TY - CHAP AU - Gold, Alexander AU - Fleischmann, Yael AU - Mai, Tobias AU - Biehler, Rolf AU - Kempen, Leander ED - Biehler, Rolf ED - Eichler, Andreas ED - Hochmuth, Reinhard ED - Rach, Stefanie ED - Schaper, Niclas ID - 35755 SN - 2197-8751 T2 - Lehrinnovationen in der Hochschulmathematik . Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik TI - Die Online-Lernmaterialien im Online-Mathematikvorkurs studiVEMINT: Konzeption und Ergebnisse von Nutzer- und Evaluationsstudien ER - TY - CHAP AU - Kempen, Leander AU - Biehler, Rolf ED - Biehler, Rolf ED - Eichler, Andreas ED - Hochmuth, Reinhard ED - Rach, Stefanie ED - Schaper, Niclas ID - 35776 SN - 2197-8751 T2 - Lehrinnovationen in der Hochschulmathematik . Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik TI - Design-Based Research in der Hochschullehre am Beispiel der Lehrveranstaltung „Einführung in die Kultur der Mathematik“ ER - TY - JOUR AU - Höper, Lukas AU - Malin, Leah AU - Biehler, Rolf ID - 35761 IS - 228 JF - mathematik lehren TI - Schatten von 3D-Objekten: Modellierung mit GeoGebra 3D und Anwendungen in der Computergrafik VL - 2021 ER - TY - JOUR AU - Hüsing, Sven AU - Weiser, Niklas AU - Biehler, Rolf ID - 35763 IS - 228 JF - mathematik lehren TI - Faszination 3D-Film: Entwicklung einer 3D-Konstruktion VL - 2021 ER - TY - JOUR AB - AbstractThe aim of the special issue is to bring together important current international research on innovative teaching and learning practices in mathematics in engineering education, and to develop deeper understandings of the characteristics of current teaching and learning practices that can inform the design and implementation of future innovative practice. The focus of this review paper is to provide a state-of-the-art overview of this emerging field at the cross-roads between mathematics and engineering education, in addition to introducing the papers of this special issue. To guide this paper, we posed three review questions: (1) How can current (teaching/learning/study) practices of mathematics in engineering education be characterized with a view towards innovation?; (2) What are the ‘resources’ (cognitive, material, digital, social) used, and what are those that appear also well suited for innovative courses?; (3) What are promising innovative practices in mathematics in engineering education, and what are the implications for curriculum reform? Looking back across the studies we summarized in the review, we conclude that they are lagging behind the more fundamental changes that are happening in engineering education, whilst addressing selected aspects of innovative changes within the current system of engineering education. At the same time, the nine papers of this special issue contribute new perspectives for innovative practices in mathematics in engineering education, for a better understanding of current practices and for future research. AU - Pepin, Birgit AU - Biehler, Rolf AU - Gueudet, Ghislaine ID - 35778 IS - 2 JF - International Journal of Research in Undergraduate Mathematics Education KW - Education KW - Mathematics (miscellaneous) SN - 2198-9745 TI - Mathematics in Engineering Education: a Review of the Recent Literature with a View towards Innovative Practices VL - 7 ER - TY - JOUR AU - Podworny, Susanne AU - Biehler, Rolf ID - 35781 IS - 4 JF - Mathematical Thinking and Learning KW - Developmental and Educational Psychology KW - Education KW - General Mathematics SN - 1098-6065 TI - The process of actively building a model for a randomization test – insights into learners’ modeling activities based on a case study VL - 24 ER - TY - CHAP AU - Winsløw, Carl AU - Biehler, Rolf AU - Jaworski, Barbara AU - Rønning, Frode AU - Wawro, Megan ED - Durand-Guerrier, V. ED - Hochmuth, R. ED - Nardi, E. ED - Winsløw, C. ID - 35704 SN - 9780429346859 T2 - Research and