Intersection of Data, AI, and Education Towards
Fostering AI and Data Science Literacy in Schools Across Disciplines.” In Proceedings
of the 1st Symposium on Integrating AI and Data Science into School Education
Across Disciplines (AIDEA 1 2025), Salzburg, Austria, 2025.'
ieee: 'R. Biehler and C. Schulte, “Lessons Learned from the ProDaBi Project: Shaping
Perspectives at the Intersection of Data, AI, and Education Towards Fostering
AI and Data Science Literacy in Schools Across Disciplines.,” in Proceedings
of the 1st Symposium on Integrating AI and Data Science into School Education
Across Disciplines (AIDEA 1 2025), Salzburg, Austria, 2025.'
mla: 'Biehler, Rolf, and Carsten Schulte. “Lessons Learned from the ProDaBi Project:
Shaping Perspectives at the Intersection of Data, AI, and Education Towards Fostering
AI and Data Science Literacy in Schools Across Disciplines.” Proceedings of
the 1st Symposium on Integrating AI and Data Science into School Education Across
Disciplines (AIDEA 1 2025), Salzburg, Austria, 2025.'
short: 'R. Biehler, C. Schulte, in: Proceedings of the 1st Symposium on Integrating
AI and Data Science into School Education Across Disciplines (AIDEA 1 2025), Salzburg,
Austria, 2025.'
date_created: 2025-07-07T07:24:30Z
date_updated: 2025-07-07T07:24:35Z
department:
- _id: '363'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://openreview.net/forum?id=TGsuaghKD3
oa: '1'
publication: Proceedings of the 1st Symposium on Integrating AI and Data Science into
School Education Across Disciplines (AIDEA 1 2025), Salzburg, Austria
status: public
title: 'Lessons Learned from the ProDaBi Project: Shaping Perspectives at the Intersection
of Data, AI, and Education Towards Fostering AI and Data Science Literacy in Schools
Across Disciplines.'
type: book_chapter
user_id: '37888'
year: '2025'
...
---
_id: '60860'
author:
- first_name: Franz Yannik
full_name: Fleischer, Franz Yannik
id: '42660'
last_name: Fleischer
orcid: https://orcid.org/0000-0003-0318-0329
- first_name: Rolf
full_name: Biehler, Rolf
id: '16274'
last_name: Biehler
citation:
ama: 'Fleischer FY, Biehler R. ANALYZING STUDENTS’INFORMAL APPROACHES TO CREATING
DECISION TREES IN THE CLASSROOM. In: Cornejo C, Felmer P, Gomez DM, et al., eds.
Proceedings of the 48th Conference of the International Group for the Psychology
of Mathematics Education: Research Reports, Vol. 1 . ; 2025:267-274.'
apa: 'Fleischer, F. Y., & Biehler, R. (2025). ANALYZING STUDENTS’INFORMAL APPROACHES
TO CREATING DECISION TREES IN THE CLASSROOM. In C. Cornejo, P. Felmer, D. M. Gomez,
P. Dartnell, P. Araya, A. Peri, & V. Randolph (Eds.), Proceedings of the
48th Conference of the International Group for the Psychology of Mathematics Education:
Research Reports, Vol. 1 (pp. 267–274).'
bibtex: '@inproceedings{Fleischer_Biehler_2025, title={ANALYZING STUDENTS’INFORMAL
APPROACHES TO CREATING DECISION TREES IN THE CLASSROOM}, booktitle={Proceedings
of the 48th Conference of the International Group for the Psychology of Mathematics
Education: Research Reports, Vol. 1 }, author={Fleischer, Franz Yannik and Biehler,
Rolf}, editor={Cornejo, C. and Felmer, P. and Gomez, D.M. and Dartnell, P. and
Araya, P. and Peri, A. and Randolph, V.}, year={2025}, pages={267–274} }'
chicago: 'Fleischer, Franz Yannik, and Rolf Biehler. “ANALYZING STUDENTS’INFORMAL
APPROACHES TO CREATING DECISION TREES IN THE CLASSROOM.” In Proceedings of
the 48th Conference of the International Group for the Psychology of Mathematics
Education: Research Reports, Vol. 1 , edited by C. Cornejo, P. Felmer, D.M.
Gomez, P. Dartnell, P. Araya, A. Peri, and V. Randolph, 267–74, 2025.'
ieee: 'F. Y. Fleischer and R. Biehler, “ANALYZING STUDENTS’INFORMAL APPROACHES TO
CREATING DECISION TREES IN THE CLASSROOM,” in Proceedings of the 48th Conference
of the International Group for the Psychology of Mathematics Education: Research
Reports, Vol. 1 , 2025, pp. 267–274.'
mla: 'Fleischer, Franz Yannik, and Rolf Biehler. “ANALYZING STUDENTS’INFORMAL APPROACHES
TO CREATING DECISION TREES IN THE CLASSROOM.” Proceedings of the 48th Conference
of the International Group for the Psychology of Mathematics Education: Research
Reports, Vol. 1 , edited by C. Cornejo et al., 2025, pp. 267–74.'
short: 'F.Y. Fleischer, R. Biehler, in: C. Cornejo, P. Felmer, D.M. Gomez, P. Dartnell,
P. Araya, A. Peri, V. Randolph (Eds.), Proceedings of the 48th Conference of the
International Group for the Psychology of Mathematics Education: Research Reports,
Vol. 1 , 2025, pp. 267–274.'
date_created: 2025-08-04T07:15:39Z
date_updated: 2025-08-04T07:17:59Z
department:
- _id: '363'
editor:
- first_name: C.
full_name: Cornejo, C.
last_name: Cornejo
- first_name: P.
full_name: Felmer, P.
last_name: Felmer
- first_name: D.M.
full_name: Gomez, D.M.
last_name: Gomez
- first_name: P.
full_name: Dartnell, P.
last_name: Dartnell
- first_name: P.
full_name: Araya, P.
last_name: Araya
- first_name: A.
full_name: Peri, A.
last_name: Peri
- first_name: V.
full_name: Randolph, V.
last_name: Randolph
language:
- iso: eng
page: 267-274
publication: 'Proceedings of the 48th Conference of the International Group for the
Psychology of Mathematics Education: Research Reports, Vol. 1 '
status: public
title: ANALYZING STUDENTS’INFORMAL APPROACHES TO CREATING DECISION TREES IN THE CLASSROOM
type: conference
user_id: '37888'
year: '2025'
...
