@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}},
}

@inbook{57952,
  author       = {{Lankeit, Elisa and Biehler, Rolf}},
  booktitle    = {{Beiträge zum Mathematikunterricht 2024 - 57. Jahrestagung der Gesellschaft für Didaktik der Mathematik.}},
  editor       = {{Ebers, P. and Rösken, F. and Barzel, B. and Büchter, A. and Schacht, F. and Scherer, P.}},
  pages        = {{1073--1076}},
  publisher    = {{WTM-Verlag}},
  title        = {{{Bedeutungsfacetten der Beziehungen von Differenzierbarkeit und Stetigkeit im Ein- und Mehrdimensionalen: Ein Blick auf die semantische Ebene}}},
  doi          = {{10.37626/GA9783959872782.0}},
  year         = {{2024}},
}

@inbook{57950,
  author       = {{Fleischer, Yannik and Biehler, Rolf}},
  booktitle    = {{Beiträge zum Mathematikunterricht 2024 - 57. Jahrestagung der Gesellschaft für Didaktik der Mathematik.}},
  editor       = {{Ebers, P. and Rösken, F. and Barzel, B. and Büchter, A. and Schacht, F. and Scherer, P.}},
  pages        = {{167--170}},
  publisher    = {{WTM-Verlag}},
  title        = {{{Intuitiver Zugang zu datenbasierten Entscheidungsbäumen}}},
  doi          = {{10.37626/GA9783959872782.0}},
  year         = {{2024}},
}

@inbook{57948,
  author       = {{Mai, Tobias and Biehler, Rolf}},
  booktitle    = {{Beiträge zum Mathematikunterricht 2024 - 57. Jahrestagung der Gesellschaft für Didaktik der Mathematik.}},
  editor       = {{Ebers, P. and Rösken, F. and Barzel, B. and Büchter, A. and Schacht, F. and Scherer, P.}},
  pages        = {{1103--1106}},
  publisher    = {{WTM-Verlag}},
  title        = {{{Transitionen zwischen Vektorobjekten in Schulbüchern}}},
  doi          = {{10.37626/GA9783959872782.0}},
  year         = {{2024}},
}

@inbook{57947,
  author       = {{Bauer, Thomas and Biehler, Rolf and Lankeit, Elisa}},
  booktitle    = {{INDRUM2024 PROCEEDINGS - Fifth conference of the International Network for Didactic Research in University Mathematics}},
  editor       = {{Gonzalez-Martin, A. S. and Gueudet, G. and Florensa, I. and Lombard, N.}},
  pages        = {{65--74}},
  publisher    = {{Escola Univeristaria Salesiana de Sarria (Univ. Autonoma de Barcelona) and INDRUM}},
  title        = {{{Designing a Concept Inventory for Real Analysis}}},
  year         = {{2024}},
}

@article{45786,
  abstract     = {{Intending to counteract Klein’s second discontinuity in teacher education, we explored and applied the innovation of “interface ePortfolio” in the context of a geometry course for preservice teachers (PSTs). The tool offers the possibility of implementing the design principle of profession orientation. In the article, we theoretically clarify what we understand by this principle and locate our innovative concept against this theoretical background. We empirically investigate the extent to which counteraction against the second discontinuity is successful by analyzing reflection texts created in the interface ePortfolio, focusing on PSTs’ perspectives. Our qualitative content analysis shows that most of them perceive the innovation as helpful in the intended sense and indicates that the course concept, in general, and the interface ePortfolio, in particular, have helped establish relevant links between the course content and their later work as teachers.}},
  author       = {{Hoffmann, Max and Biehler, Rolf}},
  issn         = {{1863-9690}},
  journal      = {{ZDM – Mathematics Education}},
  keywords     = {{General Mathematics, Education}},
  publisher    = {{Springer}},
  title        = {{{Implementing profession orientation as a design principle for overcoming Klein’s second discontinuity – preservice teacher’s perspectives on interface activities in the context of a geometry course}}},
  doi          = {{10.1007/s11858-023-01505-3}},
  year         = {{2023}},
}

@inbook{35697,
  author       = {{Ostsieker, Laura and Biehler, Rolf}},
  booktitle    = {{Practice-Oriented Research in Tertiary Mathematics Education}},
  isbn         = {{9783031141744}},
  issn         = {{1869-4918}},
  pages        = {{181--201}},
  publisher    = {{Springer International Publishing}},
  title        = {{{Supporting Students in Developing Adequate Concept Images and Definitions at University: The Case of the Convergence of Sequences}}},
  doi          = {{10.1007/978-3-031-14175-1_9}},
  year         = {{2023}},
}