Development in University Mathematics Education TI - Education and professional development of university mathematics teachers ER - TY - JOUR AU - Schürmann, Mirko AU - Liebendörfer, Michael AU - Gildehaus, Lara AU - Schaper, Niclas AU - Hochmuth, Reinhard AU - Biehler, Rolf AU - Lankeit, Elisa AU - Kuklinski, Christiane AU - Ruge, Johanna ID - 24786 JF - Sigma newsletter TI - Opportunities and Possibilities of a Network of Mathematical Learning and Support Centres in Germany VL - 22 ER - TY - CHAP AU - Rach, Stefanie AU - Liebendörfer, Michael ED - Hein, Kerstin ED - Heil, Cathleen ED - Ruwisch, Silke ED - Prediger, Susanne ID - 37485 SN - 978-3-95987-184-6 T2 - Beiträge zum Mathematikunterricht 2021 vom GDM-Monat 2021 der Gesellschaft für Didaktik der Mathematik (GDM) (1.-25. März 2021) TI - Die Bedeutung affektiver Merkmale beim Mathematiklernen ER - TY - JOUR AB - Abstract Due to the COVID-19 crisis, many courses have been offered digitally. Using data from n = 1,173 business students participating in a preparatory mathematics course at a German university that covered the same content as in 2018, 2019 and 2020, we examine how students’ participation and the effect of the preparatory course changed. The data show that the participation rate has fallen slightly, but students’ participation is rather similar to preceding years. Interestingly, students have participated more intensively. There are clear signs of dishonesty in the self-test (use of a calculator) and significant changes in predictors of performance. In particular, the effect of students’ engagement in the course on their performance substantially increased. Further, we found a gender gap in performance affecting women. Finally, the data show that digital courses can be as effective as on-campus courses. AU - Büchele, Stefan AU - Liebendörfer, Michael AU - Lankeit, Elisa ID - 37474 IS - 4 JF - Teaching Mathematics and its Applications: An International Journal of the IMA KW - Education KW - General Mathematics SN - 0268-3679 TI - Increasing the effect of a remedial mathematics course by switching to an online format during the COVID-19 crisis: evidence from a German university VL - 40 ER - TY - JOUR AB - Das gymnasiale Lehramtsstudium der Mathematik ist an deutschen Universitäten unterschiedlich organisiert. Traditionell wurden am Studienbeginn die Fachvorlesungen zur Analysis und Linearen Algebra gemeinsam mit Fachstudierenden gehört. In jüngerer Zeit verbreiten sich alternative Modelle z. B. mit Brückenvorlesungen, die oft spezifisch für das Gymnasiallehramt angeboten werden. Sie können gemeinsame Veranstaltungen mit Fachstudierenden ergänzen oder ersetzen. Dieser Beitrag zeigt auf, welche Modelle wie häufig verbreitet sind, und spricht an, welche hochschuldidaktischen Fragen an der Studiengestaltung hängen. AU - Gildehaus, Lara AU - Göller, Robin AU - Liebendörfer, Michael ID - 37483 IS - 111 JF - Mitteilungen der Gesellschaft für Didaktik der Mathematik SN - 2512-9155 TI - Gymnasiales Lehramt Mathematik studieren – eine Übersicht zur Studienorganisation in Deutschland VL - 47 ER - TY - CONF AU - Vajen, Bastian AU - Gildehaus, Lara AU - Liebendörfer, Michael AU - Wolf, Christoph ED - Kenner, Steve ED - Oeftering, T. ID - 37481 T2 - Schriftenreihe der DVPB. Standortbestimmung Politische Bildung: Gesellschaftspolitische Herausforderungen, Zivilgesellschaft und das vermeintliche Neutralitätsgebot TI - Mathematisierung als Herausforderung für die politische Bildung ER - TY - CHAP AU - Göller, Robin AU - Gildehaus, Lara AU - Liebendörfer, Michael AU - Steuding, Jörn ED - Blunck, Andrea ED - Motzer, Renate ID - 37480 T2 - Mathematik und Gender: Berichte und Beiträge des Arbeitskreise Frauen und Mathematik TI - Prüfungsformate als Ansatzpunkt gendersensibler universitärer Lehre im Fach Mathematik VL - 5 ER - TY - CONF AU - Haak, Inka AU - Gildehaus, Lara AU - Liebendörfer, Michael ID - 37478 T2 - Naturwissenschaftlicher Unterricht und Lehrerbildung im Umbruch? TI - Genese und Funktionen von Lerngruppen in der Studieneingangsphase ER - TY - JOUR AB - Abstract We investigated university students’ study of mathematics in the digital setting context of the COVID-19 pandemic. We gathered data from a survey of 89 students enrolled in a ‘Linear Algebra 1’ course including affective variables, learning strategies, social relatedness and resources considered useful. The results indicate students’ high effort and self-regulation and a high variation in affective characteristics and social relatedness. All the traditional aspects of mathematics teaching (lecture, tutorials and lecture notes) were rated as particularly useful. In addition, the videos from external resources were rated as equally useful as the teaching team’s videos. In contrast, traditional literature such as textbooks was rarely considered useful. The most useful resource rated was communication with peers, underlining the important role of social learning despite fully digital learning environments. Finally, a cluster analysis based on students’ rated usefulness of the resources led to three different user-types. Whereas the ‘digitals’ find the external digital resources very useful (videos, webpages, etc.), the ‘traditionalists’ rate the digitalized traditional resources best (lecture, tutorials, etc.). All resources receive uniformly good ratings from a third group (‘all resource users’). We reflect on our findings in light of the pandemic and describe directions for future research. AU - Kempen, Leander AU - Liebendörfer, Michael ID - 37473 IS - 4 JF - Teaching Mathematics and its Applications: An International Journal of the IMA KW - Education KW - General Mathematics SN - 0268-3679 TI - University students’ fully digital study of mathematics: an identification of student-groups via their resources usage and a characterization by personal and affective characteristics VL - 40 ER - TY - CONF AU - Liebendörfer, Michael AU - Hochmuth, Reinhard AU - Rode, Jana AU - Schukajlow, Stanislaw ED - Inprasitha, M. ED - Changsri, N. ED - Boonsena, N. ID - 37487 T2 - Interim Proceedings of the 44th Conference of the International Group for the Psychology of Mathematics Education TI - The Mathematical Beliefs and Interest Development of Pre-Service Primary Teachers VL - 3 ER - TY - JOUR AU - Krapf, Regula AU - Liebendörfer, Michael ID - 37494 IS - 44 JF - mathematica didactica KW - Extrinsische Motivation TI - Was bewirkt die Pflichtabgabe von Übungsaufgaben in der Hochschulmathematik? – Ein empirischer Vergleich VL - 2 ER - TY - JOUR AU - Winkler, Michael ID - 35616 JF - Nonlinear Analysis: Real World Applications TI - Global weak solutions in a three-dimensional Keller-Segel-Navier-Stokes system with gradient-dependent flux limitation. VL - 59 ER - TY - JOUR AU - Winkler, Michael ID - 35615 JF - Zeitschrift für Angewandte Mathematik und Physik TI - Suppressing blow-up by gradient-dependent flux limitation in a planar Keller-Segel-Navier-Stokes system. VL - 72 ER - TY - JOUR AU - Winkler, Michael ID - 35614 JF - International Mathematics Research Notices TI - Can rotational fluxes impede the tendency toward spatial homogeneity in nutrient taxis (-Stokes) systems? VL - 2021 ER - TY - JOUR AU - Winkler, Michael ID - 35617 JF - Applied Mathematics Letters TI - Boundedness in a three-dimensional Keller-Segel-Stokes system with subcritical sensitivity. VL - 112 ER - TY - JOUR AU - Winkler, Michael ID - 35613 JF - Transactions of the American Mathematical Society TI - Does spatial homogeneity ultimately prevail in nutrient taxis systems? A paradigm for structure support by rapid diffusion decay in an autonomous parabolic flow. VL - 374 ER - TY - JOUR AU - Rösler, Margit AU - Voit, Michael ID - 37659 IS - 3 JF - Proceedings of the American Mathematical Society KW - Applied Mathematics KW - General Mathematics SN - 0002-9939 TI - Positive intertwiners for Bessel functions of type B VL - 149 ER - TY - JOUR AU - Tao, Youshan AU - Winkler, Michael ID - 35603 JF - Journal of Functional Analysis TI - A fully cross-diffusive two-component evolution system: Existence and qualitative analysis via entropy-consistent thin-film-type approximation. VL - 281 ER - TY - JOUR AU - Tao, Youshan AU - Winkler, Michael ID - 35606 JF - Nonlinear Analysis, Theory, Methods and Applications TI - The dampening role of large repulsive convection in a chemotaxis system modeling tumor angiogenesis. VL - 208 ER - TY - JOUR AU - Wang, Yulan AU - Winkler, Michael AU - Xiang, Zhaoyin ID - 35612 JF - Science China Mathematics TI - Immediate regularization of measure-type population densities in a two-dimensional chemotaxis system with signal consumption. VL - 64 ER - TY - JOUR AU - Ding, Mengyao AU - Winkler, Michael ID - 35601 JF - Nonlinear Differential Equatiions and Applicatiions TI - Small-density solutiions in Keller-Segel systems involving rapidly decaying diffusivities. VL - 28 ER - TY - JOUR AU - Tao, Youshan AU - Winkler, Michael ID - 35605 JF - Communications in Mathematical Sciences TI - Global smooth solutions in a two-dimensional cross-diffusion system modeling propagation of urban crime. VL - 19 ER - TY - JOUR AU - Tao, Youshan AU - Winkler, Michael ID - 35604 JF - SIAM Journal on Mathematical Analysis TI - Taxis-driven formation of singular hotspots in a May-Nowak type model for virus infection. VL - 53 ER - TY - JOUR AU - Wang, Yulan AU - Winkler, Michael AU - Xiang, Zhaoyin ID - 35610 JF - Communications in Partial Differential Equations TI - Local energy estimates and global solvability in a threee-dimensional chemotaxis-fluid system with prescribed signal on the boundary. VL - 46 ER - TY - JOUR AU - Wang, Yulan AU - Winkler, Michael AU - Xiang, Zhaoyin ID - 35611 JF - Advances in Nonlinear Analysis TI - Global solvability in a threee-dimensional Keller-Segel.Stokes system involving arbitrary superlinear logistic degradation VL - 10 ER - TY - JOUR AU - Tao, Youshan AU - Winkler, Michael ID - 35608 IS - --A JF - Discrete and Continuous Dynamical Systems TI - Critical mass for infinite-time blow-up in a haptotaxis system with nonlinear zero-order interaction VL - 41 ER - TY - JOUR AB - In this paper we obtain a complete list of imaginary n-quadratic fields with class groups of exponent 3 and 5 under ERH for every positive integer n where an n-quadratic field is a number field of degree 2ⁿ represented as the composite of n quadratic fields. AU - Klüners, Jürgen AU - Komatsu, Toru ID - 34840 IS - 329 JF - Mathematics of Computation KW - Applied Mathematics KW - Computational Mathematics KW - Algebra and Number Theory SN - 0025-5718 TI - Imaginary multiquadratic number fields with class group of exponent $3$ and $5$ VL - 90 ER - TY - JOUR AB - Let E be an ordinary elliptic curve over a finite field and g be a positive integer. Under some technical assumptions, we give an algorithm to span the isomorphism classes of principally polarized abelian varieties in the isogeny class of E⁹ . The varieties are first described as hermitian lattices over (not necessarily maximal) quadratic orders and then geometrically in terms of their algebraic theta null point. We also show how to algebraically compute Siegel modular forms of even weight given as polynomials in the theta constants by a careful choice of an affine lift of the theta null point. We then use these results to give an algebraic computation of Serre’s obstruction for principally polarized abelian threefolds isogenous to E³ and of the Igusa modular form in dimension 4. We illustrate our algorithms with examples