@book{36475, editor = {{Gasteiger, Hedwig and Bruns, Julia}}, title = {{{Methoden empirischer Bildungsforschung im Kontext Frühkindliche Bildung und Entwicklung}}}, year = {{2018}}, } @unpublished{19940, abstract = {{Two smooth map germs are right-equivalent if and only if they generate two Lagrangian submanifolds in a cotangent bundle which have the same contact with the zero-section. In this paper we provide a reverse direction to this classical result of Golubitsky and Guillemin. Two Lagrangian submanifolds of a symplectic manifold have the same contact with a third Lagrangian submanifold if and only if the intersection problems correspond to stably right equivalent map germs. We, therefore, obtain a correspondence between local Lagrangian intersection problems and catastrophe theory while the classical version only captures tangential intersections. The correspondence is defined independently of any Lagrangian fibration of the ambient symplectic manifold, in contrast to other classical results. Moreover, we provide an extension of the correspondence to families of local Lagrangian intersection problems. This gives rise to a framework which allows a natural transportation of the notions of catastrophe theory such as stability, unfolding and (uni-)versality to the geometric setting such that we obtain a classification of families of local Lagrangian intersection problems. An application is the classification of Lagrangian boundary value problems for symplectic maps.}}, author = {{Offen, Christian}}, booktitle = {{arXiv:1811.10165}}, title = {{{Local intersections of Lagrangian manifolds correspond to catastrophe theory}}}, year = {{2018}}, } @article{19943, abstract = {{In this paper we continue our study of bifurcations of solutions of boundary-value problems for symplectic maps arising as Hamiltonian diffeomorphisms. These have been shown to be connected to catastrophe theory via generating functions and ordinary and reversal phase space symmetries have been considered. Here we present a convenient, coordinate free framework to analyse separated Lagrangian boundary value problems which include classical Dirichlet, Neumann and Robin boundary value problems. The framework is then used to prove the existence of obstructions arising from conformal symplectic symmetries on the bifurcation behaviour of solutions to Hamiltonian boundary value problems. Under non-degeneracy conditions, a group action by conformal symplectic symmetries has the effect that the flow map cannot degenerate in a direction which is tangential to the action. This imposes restrictions on which singularities can occur in boundary value problems. Our results generalise classical results about conjugate loci on Riemannian manifolds to a large class of Hamiltonian boundary value problems with, for example, scaling symmetries. }}, author = {{McLachlan, Robert I and Offen, Christian}}, journal = {{New Zealand Journal of Mathematics}}, keywords = {{Hamiltonian boundary value problems, singularities, conformal symplectic geometry, catastrophe theory, conjugate loci}}, pages = {{83--99}}, title = {{{Hamiltonian boundary value problems, conformal symplectic symmetries, and conjugate loci}}}, doi = {{10.53733/34 }}, volume = {{48}}, year = {{2018}}, } @inproceedings{56249, author = {{Fleischmann, Yael and Kempen, Leander and Mai, Tobias and Biehler, Rolf}}, booktitle = {{Hanse-Kolloquium zur Hochschuldidaktik der Mathematik}}, editor = {{Klinger, M. and Schüler-Meyer, A. and Wessel, L.}}, pages = {{101–116}}, publisher = {{WTM-Verlag}}, title = {{{Die online Lernmaterialien von studiVEMINT: Einsatzszenarien im Blended Learning Format in mathematischen Vorkursen}}}, year = {{2018}}, } @article{56254, author = {{Kempen, Leander and Biehler, Rolf}}, issn = {{2198-9745}}, journal = {{International Journal of Research in Undergraduate Mathematics Education}}, number = {{1}}, pages = {{27--55}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{Pre-Service Teachers’ Benefits from an Inquiry-Based Transition-to-Proof Course with a Focus on Generic Proofs}}}, doi = {{10.1007/s40753-018-0082-9}}, volume = {{5}}, year = {{2018}}, } @book{56253, author = {{Hochmuth, Reinhard and Biehler, Rolf and Schaper, Niclas and Kuklinski, Christiane and Lankeit, Elisa and Leis, Elena and Liebendörfer, Michael and Schürmann, Mirko}}, publisher = {{Leibniz Universität Hannover}}, title = {{{Wirkung und Gelingensbedingungen von Unterstützungsmaßnahmen für mathmatikbezogenes Lernen in der Studieneingangsphase: Schlussbericht: Teilprojekt A der Leibniz Universität Hannover, Teilprojekte B und C der Universität Paderborn: Berichtszeitraum: 01.03. 