Using scriptwriting as a response format for interface tasks: Exemplary analyses in the context of symmetry - Hoffmann, Max (Proceedings of the Fourteenth Congress of the European Society for Research in Mathematics Education (CERME14))
Keywords: hoffmann; reviewed; proceedings

Digitale Perspektiven auf das Heron-Verfahren - Hoffmann, Max (mathematik lehren)

Symmetry as a Topic for the University Education of Pre-Service Teachers - Hoffmann, Max (Recherches en Didactique des Mathématiques)
This article provides a comprehensive mathematical-didactic analysis of how the highly relevant topic symmetry can be prepared for the university education of PSTs. Methodologically, the analysis is embedded in a design research cycle and serves as preparation for the actual design of learning activities. The procedure of "specifying and structuring" learning objects is used and adapted in such a way that, in addition to mathematical aspects, profession-oriented references to school mathematics are also considered. An essential result of the analysis is the formulation of so-called interface aspects to symmetry, which prove to be helpful in establishing such references.

Using scriptwriting as a response format for interface tasks: Exemplary analyses in the context of symmetry - Hoffmann, Max (Proceedings of the Fourteenth Congress of the European Society for Research in Mathematics Education (CERME14))

Das Sieb des Eratosthenes - Hoffmann, Jan Sören; Stoppel, Hans-Jürgen (mathematik lehren)

Digitalisierung als Chance für alle Prinzipien guten Unterrichts - Barzel, Bärbel; Greefrath, Gilbert; Nagel, Mareike; Hoffmann, Max (mathematik lehren)
athematische Kompetenzen digital zu fördern und digitale Kompetenzen mathematisch zu fördern – dies ist eine Forderung der neuen Bildungsstandards mit Blick auf eine Bildung in der digitalen Welt. Gerade das Potenzial digitaler Medien für das fachliche Lernen wurde in vielen Studien bestätigt. Eine sinnvoll gestaltete Einbettung digitaler Medien bietet die Chance, allen fünf Prinzipien eines guten Unterrichts gerecht zu werden: Verstehensorientierung, Durchgängigkeit, kognitive Aktivierung, Lernendenorientierung & Adaptivität und Kommunikationsförderung. Die flächendeckende Nutzung digitaler Medien etabliert sich bislang nur zögerlich. Aber wie können wir Lehrkräfte stärken, digitale Medien sinnvoll einzusetzen? Wir möchten hier die Bandbreite der Möglichkeiten an Beispielen verdeutlichen, ihren Einsatz motivieren und Wege für einen guten Unterricht aufzeigen.

31 Sprachbildung im berufsbezogenen Mathematikunterricht. - Prediger, Susanne; Wessel, Lena (Berufs-und Fachsprache Deutsch in Wissenschaft und Praxis)

Ebene euklidische Geometrie. Algebraisierung, Axiomatisierung und Schnittstellen zur Schulmathematik - Hoffmann, Max; Hilgert, Joachim; Weich, Tobias

Using academic mathematical knowledge when working on interface tasks–analyses of pre-service teachers’ arguments about rotationally symmetric figures - Hoffmann, Max; Biehler, Rolf (ZDM – Mathematics Education)
Abstract 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.

How Do Advanced Pre-Service Teachers Develop Congruence Theorems for Quadrilaterals? - Hoffmann, Max; Schlüter, Sarah (Proceedings of the Fifth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2024, 10-14 June 2024))
In our paper, we present a study in which we investigate which strategies pre-service teachers (PSTs) use to find and, if necessary, reject possible candidates for congruence theorems for quadrilaterals. This study was conducted before the PTSs attended a university geometry course. In this way, statements about learning prerequisites can be made. For the study, we analyzed group discussions of PSTs to identify typical approaches and evaluate them from a mathematical perspective. The results can be considered for the further development of courses for PSTs and generate hypotheses for further research.
Keywords: Teachers’ and students’ practices at university level; Transition to; across and from university mathematics; Teaching and learning of specific topics in university mathematics; Congruence; Quadrilaterals

Algebraische Konzepte vertiefen und ihre Zusammenhänge im Schul- und Hoch-schulcurriculum verstehen lernen : Design-Prinzipien zur Anregung des Vereinheitlichens mathematischen Wissens im Mathematiklehramtsstudium - Wessel, Lena; Dellori, Anna (Mathematica Didactica)

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 - Hoffmann, Max; Biehler, Rolf (ZDM – Mathematics Education)
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.
Keywords: General Mathematics; Education

Sprache und Mathematiklernen - Leiss, Dominik; Gerlach, Kerstin; Wessel, Lena; Schmidt-Thieme, Barbara (Handbuch der Mathematikdidaktik)

Prospective teachers’ diagnostic judgments on students’ understanding of conditional probabilities - Dröse, Jennifer; Griese, Birgit; Wessel, Lena (Twelfth Congress of the European Society for Research in Mathematics Education (CERME12))

Entwicklung und Erprobung von professionsorientierten Lernumgebungen zur Wissensvernetzung in der Algebra - Dellori, Anna; Wessel, Lena (Beiträge zum Mathematikunterricht 2022)

Design principles for intertwining local and nonlocal mathematics - The case of relating registers and representations in abstract algebra - Dellori, Anna; Wessel, Lena (Proceedings of INDRUM2022)

Pre-service Teachers' Professional Development: Relating Abstract Algebra and School Algebra - Dellori, Anna; Wessel, Lena (Proceedings of the 24th Annual Conference on Research in Undergraduate Mathematics Education)

Schreiben will gelernt sein: Schreiblerngelegenheiten adaptiv gestalten - Wessel, Lena; Dröse, Jennifer (mathematik lehren)

Profession-Specific Curriculum Design in Mathematics Teacher Education: Connecting Disciplinary Practice to the Learning of Group Theory - Wessel, Lena; Leuders, Timo (Practice-Oriented Research in Tertiary Mathematics Education)

Lehrerbildung als staatliche und gesellschaftliche Aufgabe angesichts gegenwärtiger und zukünftiger Herausforderungen - Sjuts, Johann (Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik)