Förderung prozeduraler Flexibilität durch Lernvideos mit interaktiven Aufgaben - Krämer, Sandra; Liebendörfer, Michael (Beiträge zum Mathematikunterricht 2022. 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik)

Preservice teachers’ mathematics-related values and expectancy in the transition from school to university
Many preservice mathematics teachers lose their motivation during their first year at university. This phenomenon has been repeatedly described in recent years but is not yet fully understood. Since motivation may relate to different objects such as mathematics or teaching, we aim to qualitatively reconstruct different facets of the central motivational constructs of Situated-Expectancy-Value theory (intrinsic value, attainment value, utility value, cost, and expectancy of success) for preservice mathematics teachers. The analysis of longitudinal group interviews of 14 preservice higher-secondary mathematic teachers from a German university revealed different objects of motivation (e.g., teaching mathematics, scientific mathematics, procedural mathematics, or proof-based mathematics) in preservice teachers' values and expectancy of success. Furthermore, relations between those values and expectancy of success were identified that played a significant role in preservice teachers’ motivational development over their first semester (e.g., relations of attainment value for scientific mathematics and psychological cost). Theoretical and practical implications towards a teaching-specific conceptualization of expectancy of success and values and value interventions are being discussed.

Professional Development Enacted by Facilitators in the Context of Early Mathematics Education: Scaling up or Dilution of Effects? - Bruns, Julia; Hagena, Maike; Gasteiger, Hedwig (Teaching and Teacher Education)
Keywords: Education

Neue Wege im mathematischen Unterricht: Auf den Spuren Mathilde Vaertings - Werth, Gerda

Standardkonstruktionen eigenständig entdecken. Mathilde Vaertings Idee der Selbstständigkeitsprobe - Werth, Gerda (mathematik lehren)

Verdoppeln und Halbieren im Zahlenraum bis 100 - Erkenntnisse einer Interviewstudie in Klasse 2 - Schwerin, Imke (Mathematikdidaktik Grundschule)

Mathematik – Lesen – Lernen: Ein Vorlesungskonzept zur Förderung mathematischer Lesekompetenz - Rezat, Sebastian; Malik, Sara Naseem; Leifeld, Markus (Beiträge zum Mathematikunterricht 2022. 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik vom 29.08.2022 bis 02.09.2022 in Frankfurt am Main)

Verstehen schriftlicher Rechenverfahren durch algorithmisches Denken am Beispiel der schriftlichen Subtraktion - Leifeld, Markus; Rezat, Sebastian (Beiträge zum Mathematikunterricht 2022. 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik vom 29.08.2022 bis 02.09.2022 in Frankfurt am Main)

Herausforderungen anwendungsbezogener Aufgaben - eine curriculare Perspektive auf den Forschungsstand - Malik, Sara Naseem; Rezat, Sebastian (Beiträge zum Mathematikunterricht 2022. 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik vom 29.08.2022 bis 02.09.2022 in Frankfurt am Main)

Toward student agency in the selection and use of digital resources for learning and studying mathematics - Pepin, Birgit; Kock, Zeger-jan; Rezat, Sebastian (Handbook of Digital Resources in Mathematics Education)

Meta-Resources: Supporting the design of mathematics teaching and learning - Gueudet, Ghislaine; Pepin, Birgit; Rezat, Sebastian (Handbook of Digital Resources in Mathematics Education)

The role of digital technologies in transforming student learning landscapes - Rezat, Sebastian; Geiger, Vince (Handbook of Digital Resources in Mathematics Education)

Geometrie: Leitidee Raum und Form - Hattermann, Mathias; Rezat, Sebastian; Sträßer, Rudolf (Handbuch der Mathematikdidaktik)

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)

Supporting Students in Developing Adequate Concept Images and Definitions at University: The Case of the Convergence of Sequences - Ostsieker, Laura; Biehler, Rolf (Practice-Oriented Research in Tertiary Mathematics Education)

Analyzing the Interface Between Mathematics and Engineering in Basic Engineering Courses - Kortemeyer, Jörg; Biehler, Rolf (Practice-Oriented Research in Tertiary Mathematics Education)

The use of integrals for accumulation and mean values in basic electrical engineering courses - Kortmeyer, Jörg; Biehler, Rolf (The Learning and Teaching of Calculus Across Disciplines – Proceedings of the Second Calculus Conference)

Stochastik: Leitidee Daten und Zufall - Biehler, Rolf; Engel, Joachim; Frischemeier, Daniel (Handbuch der Mathematikdidaktik)

Impacts of Digitalization on Content and Goals of Statistics Education - Biehler, Rolf; Frischemeier, Daniel; Gould, Ronald; Pfannkuch, Maxine (Handbook of Digital Resources in Mathematics Education)