---
_id: '61125'
author:
- first_name: Rolf
full_name: Biehler, Rolf
id: '16274'
last_name: Biehler
- first_name: Michael
full_name: Liebendörfer, Michael
last_name: Liebendörfer
- first_name: Angela
full_name: Schmitz, Angela
last_name: Schmitz
- first_name: Birte
full_name: Reich, Birte
last_name: Reich
citation:
ama: Biehler R, Liebendörfer M, Schmitz A, Reich B. studiVEMINT Mathematik-Online-Vorkurs
jetzt mit 300 integrierten Lernvideos frei verfügbar. Mitteilungen der Deutschen
Mathematiker-Vereinigung. 2025;33(3):170–171.
apa: Biehler, R., Liebendörfer, M., Schmitz, A., & Reich, B. (2025). studiVEMINT
Mathematik-Online-Vorkurs jetzt mit 300 integrierten Lernvideos frei verfügbar.
Mitteilungen der Deutschen Mathematiker-Vereinigung, 33(3), 170–171.
bibtex: '@article{Biehler_Liebendörfer_Schmitz_Reich_2025, title={studiVEMINT Mathematik-Online-Vorkurs
jetzt mit 300 integrierten Lernvideos frei verfügbar}, volume={33}, number={3},
journal={Mitteilungen der Deutschen Mathematiker-Vereinigung}, publisher={De Gruyter},
author={Biehler, Rolf and Liebendörfer, Michael and Schmitz, Angela and Reich,
Birte}, year={2025}, pages={170–171} }'
chicago: 'Biehler, Rolf, Michael Liebendörfer, Angela Schmitz, and Birte Reich.
“studiVEMINT Mathematik-Online-Vorkurs jetzt mit 300 integrierten Lernvideos frei
verfügbar.” Mitteilungen der Deutschen Mathematiker-Vereinigung 33, no.
3 (2025): 170–171.'
ieee: R. Biehler, M. Liebendörfer, A. Schmitz, and B. Reich, “studiVEMINT Mathematik-Online-Vorkurs
jetzt mit 300 integrierten Lernvideos frei verfügbar,” Mitteilungen der Deutschen
Mathematiker-Vereinigung, vol. 33, no. 3, pp. 170–171, 2025.
mla: Biehler, Rolf, et al. “studiVEMINT Mathematik-Online-Vorkurs jetzt mit 300
integrierten Lernvideos frei verfügbar.” Mitteilungen der Deutschen Mathematiker-Vereinigung,
vol. 33, no. 3, De Gruyter, 2025, pp. 170–171.
short: R. Biehler, M. Liebendörfer, A. Schmitz, B. Reich, Mitteilungen der Deutschen
Mathematiker-Vereinigung 33 (2025) 170–171.
date_created: 2025-09-04T09:23:47Z
date_updated: 2025-09-04T09:25:03Z
department:
- _id: '363'
intvolume: ' 33'
issue: '3'
language:
- iso: ger
main_file_link:
- open_access: '1'
url: https://doi.org/10.1515/dmvm-2025-0053
oa: '1'
page: 170–171
publication: Mitteilungen der Deutschen Mathematiker-Vereinigung
publication_status: published
publisher: De Gruyter
status: public
title: studiVEMINT Mathematik-Online-Vorkurs jetzt mit 300 integrierten Lernvideos
frei verfügbar
type: journal_article
user_id: '37888'
volume: 33
year: '2025'
...
---
_id: '63556'
author:
- first_name: Rolf
full_name: Biehler, Rolf
id: '16274'
last_name: Biehler
- first_name: Joachim
full_name: Engel, Joachim
last_name: Engel
- first_name: Daniel
full_name: Frischemeier, Daniel
last_name: Frischemeier
- first_name: Susanne
full_name: Podworny, Susanne
last_name: Podworny
citation:
ama: 'Biehler R, Engel J, Frischemeier D, Podworny S. Civic Statistical Literacy:
Konzept und praxisnahe Umsetzung am Beispiel des Klimawandels. mathematica
didactica. 2025;48(2). doi:10.18716/ojs/md/2025.2297'
apa: 'Biehler, R., Engel, J., Frischemeier, D., & Podworny, S. (2025). Civic
Statistical Literacy: Konzept und praxisnahe Umsetzung am Beispiel des Klimawandels.
mathematica didactica, 48(2). https://doi.org/10.18716/ojs/md/2025.2297'
bibtex: '@article{Biehler_Engel_Frischemeier_Podworny_2025, title={Civic Statistical
Literacy: Konzept und praxisnahe Umsetzung am Beispiel des Klimawandels}, volume={48},
DOI={10.18716/ojs/md/2025.2297},
number={2}, journal={mathematica didactica}, author={Biehler, Rolf and Engel,
Joachim and Frischemeier, Daniel and Podworny, Susanne}, year={2025} }'
chicago: 'Biehler, Rolf, Joachim Engel, Daniel Frischemeier, and Susanne Podworny.
“Civic Statistical Literacy: Konzept und praxisnahe Umsetzung am Beispiel des
Klimawandels.” mathematica didactica 48, no. 2 (2025). https://doi.org/10.18716/ojs/md/2025.2297.'
ieee: 'R. Biehler, J. Engel, D. Frischemeier, and S. Podworny, “Civic Statistical
Literacy: Konzept und praxisnahe Umsetzung am Beispiel des Klimawandels,” mathematica
didactica, vol. 48, no. 2, 2025, doi: 10.18716/ojs/md/2025.2297.'
mla: 'Biehler, Rolf, et al. “Civic Statistical Literacy: Konzept und praxisnahe
Umsetzung am Beispiel des Klimawandels.” mathematica didactica, vol. 48,
no. 2, 2025, doi:10.18716/ojs/md/2025.2297.'
short: R. Biehler, J. Engel, D. Frischemeier, S. Podworny, mathematica didactica
48 (2025).
date_created: 2026-01-12T11:23:57Z
date_updated: 2026-01-12T11:26:40Z
department:
- _id: '363'
doi: 10.18716/ojs/md/2025.2297
intvolume: ' 48'
issue: '2'
language:
- iso: ger
main_file_link:
- open_access: '1'
url: https://journals.ub.uni-koeln.de/index.php/mathematica_didactica/article/view/2297
oa: '1'
publication: mathematica didactica
status: public
title: 'Civic Statistical Literacy: Konzept und praxisnahe Umsetzung am Beispiel des
Klimawandels'
type: journal_article
user_id: '37888'
volume: 48
year: '2025'
...