@inbook{35678,
  author       = {{Kortemeyer, Jörg and Biehler, Rolf}},
  booktitle    = {{Practice-Oriented Research in Tertiary Mathematics Education}},
  isbn         = {{9783031141744}},
  issn         = {{1869-4918}},
  pages        = {{669--692}},
  publisher    = {{Springer International Publishing}},
  title        = {{{Analyzing the Interface Between Mathematics and Engineering in Basic Engineering Courses}}},
  doi          = {{10.1007/978-3-031-14175-1_32}},
  year         = {{2023}},
}

@inbook{48480,
  author       = {{Kortmeyer, Jörg and Biehler, Rolf}},
  booktitle    = {{The Learning and Teaching of Calculus Across Disciplines – Proceedings of the Second Calculus Conference}},
  editor       = {{Dreyfus, T. and Gonzalez-Martin, A. S. and Nardi, E. and Monaghan, J. and Thompson, P. W.}},
  pages        = {{121--124}},
  publisher    = {{MatRIC}},
  title        = {{{The use of integrals for accumulation and mean values in basic electrical engineering courses}}},
  year         = {{2023}},
}

@inbook{47416,
  author       = {{Biehler, Rolf and Engel, Joachim and Frischemeier, Daniel}},
  booktitle    = {{Handbuch der Mathematikdidaktik}},
  editor       = {{Bruder, Regina and Büchter, A. and Gasteiger, H. and Schmidt-Thieme, B. and Weigand, HG.}},
  isbn         = {{9783662666036}},
  publisher    = {{Springer}},
  title        = {{{Stochastik: Leitidee Daten und Zufall}}},
  doi          = {{10.1007/978-3-662-66604-3_8}},
  year         = {{2023}},
}

@inbook{48042,
  author       = {{Biehler, Rolf and Frischemeier, Daniel and Gould, Ronald and Pfannkuch, Maxine}},
  booktitle    = {{Handbook of Digital Resources in Mathematics Education}},
  editor       = {{Pepin, Birgit and Gueudet, Ghislaine and Choppin, Jeffrey}},
  publisher    = {{Springer International Publishing}},
  title        = {{{Impacts of Digitalization on Content and Goals of Statistics Education}}},
  year         = {{2023}},
}

@article{49049,
  author       = {{Biehler, Rolf and Krüger, Katja}},
  journal      = {{GDM-Mitteilungen}},
  number       = {{115}},
  pages        = {{57--65}},
  title        = {{{Von Glückstal (Ukraine) nach Frankfurt: Problemlösen, Algorithmen, Stochastik – Nachruf auf Arthur Engel}}},
  year         = {{2023}},
}

@inbook{35669,
  author       = {{Biehler, Rolf and Liebendörfer, Michael and Gueudet, Ghislaine and Rasmussen, Chris and Winsløw, Carl}},
  booktitle    = {{Practice-Oriented Research in Tertiary Mathematics Education}},
  isbn         = {{9783031141744}},
  issn         = {{1869-4918}},
  publisher    = {{Springer International Publishing}},
  title        = {{{Practice-Oriented Research in Tertiary Mathematics Education – An Introduction}}},
  doi          = {{10.1007/978-3-031-14175-1_1}},
  year         = {{2023}},
}

@inbook{35681,
  author       = {{Liebendörfer, Michael and Büdenbender-Kuklinski, Christiane and Lankeit, Elisa and Schürmann, Mirko and Biehler, Rolf and Schaper, Niclas}},
  booktitle    = {{Practice-Oriented Research in Tertiary Mathematics Education}},
  isbn         = {{9783031141744}},
  issn         = {{1869-4918}},
  pages        = {{91--117}},
  publisher    = {{Springer International Publishing}},
  title        = {{{Framing Goals of Mathematics Support Measures}}},
  doi          = {{10.1007/978-3-031-14175-1_5}},
  year         = {{2023}},
}

@book{46157,
  editor       = {{Biehler, Rolf and Liebendörfer, Michael and Gueudet, Ghislaine and Rasmussen, Chris and Winsløw, Carl}},
  isbn         = {{9783031141744}},
  issn         = {{1869-4918}},
  publisher    = {{Springer International Publishing}},
  title        = {{{Practice-Oriented Research in Tertiary Mathematics Education}}},
  doi          = {{10.1007/978-3-031-14175-1}},
  year         = {{2023}},
}