of curves with many rational points over finite fields. AU - Kirschmer, Markus AU - Narbonne, Fabien AU - Ritzenthaler, Christophe AU - Robert, Damien ID - 34912 IS - 333 JF - Mathematics of Computation KW - Applied Mathematics KW - Computational Mathematics KW - Algebra and Number Theory SN - 0025-5718 TI - Spanning the isogeny class of a power of an elliptic curve VL - 91 ER - TY - JOUR AB - This paper is devoted to algebro-geometric study of infinite dimensional Lie bialgebras, which arise from solutions of the classical Yang–Baxter equation. We regard trigonometric solutions of this equation as twists of the standard Lie bialgebra cobracket on an appropriate affine Lie algebra and work out the corresponding theory of Manin triples, putting it into an algebro-geometric context. As a consequence of this approach, we prove that any trigonometric solution of the classical Yang–Baxter equation arises from an appropriate algebro-geometric datum. The developed theory is illustrated by some concrete examples. AU - Burban, Igor AU - Abedin, R. ID - 44329 IS - 2 JF - Communications in Mathematical Physics TI - Algebraic geometry of Lie bialgebras defined by solutions of the classical Yang-Baxter equation VL - 387 ER - TY - JOUR AB - The role of domain-specific content knowledge is discussed controversially for the early childhood context. Therefore, this review aims at untangling the research on domain-specific content knowledge for early childhood educators by systematically reviewing the conceptual and operational definition of and results on early childhood educators' content knowledge in different domains. Using the scientific databases ERIC, PsycInfo and Web of Sciences, we identified 36 studies on early childhood educators' domain-specific content knowledge. By comparing these studies, we found that conceptualizations of early childhood educators' content knowledge move on a continuum between a scientific related perspective and a practice related perspective. The scientific related perspective defines content knowledge as the knowledge of key concepts, facts and rules of the domain integrating knowledge taught in primary, secondary or upper secondary school. The practice related perspective includes knowledge of key concepts, facts and rules of the domain limited to the knowledge explicitly relevant for teaching in early childhood education as well as selected domain-specific knowledge of children and teaching. Our review shows that the results and implications drawn by the study authors depend on how these authors conceptualize early childhood educators' content knowledge on this continuum. Further research, therefore, needs to consider carefully how early childhood educators' content knowledge is conceptualized. The paper further discusses gaps in this research field, such as validating methods for measuring early childhood educators' content knowledge or implementing more rigorous experimental designs to examine effects of early childhood educators' content knowledge. AU - Bruns, Julia AU - Gasteiger, Hedwig AU - Strahl, Carolin ID - 34822 IS - 2 JF - Review of Education KW - content knowledge KW - domain-specific learning KW - early childhood education KW - teacher knowledge SN - 2049-6613 TI - Conceptualising and measuring domain-specific content knowledge of early childhood educators: A systematic review VL - 9 ER - TY - JOUR AU - Bruns, Julia AU - Schopferer, T. ID - 45687 JF - . TPS – Theorie und Praxis der Sozialpädagogik TI - Eine mustergültige Wissenschaft VL - 11 ER - TY - CONF AU - Jensen, Solveig AU - Gasteiger, Hedwig AU - Bruns, Julia ED - Inprasitha, Maitree ED - Changsri, Narumon ED - Boonsena, Nisakorn ID - 36527 T2 - Proceedings of the 44th Conference of the International Group for the Psychology of Mathematics Education TI - Place value and regrouping as seperate