---
_id: '54144'
abstract:
- lang: eng
text: "AbstractIn this paper, we propose a novel
conceptual framework tailored for modeling the meaning of mathematical concepts
in university-level mathematics, addressing their rigorous nature and their relationships
with related concepts as well as interpretations in various contexts. Within this
framework, we present a model of meaning for the concepts of total differentiability
and total derivative that provides a variety of possible interpretations and aspects.
We then use the proposed model of meaning as a tool for analyzing three different
textbooks for mathematics majors on the topic of multidimensional differentiability.
\uFEFFOur paper is an example of a subject matter analysis of a topic in university
mathematics carried out in a structured way. The model of meaning for total differentiability
presented in this paper could inspire course design and analysis including the
design of assignments and assessments for students. Moreover, it could serve as
a valuable research tool for further analyses. For example, it could be used as
a framework for analyzing courses taught or as a basis for developing a test instrument
to assess students’ understanding. With our textbook analysis, we begin to examine
the landscape of textbooks regarding differentiability concepts in the multidimensional
case, shedding light on the diversity of meaning facets that are covered in the
textbooks. These results could be useful for guiding instructors and learners
in selecting and using textbooks for teaching and learning based on their respective
needs."
author:
- first_name: Elisa
full_name: Lankeit, Elisa
last_name: Lankeit
- first_name: Rolf
full_name: Biehler, Rolf
id: '16274'
last_name: Biehler
citation:
ama: 'Lankeit E, Biehler R. The meaning landscape of the concept of the total derivative
in multivariable real analysis textbooks: an analysis based on a new model of
meaning. ZDM – Mathematics Education. Published online 2024. doi:10.1007/s11858-024-01584-w'
apa: 'Lankeit, E., & Biehler, R. (2024). The meaning landscape of the concept
of the total derivative in multivariable real analysis textbooks: an analysis
based on a new model of meaning. ZDM – Mathematics Education. https://doi.org/10.1007/s11858-024-01584-w'
bibtex: '@article{Lankeit_Biehler_2024, title={The meaning landscape of the concept
of the total derivative in multivariable real analysis textbooks: an analysis
based on a new model of meaning}, DOI={10.1007/s11858-024-01584-w},
journal={ZDM – Mathematics Education}, publisher={Springer Science and Business
Media LLC}, author={Lankeit, Elisa and Biehler, Rolf}, year={2024} }'
chicago: 'Lankeit, Elisa, and Rolf Biehler. “The Meaning Landscape of the Concept
of the Total Derivative in Multivariable Real Analysis Textbooks: An Analysis
Based on a New Model of Meaning.” ZDM – Mathematics Education, 2024. https://doi.org/10.1007/s11858-024-01584-w.'
ieee: 'E. Lankeit and R. Biehler, “The meaning landscape of the concept of the total
derivative in multivariable real analysis textbooks: an analysis based on a new
model of meaning,” ZDM – Mathematics Education, 2024, doi: 10.1007/s11858-024-01584-w.'
mla: 'Lankeit, Elisa, and Rolf Biehler. “The Meaning Landscape of the Concept of
the Total Derivative in Multivariable Real Analysis Textbooks: An Analysis Based
on a New Model of Meaning.” ZDM – Mathematics Education, Springer Science
and Business Media LLC, 2024, doi:10.1007/s11858-024-01584-w.'
short: E. Lankeit, R. Biehler, ZDM – Mathematics Education (2024).
date_created: 2024-05-10T07:48:10Z
date_updated: 2024-05-10T07:49:19Z
department:
- _id: '363'
doi: 10.1007/s11858-024-01584-w
language:
- iso: eng
publication: ZDM – Mathematics Education
publication_identifier:
issn:
- 1863-9690
- 1863-9704
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: 'The meaning landscape of the concept of the total derivative in multivariable
real analysis textbooks: an analysis based on a new model of meaning'
type: journal_article
user_id: '37888'
year: '2024'
...
---
_id: '55667'
abstract:
- lang: eng
text: This study investigates how 11- to 12-year-old students construct
data-based decision trees using data cards for classification purposes. We examine
the students' heuristics and reasoning during this process. The research is based
on an eight-week teaching unit during which students labeled data, built decision
trees, and assessed them using test data. They learned to manually construct decision
trees to classify food items as recommendable or not. They utilized data cards
with a heuristic that is a simplified form of a machine learning algorithm. We
report on evidence that this topic is teachable to middle school students, along
with insights for refining our teaching approach and broader implications for
teaching machine learning at the school level.
article_number: '3'
author:
- first_name: Franz Yannik
full_name: Fleischer, Franz Yannik
id: '42660'
last_name: Fleischer
orcid: https://orcid.org/0000-0003-0318-0329
- first_name: Susanne
full_name: Podworny, Susanne
id: '30619'
last_name: Podworny
orcid: 0000-0002-6313-5987
- first_name: Rolf
full_name: Biehler, Rolf
id: '16274'
last_name: Biehler
citation:
ama: Fleischer FY, Podworny S, Biehler R. Teaching and Learning to Construct Data-Based
Decision Trees Using Data Cards as the First Introduction to Machine Learning
in Middle School. Statistics Education Research Journal. 2024;23(1). doi:10.52041/serj.v23i1.450
apa: Fleischer, F. Y., Podworny, S., & Biehler, R. (2024). Teaching and Learning
to Construct Data-Based Decision Trees Using Data Cards as the First Introduction
to Machine Learning in Middle School. Statistics Education Research Journal,
23(1), Article 3. https://doi.org/10.52041/serj.v23i1.450
bibtex: '@article{Fleischer_Podworny_Biehler_2024, title={Teaching and Learning
to Construct Data-Based Decision Trees Using Data Cards as the First Introduction
to Machine Learning in Middle School}, volume={23}, DOI={10.52041/serj.v23i1.450},
number={13}, journal={Statistics Education Research Journal}, publisher={International
Association for Statistical Education}, author={Fleischer, Franz Yannik and Podworny,
Susanne and Biehler, Rolf}, year={2024} }'
chicago: Fleischer, Franz Yannik, Susanne Podworny, and Rolf Biehler. “Teaching
and Learning to Construct Data-Based Decision Trees Using Data Cards as the First
Introduction to Machine Learning in Middle School.” Statistics Education Research
Journal 23, no. 1 (2024). https://doi.org/10.52041/serj.v23i1.450.
ieee: 'F. Y. Fleischer, S. Podworny, and R. Biehler, “Teaching and Learning to Construct
Data-Based Decision Trees Using Data Cards as the First Introduction to Machine
Learning in Middle School,” Statistics Education Research Journal, vol.
