@inproceedings{64625,
  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}},
  booktitle    = {{Proceedings of the IASE 2025 Satellite Conference - Statistics and Data Science Education in STEAM}},
  publisher    = {{International Association for Statistics Education}},
  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}},
  year         = {{2026}},
}

@article{58353,
  abstract     = {{<jats:title>Abstract</jats:title>
          <jats:p>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.</jats:p>}},
  author       = {{Podworny, Susanne and Biehler, Rolf and Fleischer, Yannik}},
  issn         = {{1863-9690}},
  journal      = {{ZDM – Mathematics Education}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{Young students’ engagement with data to create decision trees}}},
  doi          = {{10.1007/s11858-024-01649-w}},
  year         = {{2025}},
}

@article{59622,
  abstract     = {{<jats:title>Abstract</jats:title>
          <jats:p>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.</jats:p>}},
  author       = {{Fleischer, Yannik and Biehler, Rolf}},
  issn         = {{1863-9690}},
  journal      = {{ZDM – Mathematics Education}},
  number       = {{1}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{Exploring students’ constructions of data-based decision trees after an introductory teaching unit on machine learning}}},
  doi          = {{10.1007/s11858-025-01663-6}},
  volume       = {{57}},
  year         = {{2025}},
}

@article{59053,
  author       = {{Frischemeier, Daniel and Biehler, Rolf}},
  journal      = {{Stochastik in der Schule}},
  number       = {{1}},
  pages        = {{22--33}},
  title        = {{{Förderung von statistischem Denken im Mathematikunterricht der Primarstufe: Bedeutsame Ideen und Förderungsmöglichkeiten}}},
  volume       = {{45}},
  year         = {{2025}},
}

@article{60351,
  abstract     = {{<jats:p>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.</jats:p>}},
  author       = {{Biehler, Rolf and Kawakami, Takashi and Lampen, Erna and Weiland, Travis and Zapata-Cardona, Lucía}},
  issn         = {{2747-7894}},
  journal      = {{European Mathematical Society Magazine}},
  publisher    = {{European Mathematical Society - EMS - Publishing House GmbH}},
  title        = {{{Statistics and data science education as a vehicle for empowering citizens – short summary of a survey}}},
  doi          = {{10.4171/mag/257}},
  year         = {{2025}},
}

@article{60495,
  author       = {{Podworny, Susanne and Fleischer, Yannik and Biehler, Rolf}},
  journal      = {{Stochastik in der Schule}},
  number       = {{2}},
  pages        = {{9--16}},
  title        = {{{Explorative Datenanalyse in der Schule – Analyse der Mediennutzung von Jugendlichen mit den YOU‑PB Daten}}},
  volume       = {{45}},
  year         = {{2025}},
}

@inbook{60532,
  author       = {{Biehler, Rolf and Schulte, Carsten}},
  booktitle    = {{Proceedings of the 1st Symposium on Integrating AI and Data Science into School Education Across Disciplines (AIDEA 1 2025), Salzburg, Austria}},
  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.}}},
  year         = {{2025}},
}

@inproceedings{60860,
  author       = {{Fleischer, Franz Yannik and Biehler, Rolf}},
  booktitle    = {{Proceedings of the 48th Conference of the International Group for the Psychology of Mathematics Education: Research Reports, Vol. 1 }},
  editor       = {{Cornejo, C. and Felmer, P. and Gomez, D.M. and Dartnell, P. and Araya, P. and Peri, A. and Randolph, V.}},
  pages        = {{267--274}},
  title        = {{{ANALYZING STUDENTS’INFORMAL APPROACHES TO CREATING DECISION TREES IN THE CLASSROOM}}},
  year         = {{2025}},
}

@article{61125,
  author       = {{Biehler, Rolf and Liebendörfer, Michael and Schmitz, Angela and Reich, Birte}},
  journal      = {{Mitteilungen der Deutschen Mathematiker-Vereinigung}},
  number       = {{3}},
  pages        = {{170–171}},
  publisher    = {{De Gruyter}},
  title        = {{{studiVEMINT Mathematik-Online-Vorkurs jetzt mit 300 integrierten Lernvideos frei verfügbar}}},
  volume       = {{33}},
  year         = {{2025}},
}

@article{63556,
  author       = {{Biehler, Rolf and Engel, Joachim and Frischemeier, Daniel and Podworny, Susanne}},
  journal      = {{mathematica didactica}},
  number       = {{2}},
  title        = {{{Civic Statistical Literacy: Konzept und praxisnahe Umsetzung am Beispiel des Klimawandels}}},
  doi          = {{10.18716/ojs/md/2025.2297}},
  volume       = {{48}},
  year         = {{2025}},
}

@article{54144,
  abstract     = {{<jats:title>Abstract</jats:title><jats:p>In 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. Our 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.</jats:p>}},
  author       = {{Lankeit, Elisa and Biehler, Rolf}},
  issn         = {{1863-9690}},
  journal      = {{ZDM – Mathematics Education}},
  publisher    = {{Springer Science and Business Media LLC}},
  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}},
  year         = {{2024}},
}