constructs of place value understanding VL - 3 ER - TY - JOUR AU - Bruns, Julia AU - Gasteiger, Hedwig AU - Strahl, Carolin ID - 34823 IS - 2 JF - Review of Education SN - 2049-6613 TI - Context and Implications Document for: Conceptualising and measuring domain-specific content knowledge of early childhood educators: A systematic review VL - 9 ER - TY - CONF AU - Jensen, Solveig AU - Gasteiger, Hedwig AU - Bruns, Julia ID - 36536 T2 - Beiträge zum Mathematikunterricht 2021 TI - Stellenwertverständnis: Verständnis von Stellenwertprinzip und Bündelungsprinzip als separate Konstrukte ER - TY - JOUR AU - Schönherr, Johanna AU - Blomberg, J. AU - Schukajlow, S. AU - Leopold, C. ID - 45342 JF - Contemporary Educational Psychology TI - Do emotions and prior performance facilitate the use of the learner-generated drawing strategy? Effects of enjoyment, anxiety, and intramathematical performance on the use of the drawing strategy and modelling performance VL - 65 ER - TY - JOUR AU - Schönherr, Johanna AU - Schukajlow, S. AU - Blomberg, J. AU - Leopold, C. ID - 45333 JF - Mathematical Thinking and Learning TI - Does strategic knowledge matter? Effects of strategic knowledge about drawing on students’ modeling competencies in the domain of geometry ER - TY - JOUR AU - Schönherr, Johanna AU - Schukajlow, S. AU - Blomberg, J. AU - Leopold, C. ID - 45343 JF - Learning and Instruction TI - The role of strategy-based motivation in mathematical problem solving: The case of learner-generated drawings VL - 80 ER - TY - JOUR AU - Schönherr, Johanna AU - Schukajlow, S. AU - Blomberg, J. ID - 45335 JF - mathematik lehren TI - Was ist eine gute Skizze? Strategiewissen beim mathematischen Modellieren im Bereich der Geometrie fördern VL - 224 ER - TY - JOUR AU - Black, Tobias AU - Fuest, Mario AU - Lankeit, Johannes ID - 34673 IS - 3 JF - Zeitschrift für angewandte Mathematik und Physik KW - Applied Mathematics KW - General Physics and Astronomy KW - General Mathematics SN - 0044-2275 TI - Relaxed parameter conditions for chemotactic collapse in logistic-type parabolic–elliptic Keller–Segel systems VL - 72 ER - TY - JOUR AU - Black, Tobias AU - Wu, Chunyan ID - 34675 IS - 4 JF - Zeitschrift für angewandte Mathematik und Physik KW - Applied Mathematics KW - General Physics and Astronomy KW - General Mathematics SN - 0044-2275 TI - Prescribed signal concentration on the boundary: Weak solvability in a chemotaxis-Stokes system with proliferation VL - 72 ER - TY - JOUR AU - Dröse, Jennifer AU - Prediger, S. AU - Neugebauer, P. AU - Danhier, R. D. AU - Mertins, B. ID - 45381 JF - International Electronic Journal of Mathematics Education, 16(1), em0625 TI - Investigating students' processes of noticing and interpreting syntactic language features in word problem solving through eye-tracking ER - TY - JOUR AU - Dröse, Jennifer AU - Prediger, S. ID - 45380 JF - Studies in Educational Evaluation, 68 (100953) TI - Identifying obstacles is not enough for everybody – Differential efficacy of an intervention fostering fifth graders’ comprehension for word problems ER - TY - JOUR AU - Häsel-Weide, Uta AU - Seitz, Simone AU - Wallner, Melina AU - Wilke, Yannik AU - Heckmann, Lara ID - 31578 IS - 1 JF - QfI - Qualifizierung für Inklusion. Online-Zeitschrift zur Forschung über Aus-, Fort- und Weiterbildung pädagogischer Fachkräfte TI - Mit Aufgaben im inklusiven Mathematikunterricht professionell umgehen - Erkenntnisse einer Interviewstudie mit Lehrpersonen der Sekundarstufe VL - 3 ER - TY - CONF AU - Hattermann, Mathias AU - Häsel-Weide, Uta AU - Wallner, Melina ED - Inprasitha, M. ED - Changsri, N. ED - Boonsena, N. ID - 31583 T2 - Proceedings of the 44th Conference of the International Group for the Psychology of Mathematics Education TI - Conceptualiziation processes of 6th graders for rotational symmetry VL - 3 ER -