23, no. 1, Art. no. 3, 2024, doi: 10.52041/serj.v23i1.450.'
mla: Fleischer, Franz Yannik, et al. “Teaching and Learning to Construct Data-Based
Decision Trees Using Data Cards as the First Introduction to Machine Learning
in Middle School.” Statistics Education Research Journal, vol. 23, no.
1, 3, International Association for Statistical Education, 2024, doi:10.52041/serj.v23i1.450.
short: F.Y. Fleischer, S. Podworny, R. Biehler, Statistics Education Research Journal
23 (2024).
date_created: 2024-08-21T09:59:33Z
date_updated: 2024-08-21T10:02:38Z
department:
- _id: '363'
doi: 10.52041/serj.v23i1.450
intvolume: ' 23'
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.52041/serj.v23i1.450
oa: '1'
publication: Statistics Education Research Journal
publication_identifier:
issn:
- 1570-1824
publication_status: published
publisher: International Association for Statistical Education
status: public
title: Teaching and Learning to Construct Data-Based Decision Trees Using Data Cards
as the First Introduction to Machine Learning in Middle School
type: journal_article
user_id: '37888'
volume: 23
year: '2024'
...
---
_id: '55756'
author:
- first_name: Rolf
full_name: Biehler, Rolf
id: '16274'
last_name: Biehler
- first_name: Daniel
full_name: Frischemeier, Daniel
last_name: Frischemeier
citation:
ama: 'Biehler R, Frischemeier D. Eine inklusive Lehr-Lernumgebung für die Leitidee
„Daten und Zufall“ in der Primarstufe. In: Inklusives Lehren und Lernen von
Mathematik. Springer Fachmedien Wiesbaden; 2024. doi:10.1007/978-3-658-43964-4_13'
apa: Biehler, R., & Frischemeier, D. (2024). Eine inklusive Lehr-Lernumgebung
für die Leitidee „Daten und Zufall“ in der Primarstufe. In Inklusives Lehren
und Lernen von Mathematik. Springer Fachmedien Wiesbaden. https://doi.org/10.1007/978-3-658-43964-4_13
bibtex: '@inbook{Biehler_Frischemeier_2024, place={Wiesbaden}, title={Eine inklusive
Lehr-Lernumgebung für die Leitidee „Daten und Zufall“ in der Primarstufe}, DOI={10.1007/978-3-658-43964-4_13},
booktitle={Inklusives Lehren und Lernen von Mathematik}, publisher={Springer Fachmedien
Wiesbaden}, author={Biehler, Rolf and Frischemeier, Daniel}, year={2024} }'
chicago: 'Biehler, Rolf, and Daniel Frischemeier. “Eine inklusive Lehr-Lernumgebung
für die Leitidee „Daten und Zufall“ in der Primarstufe.” In Inklusives Lehren
und Lernen von Mathematik. Wiesbaden: Springer Fachmedien Wiesbaden, 2024.
https://doi.org/10.1007/978-3-658-43964-4_13.'
ieee: 'R. Biehler and D. Frischemeier, “Eine inklusive Lehr-Lernumgebung für die
Leitidee „Daten und Zufall“ in der Primarstufe,” in Inklusives Lehren und Lernen
von Mathematik, Wiesbaden: Springer Fachmedien Wiesbaden, 2024.'
mla: Biehler, Rolf, and Daniel Frischemeier. “Eine inklusive Lehr-Lernumgebung für
die Leitidee „Daten und Zufall“ in der Primarstufe.” Inklusives Lehren und
Lernen von Mathematik, Springer Fachmedien Wiesbaden, 2024, doi:10.1007/978-3-658-43964-4_13.
short: 'R. Biehler, D. Frischemeier, in: Inklusives Lehren und Lernen von Mathematik,
Springer Fachmedien Wiesbaden, Wiesbaden, 2024.'
date_created: 2024-08-26T09:18:57Z
date_updated: 2024-08-26T09:33:50Z
department:
- _id: '363'
doi: 10.1007/978-3-658-43964-4_13
language:
- iso: ger
main_file_link:
- open_access: '1'
url: https://doi.org/10.1007/978-3-658-43964-4_13
oa: '1'
place: Wiesbaden
publication: Inklusives Lehren und Lernen von Mathematik
publication_identifier:
isbn:
- '9783658439637'
- '9783658439644'
publication_status: published
publisher: Springer Fachmedien Wiesbaden
status: public
title: Eine inklusive Lehr-Lernumgebung für die Leitidee „Daten und Zufall“ in der
Primarstufe
type: book_chapter
user_id: '37888'
year: '2024'
...
---
_id: '55758'
author:
- first_name: Rolf
full_name: Biehler, Rolf
id: '16274'
last_name: Biehler
- first_name: Daniel
full_name: Frischemeier, Daniel
last_name: Frischemeier
citation:
ama: 'Biehler R, Frischemeier D. Daten-Spürnasen Auf Spurensuche: Datenanalyse
in Der Grundschule Mit Digitalen Werkzeugen. Klett Kallmeyer; 2024.'
apa: 'Biehler, R., & Frischemeier, D. (2024). Daten-Spürnasen auf Spurensuche:
Datenanalyse in der Grundschule mit digitalen Werkzeugen. Klett Kallmeyer.'
bibtex: '@book{Biehler_Frischemeier_2024, title={Daten-Spürnasen auf Spurensuche:
Datenanalyse in der Grundschule mit digitalen Werkzeugen}, publisher={Klett Kallmeyer},
author={Biehler, Rolf and Frischemeier, Daniel}, year={2024} }'
chicago: 'Biehler, Rolf, and Daniel Frischemeier. Daten-Spürnasen Auf Spurensuche:
Datenanalyse in Der Grundschule Mit Digitalen Werkzeugen. Klett Kallmeyer,
2024.'
ieee: 'R. Biehler and D. Frischemeier, Daten-Spürnasen auf Spurensuche: Datenanalyse
in der Grundschule mit digitalen Werkzeugen. Klett Kallmeyer, 2024.'
mla: 'Biehler, Rolf, and Daniel Frischemeier. Daten-Spürnasen Auf Spurensuche:
Datenanalyse in Der Grundschule Mit Digitalen Werkzeugen. Klett Kallmeyer,
2024.'
short: 'R. Biehler, D. Frischemeier, Daten-Spürnasen Auf Spurensuche: Datenanalyse
in Der Grundschule Mit Digitalen Werkzeugen, Klett Kallmeyer, 2024.'
date_created: 2024-08-26T09:38:05Z
date_updated: 2024-08-26T09:38:17Z
department:
- _id: '363'
language:
- iso: eng
publisher: Klett Kallmeyer
status: public
title: 'Daten-Spürnasen auf Spurensuche: Datenanalyse in der Grundschule mit digitalen
Werkzeugen'
type: book
user_id: '37888'
year: '2024'
...