@article{55667,
  abstract     = {{<jats:p>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.</jats:p>}},
  author       = {{Fleischer, Franz Yannik and Podworny, Susanne and Biehler, Rolf}},
  issn         = {{1570-1824}},
  journal      = {{Statistics Education Research Journal}},
  number       = {{1}},
  publisher    = {{International Association for Statistical Education}},
  title        = {{{Teaching and Learning to Construct Data-Based Decision Trees Using Data Cards as the First Introduction to Machine Learning in Middle School}}},
  doi          = {{10.52041/serj.v23i1.450}},
  volume       = {{23}},
  year         = {{2024}},
}

@inbook{55756,
  author       = {{Biehler, Rolf and Frischemeier, Daniel}},
  booktitle    = {{Inklusives Lehren und Lernen von Mathematik}},
  isbn         = {{9783658439637}},
  publisher    = {{Springer Fachmedien Wiesbaden}},
  title        = {{{Eine inklusive Lehr-Lernumgebung für die Leitidee „Daten und Zufall“ in der Primarstufe}}},
  doi          = {{10.1007/978-3-658-43964-4_13}},
  year         = {{2024}},
}

@book{55758,
  author       = {{Biehler, Rolf and Frischemeier, Daniel}},
  publisher    = {{Klett Kallmeyer}},
  title        = {{{Daten-Spürnasen auf Spurensuche: Datenanalyse in der Grundschule mit digitalen Werkzeugen}}},
  year         = {{2024}},
}

@article{56016,
  abstract     = {{<jats:title>Abstract</jats:title><jats:p>Special 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.</jats:p>}},
  author       = {{Hoffmann, Max and Biehler, Rolf}},
  issn         = {{1863-9690}},
  journal      = {{ZDM – Mathematics Education}},
  publisher    = {{Springer Science and Business Media LLC}},
  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}},
  year         = {{2024}},
}

@article{56197,
  abstract     = {{<jats:title>Abstract</jats:title><jats:p>Special 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.</jats:p>}},
  author       = {{Hoffmann, Max and Biehler, Rolf}},
  issn         = {{1863-9690}},
  journal      = {{ZDM – Mathematics Education}},
  publisher    = {{Springer Science and Business Media LLC}},
  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}},
  year         = {{2024}},
}

@book{56199,
  editor       = {{Liebendörfer, Michael and Schmitz, Angelika and Biehler, Rolf}},
  title        = {{{Lernvideos in der Mathematik – Beiträge zur Abschlusstagung des Projektes studiVEMINTvideos der Universität Paderborn und der TH Köln}}},
  year         = {{2024}},
}

@article{56780,
  abstract     = {{<jats:title>Abstract</jats:title><jats:p>Recent 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.</jats:p>}},
  author       = {{Biehler, Rolf and Durand-Guerrier, Viviane and Trigueros, María}},
  issn         = {{1863-9690}},
  journal      = {{ZDM – Mathematics Education}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{New trends in didactic research in university mathematics education}}},
  doi          = {{10.1007/s11858-024-01643-2}},
  year         = {{2024}},
}

@inproceedings{59467,
  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 Matuk, Camillia and DesPortes, Kayla and Amato, Anna and Dikker, Suzanne and Ochoa, Xavier and Romero, Esteban and Podworny, Susanne and Fleischer, Yannik and Biehler, Rolf and Walker, Justice T. and Barany, Amanda and Acquah, Alex and Scarola, Andi and Reza, Sayed and Tran, Trang C. and Vacca, Ralph and Silander, Megan and Woods, Peter J. and Fernandez, Cassia and Eloy, Adelmo and Blikstein, Paulo and de Deus Lopes, Roseli and Radinsky, Josh and Tabak, Iris and Lee, Victor R. and Demszky, Dorottya and Levine, Sarah and Louie, Josephine}},
  booktitle    = {{Proceedings of the 18th International Conference of the Learning Sciences-ICLS 2024}},
  editor       = {{Lindgren, R. and Asino, T. I. and Kyza, E. A. and Looi, C. K. and Keifert, D. T. and Suárez, E.}},
  pages        = {{1863--1870}},
  publisher    = {{International Society of the Learning Sciences}},
  title        = {{{Data and Social Worlds: How Data Science Education Supports Civic Participation and Social Discourse}}},
  year         = {{2024}},
}

@misc{56198,
  author       = {{Liebendörfer, Michael and Biehler, Rolf and Schmitz, Angelika}},
  publisher    = {{Universität Kassel}},
  title        = {{{Mathematische Lernvideos zu Studieneinstieg und Studienvorbereitung}}},
  doi          = {{10.17170/KOBRA-2024081810686-004}},
  year         = {{2024}},
}