2015-31.08. 2018}}}, year = {{2018}}, } @inbook{56349, author = {{Barzel, Bärbel and Biehler, Rolf and Blömeke, Sigrid and Brandtner, Regine and Bruns, Julia and Dohrmann, Christian and Kortenkamp, Ulrich and Lange, Thomas and Leuders, Timo and Rösken-Winter, Bettina and Scherer, Petra and Selter, Christoph}}, booktitle = {{Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik}}, isbn = {{9783658190279}}, issn = {{2197-8751}}, pages = {{7--40}}, publisher = {{Springer Fachmedien Wiesbaden}}, title = {{{Das Deutsche Zentrum für Lehrerbildung Mathematik – DZLM}}}, doi = {{10.1007/978-3-658-19028-6_2}}, year = {{2018}}, } @book{56354, editor = {{Biehler, Rolf and Budde, Lea and Frischemeier, Daniel and Heinemann, B. and Podworny, Susanne and Schulte, Carsten and Wassong, Thomas}}, publisher = {{Universitätsbibliothek Paderborn}}, title = {{{Paderborn symposium on data science education at school level 2017: The collected extended abstracts. Universitätsbibliothek Paderborn}}}, year = {{2018}}, } @article{56361, author = {{Biehler, Rolf and Frischemeier, Daniel and Podworny, Susanne}}, issn = {{1863-9690}}, journal = {{ZDM}}, number = {{7}}, pages = {{1237--1251}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{Elementary preservice teachers’ reasoning about statistical modeling in a civic statistics context}}}, doi = {{10.1007/s11858-018-1001-x}}, volume = {{50}}, year = {{2018}}, } @article{56360, author = {{Biehler, Rolf and Frischemeier, Daniel and Podworny, Susanne}}, journal = {{Zeitschrift für Hochschulentwicklung}}, number = {{2}}, pages = {{169--182}}, title = {{{ Civic Engagement in Higher Education: A university course in civic statistics for mathematics preservice teachers - Civic Engagement in Higher Education: A university course in civic statistics for mathematics preservice teachers}}}, doi = {{10.3217/ZFHE-13-02/11}}, volume = {{13}}, year = {{2018}}, } @inproceedings{56351, author = {{Biehler, Rolf}}, booktitle = {{Looking back, looking forward. Proceedings of the Tenth International Conference on Teaching Statistics (ICOTS10, July 8–13), Kyoto, Japan. https://iase-web. org/icots/10/proceedings/pdfs/ICOTS10_1B1. pdf}}, title = {{{Design principles, realizations and uses of software supporting the learning and the doing of statistics: A reflection on developments since the late 1990s}}}, year = {{2018}}, } @inbook{56355, author = {{Biehler, Rolf and Fleischmann, Yael and Gold, Alexander}}, booktitle = {{Beiträge zum Mathematikunterricht 2018, Band I}}, pages = {{277--280}}, publisher = {{WTM-Verlag}}, title = {{{Konzepte für die Gestaltung von Online-Vorkursen für Mathematik und für ihre Integration in Blended-Learning-Szenarien}}}, year = {{2018}}, } @article{56362, author = {{Biehler, Rolf and Frischemeier, Daniel and Podworny, Susanne and Wassong, Thomas and Budde, Lea and Heinemann, B. and Schulte, Carsten}}, journal = {{Archives of Data Science, Series A}}, number = {{1}}, title = {{{Data Science and Big Data in Upper Secondary Schools: A Module to Build up First Components of Statistical Thinking in a Data Science Curriculum}}}, doi = {{10.5445/KSP/1000087327/28}}, volume = {{5}}, year = {{2018}}, } @book{56692, editor = {{Biehler, Rolf and Lange, Thomas and Leuders, Timo and Rösken-Winter, Bettina and Scherer, Petra and Selter, Christoph}}, isbn = {{9783658190279}}, issn = {{2197-8751}}, publisher = {{Springer Fachmedien Wiesbaden}}, title = {{{Mathematikfortbildungen professionalisieren}}}, doi = {{10.1007/978-3-658-19028-6}}, year = {{2018}}, } @article{56706, abstract = {{Group comparisons offer students opportunities to reason about many fundamental statistical concepts like center, variation, or distribution. When doing such activities using large, real datasets, technology becomes and essential tool for exploring the data. With its large variety of features and its user-friendly handling, TinkerPlotsTM --as a software for learners and teachers--can facilitate the process of comparing distributions. In this article we focus on eight preservice teachers´  reasoning when comparing groups with TinkerPlots. We present ideas on the design of a course to develop statistical reasoning with TinkerPlots, present a framework to rate learners´  performance when comparing groups with TinkerPlots, and present results of a laboratory study about preservice teachers´  reasoning when comparing groups with TinkerPlots. Findings suggest that the TinkerPlots tool and design of the course supported these preservice teachers´  reasoning and that more learning opportunities are needed to increase their group comparison elements´  repertoire and interpretation in context. First published May 2018 at Statistics Education Research Journal Archives}}, author = {{Frischemeier, Daniel and Biehler, Rolf}}, issn = {{1570-1824}}, journal = {{Statistics Education Research Journal}}, number = {{1}}, pages = {{35--60}}, publisher = {{International Association for Statistical Education}}, title = {{{Preservice teachers´ comparing groups with TinkerPlots - An exploratory video study}}}, doi = {{10.52041/serj.v17i1.175}}, volume = {{17}}, year = {{2018}}, } @inbook{56713, author = {{Kolter, Jana and Blum, Werner and Bender, Peter and Biehler, Rolf and Haase, Jürgen and Hochmuth, Reinhard and Schukajlow, Stanislaw}}, booktitle = {{Innovative Konzepte für die Grundschullehrerausbildung im Fach Mathematik}}, editor = {{Möller, R. and Vogel, R.}}, isbn = {{9783658102647}}, issn = {{2197-8751}}, pages = {{95--121}}, publisher = {{Springer Fachmedien Wiesbaden}}, title = {{{Zum Erwerb, zur Messung und zur Förderung studentischen (Fach-)Wissens in der Vorlesung „Arithmetik für die Grundschule“ – Ergebnisse aus dem KLIMAGS-Projekt}}}, doi = {{10.1007/978-3-658-10265-4_4}}, year = {{2018}}, } @inbook{56709, author = {{Haase, Jürgen and Hochmuth, Reinhard and Bender, Peter and Biehler, Rolf and Blum, Werner and Kolter, Jana and Schukajlow, Stanislaw}}, booktitle = {{Innovative Konzepte für die Grundschullehrerausbildung im Fach Mathematik}}, editor = {{Möller, R. and Vogel, R.}}, isbn = {{9783658102647}}, issn = {{2197-8751}}, pages = {{235--253}}, publisher = {{Springer Fachmedien Wiesbaden}}, title = {{{Tutorenschulung als Basis für ein kompetenzorientiertes Feedback in fachmathematischen Anfängervorlesungen}}}, doi = {{10.1007/978-3-658-10265-4_10}}, year = {{2018}}, } @inproceedings{56711, author = {{Heinemann, Birte and Opel, Simone and Budde, Lea and Schulte, Carsten and Frischemeier, Daniel and Biehler, Rolf and Podworny, Susanne and Wassong, Thomas}}, booktitle = {{Proceedings of the 18th Koli Calling International Conference on Computing Education Research, November 22–25, 2018, Koli, Finland}}, publisher = {{ACM}}, title = {{{Drafting a Data Science Curriculum for Secondary Schools}}}, doi = {{10.1145/3279720.3279737}}, year = {{2018}}, } @article{56710, author = {{Heinemann, Birte and Budde, Lea and Schulte, Carsten and Biehler, Rolf and Frischemeier, Daniel and Podworny, Susanne and Wassong, Thomas}}, journal = {{Archives of Data Science, Series A}}, number = {{1}}, pages = {{1–18}}, title = {{{Data Science and Big Data in Upper Secondary Schools: What Should Be Discussed From a Perspective of Computer Science Education?}}}, volume = {{5}}, year = {{2018}}, } @inbook{56712, author = {{Hoffmann, Max and Biehler, Rolf}}, booktitle = {{Beiträge zum Mathematikunterricht 2017}}, editor = {{Kortenkamp, U. and Kuzle, A.}}, pages = {{441--444}}, publisher = {{WTM-Verlag}}, title = {{{Schnittstellenaufgaben für die Analysis I-Konzept, Beispiele und Evaluationsergebnisse}}}, year = {{2018}}, }