---
_id: '56016'
abstract:
- lang: eng
text: AbstractSpecial tasks for pre-service teachers
(PSTs) in university mathematics courses (“interface tasks”) are a common innovation
in recent years to overcome the second discontinuity. By this, we mean tasks that
are situated by typical everyday challenges of mathematics teaching and in which
PSTs must use their mathematical knowledge and skills in a professionally relevant
way. In this paper, we analyze answers that PSTs have created to an interface
task on symmetry. The PSTs were asked to clarify a student’s question from a mathematical
perspective and then give a suitable elementarized answer. We situate these two
steps theoretically and reconstruct the mathematical reasoning in PSTs' answers.
Through qualitative content analysis, we examined how PSTs justify figures' symmetries
from a university mathematics perspective and when responding to the fictitious
student. The scenario of a student questioning the existence of 100° rotationally
symmetrical figures elicited rich and varied responses, proving suitable for an
interface task. We compared PSTs' reasoning related to mathematical clarification
with the reasoning related to elementarization. In many cases, this revealed a
productive use of course content. An interesting result is that there is no uniform
picture as to whether the arguments are more detailed in the mathematical clarification
or in the elementarization.
article_type: original
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. Using academic mathematical knowledge when working on
interface tasks–analyses of pre-service teachers’ arguments about rotationally
symmetric figures. ZDM – Mathematics Education. Published online 2024.
doi:10.1007/s11858-024-01633-4
apa: Hoffmann, M., & Biehler, R. (2024). Using academic mathematical knowledge
when working on interface tasks–analyses of pre-service teachers’ arguments about
rotationally symmetric figures. ZDM – Mathematics Education. https://doi.org/10.1007/s11858-024-01633-4
bibtex: '@article{Hoffmann_Biehler_2024, title={Using academic mathematical knowledge
when working on interface tasks–analyses of pre-service teachers’ arguments about
rotationally symmetric figures}, DOI={10.1007/s11858-024-01633-4},
journal={ZDM – Mathematics Education}, publisher={Springer Science and Business
Media LLC}, author={Hoffmann, Max and Biehler, Rolf}, year={2024} }'
chicago: Hoffmann, Max, and Rolf Biehler. “Using Academic Mathematical Knowledge
When Working on Interface Tasks–Analyses of Pre-Service Teachers’ Arguments about
Rotationally Symmetric Figures.” ZDM – Mathematics Education, 2024. https://doi.org/10.1007/s11858-024-01633-4.
ieee: 'M. Hoffmann and R. Biehler, “Using academic mathematical knowledge when working
on interface tasks–analyses of pre-service teachers’ arguments about rotationally
symmetric figures,” ZDM – Mathematics Education, 2024, doi: 10.1007/s11858-024-01633-4.'
mla: Hoffmann, Max, and Rolf Biehler. “Using Academic Mathematical Knowledge When
Working on Interface Tasks–Analyses of Pre-Service Teachers’ Arguments about Rotationally
Symmetric Figures.” ZDM – Mathematics Education, Springer Science and Business
Media LLC, 2024, doi:10.1007/s11858-024-01633-4.
short: M. Hoffmann, R. Biehler, ZDM – Mathematics Education (2024).
date_created: 2024-09-04T09:32:26Z
date_updated: 2024-09-04T09:33:45Z
department:
- _id: '97'
- _id: '643'
doi: 10.1007/s11858-024-01633-4
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://link.springer.com/content/pdf/10.1007/s11858-024-01633-4.pdf
oa: '1'
publication: ZDM – Mathematics Education
publication_identifier:
issn:
- 1863-9690
- 1863-9704
publication_status: published
publisher: Springer Science and Business Media LLC
quality_controlled: '1'
status: public
title: Using academic mathematical knowledge when working on interface tasks–analyses
of pre-service teachers’ arguments about rotationally symmetric figures
type: journal_article
user_id: '32202'
year: '2024'
...
---
_id: '56197'
abstract:
- lang: eng
text: AbstractSpecial tasks for pre-service teachers
(PSTs) in university mathematics courses (“interface tasks”) are a common innovation
in recent years to overcome the second discontinuity. By this, we mean tasks that
are situated by typical everyday challenges of mathematics teaching and in which
PSTs must use their mathematical knowledge and skills in a professionally relevant
way. In this paper, we analyze answers that PSTs have created to an interface
task on symmetry. The PSTs were asked to clarify a student’s question from a mathematical
perspective and then give a suitable elementarized answer. We situate these two
steps theoretically and reconstruct the mathematical reasoning in PSTs' answers.
Through qualitative content analysis, we examined how PSTs justify figures' symmetries
from a university mathematics perspective and when responding to the fictitious
student. The scenario of a student questioning the existence of 100° rotationally
symmetrical figures elicited rich and varied responses, proving suitable for an
interface task. We compared PSTs' reasoning related to mathematical clarification
with the reasoning related to elementarization. In many cases, this revealed a
productive use of course content. An interesting result is that there is no uniform
picture as to whether the arguments are more detailed in the mathematical clarification
or in the elementarization.
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. Using academic mathematical knowledge when working on
interface tasks–analyses of pre-service teachers’ arguments about rotationally
symmetric figures. ZDM – Mathematics Education. Published online 2024.
doi:10.1007/s11858-024-01633-4
apa: Hoffmann, M., & Biehler, R. (2024). Using academic mathematical knowledge
when working on interface tasks–analyses of pre-service teachers’ arguments about
rotationally symmetric figures. ZDM – Mathematics Education. https://doi.org/10.1007/s11858-024-01633-4
bibtex: '@article{Hoffmann_Biehler_2024, title={Using academic mathematical knowledge
when working on interface tasks–analyses of pre-service teachers’ arguments about
rotationally symmetric figures}, DOI={10.1007/s11858-024-01633-4},
journal={ZDM – Mathematics Education}, publisher={Springer Science and Business
Media LLC}, author={Hoffmann, Max and Biehler, Rolf}, year={2024} }'
chicago: Hoffmann, Max, and Rolf Biehler. “Using Academic Mathematical Knowledge
When Working on Interface Tasks–Analyses of Pre-Service Teachers’ Arguments about
Rotationally Symmetric Figures.” ZDM – Mathematics Education, 2024. https://doi.org/10.1007/s11858-024-01633-4.
ieee: 'M. Hoffmann and R. Biehler, “Using academic mathematical knowledge when working
on interface tasks–analyses of pre-service teachers’ arguments about rotationally
symmetric figures,” ZDM – Mathematics Education, 2024, doi: 10.1007/s11858-024-01633-4.'
mla: Hoffmann, Max, and Rolf Biehler. “Using Academic Mathematical Knowledge When
Working on Interface Tasks–Analyses of Pre-Service Teachers’ Arguments about Rotationally
Symmetric Figures.” ZDM – Mathematics Education, Springer Science and Business
Media LLC, 2024, doi:10.1007/s11858-024-01633-4.
short: M. Hoffmann, R. Biehler, ZDM – Mathematics Education (2024).
date_created: 2024-09-23T07:36:35Z
date_updated: 2024-09-23T07:44:49Z
department:
- _id: '363'
doi: 10.1007/s11858-024-01633-4
language:
- iso: eng
main_file_link:
- url: https://doi.org/10.1007/s11858-024-01633-4
publication: ZDM – Mathematics Education
publication_identifier:
issn:
- 1863-9690
- 1863-9704
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Using academic mathematical knowledge when working on interface tasks–analyses
of pre-service teachers’ arguments about rotationally symmetric figures
type: journal_article
user_id: '37888'
year: '2024'
...
---
_id: '56199'
citation:
ama: Liebendörfer M, Schmitz A, Biehler R, eds. Lernvideos in der Mathematik
– Beiträge zur Abschlusstagung des Projektes studiVEMINTvideos der Universität
Paderborn und der TH Köln.; 2024.
apa: Liebendörfer, M., Schmitz, A., & Biehler, R. (Eds.). (2024). Lernvideos
in der Mathematik – Beiträge zur Abschlusstagung des Projektes studiVEMINTvideos
der Universität Paderborn und der TH Köln.
bibtex: '@book{Liebendörfer_Schmitz_Biehler_2024, title={Lernvideos in der Mathematik
– Beiträge zur Abschlusstagung des Projektes studiVEMINTvideos der Universität
Paderborn und der TH Köln}, year={2024} }'
chicago: Liebendörfer, Michael, Angelika Schmitz, and Rolf Biehler, eds. Lernvideos
in der Mathematik – Beiträge zur Abschlusstagung des Projektes studiVEMINTvideos
der Universität Paderborn und der TH Köln, 2024.
ieee: M. Liebendörfer, A. Schmitz, and R. Biehler, Eds., Lernvideos in der Mathematik
– Beiträge zur Abschlusstagung des Projektes studiVEMINTvideos der Universität
Paderborn und der TH Köln. 2024.
mla: Liebendörfer, Michael, et al., editors. Lernvideos in der Mathematik – Beiträge
zur Abschlusstagung des Projektes studiVEMINTvideos der Universität Paderborn
und der TH Köln. 2024.
short: M. Liebendörfer, A. Schmitz, R. Biehler, eds., Lernvideos in der Mathematik
– Beiträge zur Abschlusstagung des Projektes studiVEMINTvideos der Universität
Paderborn und der TH Köln, 2024.
date_created: 2024-09-23T07:42:26Z
date_updated: 2024-09-25T08:26:10Z
department:
- _id: '363'
editor:
- first_name: Michael
full_name: Liebendörfer, Michael
id: '30933'
last_name: Liebendörfer
orcid: 0000-0001-9887-2074
- first_name: Angelika
full_name: Schmitz, Angelika
last_name: Schmitz
- first_name: Rolf
full_name: Biehler, Rolf
id: '16274'
last_name: Biehler
language:
- iso: ger
main_file_link:
- url: https://kobra.uni-kassel.de/handle/123456789/15993
publication_status: published
status: public
title: Lernvideos in der Mathematik – Beiträge zur Abschlusstagung des Projektes studiVEMINTvideos
der Universität Paderborn und der TH Köln
type: book_editor
user_id: '37888'
year: '2024'
...
---
_id: '56780'
abstract:
- lang: eng
text: 'AbstractRecent research in university mathematics
education has moved beyond the traditional focus on the transition from secondary
to tertiary education and students'' understanding of introductory courses such
as pre-calculus and calculus. There is growing interest in the challenges students
face as they move into more advanced mathematics courses that require a shift
toward formal reasoning, proof, modeling, and problem-solving skills. This survey
paper explores emerging trends and innovations in the field, focusing on three
key areas: innovations in teaching and learning advanced mathematical topics,
transitions between different levels and contexts of mathematics education, and
the role of proof and proving in advanced university mathematics. The survey reflects
the evolving landscape of mathematics education research and addresses the theoretical
and practical challenges of teaching and learning advanced mathematics across
various contexts.'
author:
- first_name: Rolf
full_name: Biehler, Rolf
id: '16274'
last_name: Biehler
- first_name: Viviane
full_name: Durand-Guerrier, Viviane
last_name: Durand-Guerrier
- first_name: María
full_name: Trigueros, María
last_name: Trigueros
citation:
ama: Biehler R, Durand-Guerrier V, Trigueros M. New trends in didactic research
in university mathematics education. ZDM – Mathematics Education. Published
online 2024. doi:10.1007/s11858-024-01643-2
apa: Biehler, R., Durand-Guerrier, V., & Trigueros, M. (2024). New trends in
didactic research in university mathematics education. ZDM – Mathematics Education.
https://doi.org/10.1007/s11858-024-01643-2
bibtex: '@article{Biehler_Durand-Guerrier_Trigueros_2024, title={New trends in didactic
research in university mathematics education}, DOI={10.1007/s11858-024-01643-2},
journal={ZDM – Mathematics Education}, publisher={Springer Science and Business
Media LLC}, author={Biehler, Rolf and Durand-Guerrier, Viviane and Trigueros,
María}, year={2024} }'
chicago: Biehler, Rolf, Viviane Durand-Guerrier, and María Trigueros. “New Trends
in Didactic Research in University Mathematics Education.” ZDM – Mathematics
Education, 2024. https://doi.org/10.1007/s11858-024-01643-2.
ieee: 'R. Biehler, V. Durand-Guerrier, and M. Trigueros, “New trends in didactic
research in university mathematics education,” ZDM – Mathematics Education,
2024, doi: 10.1007/s11858-024-01643-2.'
mla: Biehler, Rolf, et al. “New Trends in Didactic Research in University Mathematics
Education.” ZDM – Mathematics Education, Springer Science and Business
Media LLC, 2024, doi:10.1007/s11858-024-01643-2.
short: R. Biehler, V. Durand-Guerrier, M. Trigueros, ZDM – Mathematics Education
(2024).
date_created: 2024-10-29T09:22:06Z
date_updated: 2024-10-29T10:56:14Z
department:
- _id: '363'
doi: 10.1007/s11858-024-01643-2
language:
- iso: eng
main_file_link:
- url: https://link.springer.com/article/10.1007/s11858-024-01643-2
publication: ZDM – Mathematics Education
publication_identifier:
issn:
- 1863-9690
- 1863-9704
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: New trends in didactic research in university mathematics education
type: journal_article
user_id: '37888'
year: '2024'
...
---
_id: '59467'
author:
- first_name: Katherine M
full_name: Miller, Katherine M
last_name: Miller
- first_name: Joseph L
full_name: Polman, Joseph L
last_name: Polman
- first_name: Susan A
full_name: Yoon, Susan A
last_name: Yoon
- first_name: Jooeun
full_name: Shim, Jooeun
last_name: Shim
- first_name: Vivian Y
full_name: Leung, Vivian Y
last_name: Leung
- first_name: Yen
full_name: Nguyen, Yen
last_name: Nguyen
- first_name: Andee
full_name: Rubin, Andee
last_name: Rubin
- first_name: Traci
full_name: Higgins, Traci
last_name: Higgins
- first_name: Jessica M
full_name: Karch, Jessica M
last_name: Karch
- first_name: James KL
full_name: Hammerman, James KL
last_name: Hammerman
- first_name: Camillia
full_name: Matuk, Camillia
last_name: Matuk
- first_name: Kayla
full_name: DesPortes, Kayla
last_name: DesPortes
- first_name: Anna
full_name: Amato, Anna
last_name: Amato
- first_name: Suzanne
full_name: Dikker, Suzanne
last_name: Dikker
- first_name: Xavier
full_name: Ochoa, Xavier
last_name: Ochoa
- first_name: Esteban
full_name: Romero, Esteban
last_name: Romero
- first_name: Susanne
full_name: Podworny, Susanne
id: '30619'
last_name: Podworny
orcid: 0000-0002-6313-5987
- first_name: Yannik
full_name: Fleischer, Yannik
id: '42660'
last_name: Fleischer
orcid: https://orcid.org/0000-0003-0318-0329
- first_name: Rolf
full_name: Biehler, Rolf
id: '16274'
last_name: Biehler
- first_name: Justice T.
full_name: Walker, Justice T.
last_name: Walker
- first_name: Amanda
full_name: Barany, Amanda
last_name: Barany
- first_name: Alex
full_name: Acquah, Alex
last_name: Acquah
- first_name: Andi
full_name: Scarola, Andi
last_name: Scarola
- first_name: Sayed
full_name: Reza, Sayed
last_name: Reza
- first_name: Trang C.
full_name: Tran, Trang C.
last_name: Tran
- first_name: Ralph
full_name: Vacca, Ralph
last_name: Vacca
- first_name: Megan
full_name: Silander, Megan
last_name: Silander
- first_name: Peter J.
full_name: Woods, Peter J.
last_name: Woods
- first_name: Cassia
full_name: Fernandez, Cassia
last_name: Fernandez
- first_name: Adelmo
full_name: Eloy, Adelmo
last_name: Eloy
- first_name: Paulo
full_name: Blikstein, Paulo
last_name: Blikstein
- first_name: Roseli
full_name: de Deus Lopes, Roseli
last_name: de Deus Lopes
- first_name: Josh
full_name: Radinsky, Josh
last_name: Radinsky
- first_name: Iris
full_name: Tabak, Iris
last_name: Tabak
- first_name: Victor R.
full_name: Lee, Victor R.
last_name: Lee
- first_name: Dorottya
full_name: Demszky, Dorottya
last_name: Demszky
- first_name: Sarah
full_name: Levine, Sarah
last_name: Levine
- first_name: Josephine
full_name: Louie, Josephine
last_name: Louie
citation:
ama: 'Miller KM, Polman JL, Yoon SA, et al. Data and Social Worlds: How Data Science
Education Supports Civic Participation and Social Discourse. In: Lindgren R, Asino
TI, Kyza EA, Looi CK, Keifert DT, Suárez E, eds. Proceedings of the 18th International
Conference of the Learning Sciences-ICLS 2024. International Society of the
Learning Sciences; 2024:1863-1870.'
apa: 'Miller, K. M., Polman, J. L., Yoon, S. A., Shim, J., Leung, V. Y., Nguyen,
Y., Rubin, A., Higgins, T., Karch, J. M., Hammerman, J. K., Matuk, C., DesPortes,
K., Amato, A., Dikker, S., Ochoa, X., Romero, E., Podworny, S., Fleischer, Y.,
Biehler, R., … Louie, J. (2024). Data and Social Worlds: How Data Science Education
Supports Civic Participation and Social Discourse. In R. Lindgren, T. I. Asino,
E. A. Kyza, C. K. Looi, D. T. Keifert, & E. Suárez (Eds.), Proceedings
of the 18th International Conference of the Learning Sciences-ICLS 2024 (pp.
1863–1870). International Society of the Learning Sciences.'
bibtex: '@inproceedings{Miller_Polman_Yoon_Shim_Leung_Nguyen_Rubin_Higgins_Karch_Hammerman_et
al._2024, title={Data and Social Worlds: How Data Science Education Supports Civic
Participation and Social Discourse}, booktitle={Proceedings of the 18th International
Conference of the Learning Sciences-ICLS 2024}, publisher={International Society
of the Learning Sciences}, author={Miller, Katherine M and Polman, Joseph L and
Yoon, Susan A and Shim, Jooeun and Leung, Vivian Y and Nguyen, Yen and Rubin,
Andee and Higgins, Traci and Karch, Jessica M and Hammerman, James KL and et al.},
editor={Lindgren, R. and Asino, T. I. and Kyza, E. A. and Looi, C. K. and Keifert,
D. T. and Suárez, E.}, year={2024}, pages={1863–1870} }'
chicago: 'Miller, Katherine M, Joseph L Polman, Susan A Yoon, Jooeun Shim, Vivian
Y Leung, Yen Nguyen, Andee Rubin, et al. “Data and Social Worlds: How Data Science
Education Supports Civic Participation and Social Discourse.” In Proceedings
of the 18th International Conference of the Learning Sciences-ICLS 2024, edited
by R. Lindgren, T. I. Asino, E. A. Kyza, C. K. Looi, D. T. Keifert, and E. Suárez,
1863–70. International Society of the Learning Sciences, 2024.'
ieee: 'K. M. Miller et al., “Data and Social Worlds: How Data Science Education
Supports Civic Participation and Social Discourse,” in Proceedings of the 18th
International Conference of the Learning Sciences-ICLS 2024, 2024, pp. 1863–1870.'
mla: 'Miller, Katherine M., et al. “Data and Social Worlds: How Data Science Education
Supports Civic Participation and Social Discourse.” Proceedings of the 18th
International Conference of the Learning Sciences-ICLS 2024, edited by R.
Lindgren et al., International Society of the Learning Sciences, 2024, pp. 1863–70.'
short: 'K.M. Miller, J.L. Polman, S.A. Yoon, J. Shim, V.Y. Leung, Y. Nguyen, A.
Rubin, T. Higgins, J.M. Karch, J.K. Hammerman, C. Matuk, K. DesPortes, A. Amato,
S. Dikker, X. Ochoa, E. Romero, S. Podworny, Y. Fleischer, R. Biehler, J.T. Walker,
A. Barany, A. Acquah, A. Scarola, S. Reza, T.C. Tran, R. Vacca, M. Silander, P.J.
Woods, C. Fernandez, A. Eloy, P. Blikstein, R. de Deus Lopes, J. Radinsky, I.
Tabak, V.R. Lee, D. Demszky, S. Levine, J. Louie, in: R. Lindgren, T.I. Asino,
E.A. Kyza, C.K. Looi, D.T. Keifert, E. Suárez (Eds.), Proceedings of the 18th
International Conference of the Learning Sciences-ICLS 2024, International Society
of the Learning Sciences, 2024, pp. 1863–1870.'
date_created: 2025-04-10T07:38:59Z
date_updated: 2025-04-10T09:12:03Z
ddc:
- '510'
department:
- _id: '363'
editor:
- first_name: R.
full_name: Lindgren, R.
last_name: Lindgren
- first_name: T. I.
full_name: Asino, T. I.
last_name: Asino
- first_name: E. A.
full_name: Kyza, E. A.
last_name: Kyza
- first_name: C. K.
full_name: Looi, C. K.
last_name: Looi
- first_name: D. T.
full_name: Keifert, D. T.
last_name: Keifert
- first_name: E.
full_name: Suárez, E.
last_name: Suárez
file:
- access_level: closed
content_type: application/pdf
creator: krueter
date_created: 2025-04-10T07:44:19Z
date_updated: 2025-04-10T07:44:19Z
file_id: '59470'
file_name: ICLS2024_1863-1870.pdf
file_size: 343448
relation: main_file
success: 1
file_date_updated: 2025-04-10T07:44:19Z
has_accepted_license: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://repository.isls.org/handle/1/10830
oa: '1'
page: 1863-1870
publication: Proceedings of the 18th International Conference of the Learning Sciences-ICLS
2024
publisher: International Society of the Learning Sciences
status: public
title: 'Data and Social Worlds: How Data Science Education Supports Civic Participation
and Social Discourse'
type: conference
user_id: '37888'
year: '2024'
...
---
_id: '56198'
author:
- first_name: Michael
full_name: Liebendörfer, Michael
id: '30933'
last_name: Liebendörfer
orcid: 0000-0001-9887-2074
- first_name: Rolf
full_name: Biehler, Rolf
id: '16274'
last_name: Biehler
- first_name: Angelika
full_name: Schmitz, Angelika
last_name: Schmitz
citation:
ama: Liebendörfer M, Biehler R, Schmitz A. Mathematische Lernvideos Zu Studieneinstieg
Und Studienvorbereitung. Universität Kassel; 2024. doi:10.17170/KOBRA-2024081810686-004
apa: Liebendörfer, M., Biehler, R., & Schmitz, A. (2024). Mathematische Lernvideos
zu Studieneinstieg und Studienvorbereitung. Universität Kassel. https://doi.org/10.17170/KOBRA-2024081810686-004
bibtex: '@book{Liebendörfer_Biehler_Schmitz_2024, title={Mathematische Lernvideos
zu Studieneinstieg und Studienvorbereitung}, DOI={10.17170/KOBRA-2024081810686-004},
publisher={Universität Kassel}, author={Liebendörfer, Michael and Biehler, Rolf
and Schmitz, Angelika}, year={2024} }'
chicago: Liebendörfer, Michael, Rolf Biehler, and Angelika Schmitz. Mathematische
Lernvideos Zu Studieneinstieg Und Studienvorbereitung. Universität Kassel,
2024. https://doi.org/10.17170/KOBRA-2024081810686-004.
ieee: M. Liebendörfer, R. Biehler, and A. Schmitz, Mathematische Lernvideos zu
Studieneinstieg und Studienvorbereitung. Universität Kassel, 2024.
mla: Liebendörfer, Michael, et al. Mathematische Lernvideos Zu Studieneinstieg
Und Studienvorbereitung. Universität Kassel, 2024, doi:10.17170/KOBRA-2024081810686-004.
short: M. Liebendörfer, R. Biehler, A. Schmitz, Mathematische Lernvideos Zu Studieneinstieg
Und Studienvorbereitung, Universität Kassel, 2024.
date_created: 2024-09-23T07:38:29Z
date_updated: 2024-11-26T11:39:10Z
department:
- _id: '363'
doi: 10.17170/KOBRA-2024081810686-004
publisher: Universität Kassel
related_material:
link:
- relation: confirmation
url: https://doi.org/10.17170/kobra-2024081810686-004
status: public
title: Mathematische Lernvideos zu Studieneinstieg und Studienvorbereitung
type: research_data
user_id: '37888'
year: '2024'
...