Von Glückstal (Ukraine) nach Frankfurt: Problemlösen, Algorithmen, Stochastik – Nachruf auf Arthur Engel - Biehler, Rolf; Krüger, Katja (GDM-Mitteilungen)

Practice-Oriented Research in Tertiary Mathematics Education – An Introduction - Biehler, Rolf; Liebendörfer, Michael; Gueudet, Ghislaine; Rasmussen, Chris; Winsløw, Carl (Practice-Oriented Research in Tertiary Mathematics Education)

Framing Goals of Mathematics Support Measures - Liebendörfer, Michael; Büdenbender-Kuklinski, Christiane; Lankeit, Elisa; Schürmann, Mirko; Biehler, Rolf; Schaper, Niclas (Practice-Oriented Research in Tertiary Mathematics Education)

Practice-Oriented Research in Tertiary Mathematics Education

Lernvideos und ihre Erstellung - Das Projekt studiVEMINTvideos - Biehler, Rolf; Liebendörfer, Michael; Schmitz, A. (Mitteilungen der Gesellschaft für Didaktik der Mathematik)

Think-aloud beim hochschulischen Mathematiklernen – Ergebnisse einer Pilotierung - Kolbe, Tim (Beiträge zum Mathematikunterricht 2022. 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik)

Characterizing external visualization in mathematics education research: a scoping review - Schoenherr, Johanna; Schukajlow, Stanislaw (ZDM – Mathematics Education)
Abstract External visualization (i.e., physically embodied visualization) is central to the teaching and learning of mathematics. As external visualization is an important part of mathematics at all levels of education, it is diverse, and research on external visualization has become a wide and complex field. The aim of this scoping review is to characterize external visualizations in recent mathematics education research in order to develop a common ground and guide future research. A qualitative content analysis of the full texts of 130 studies published between 2018 and 2022 applied a deductive-inductive coding procedure to assess four dimensions: visualization product or process, type of visualization, media, and purpose. The analysis revealed different types of external visualizations including visualizations with physical resemblance ranging from pictorial to abstract visualizations as well as three types of visualizations with structural resemblance: length, area, and relational visualizations. Future research should include measures of visualization products or processes to help explain the demands and affordances that different types of visualizations present to learners and teachers.
Keywords: General Mathematics; Education

Symmetrieverständnis von Anfang an - Häsel-Weide, Uta; Wallner, Melina; Hattermann, M. (Anfangsunterricht für alle Kinder - Willkommen in der Schule!)

Professionalisierung für inklusiven Mathematikunterricht. Interdisziplinäre Seminarkonzeption zur reflexiven Professionalisierung angehender Mathematiklehrkräfte in der Sekundarstufe - Häsel-Weide, Uta; Seitz, S.; Wallner, Melina; Wilke, Y. (Qualifizierung für Inklusion. Sekundarstufe)

Diagnosegeleitete Förderung im inklusiven Mathematikunterricht der Grundschule – Professionalisierung durch reflektierte Handlungspraxis in der Lehrer*innenbildung. - Hähn, K.; Häsel-Weide, Uta; Scherer, P. (QfI - Qualifizierung für Inklusion)

Inclusive math practices in primary school. Twelfth Congress of the European Society for Research in Mathematics Education - Häsel-Weide, Uta; Nührenbörger, M. (Twelfth Congress of the European Society for Research in Mathematics Education (CERME12))

Multiplikative Beziehungen erkennen und nutzen – Initiierung von Lernprozessen durch Entdeckervideos - Häsel-Weide, Uta; Wienhues, Inga; Kordes, L. (Digitale Medien und Heterogenität – Chancen und Herausforderungen für die Mathematikdidaktik)

„Ich hab als Erstes die angeguckt“ – Muster- und Strukturerkennung mit Eye-Tracking besser verstehen? - Bruns, Julia; Reuter, D. (Beiträge zum Mathematikunterricht 2022)

Effects of Facilitator Professional Development on Teachers’ Learning – An Intervention Study in the Context of Early Mathematics Education - Bruns, Julia; Hagena, M.; Gasteiger, H. (Proceedings of the Twelfth Congress of the European Society for Research in Mathematics Education (CERME12))

Entwicklung und Validierung eines videobasierten Testinstruments zur Erfassung des Noticing mit dem Fokus auf Anerkennungsprozesse im inklusiven Sportunterricht - Bruns, Julia; Langer, W.; Erhorn, J. (German Journal of Exercise and Sport Research)

Development and validation of a video-based test instrument to measure noticing with regard to processes ofrecognition in inclusive physical education - Langer, Wiebke; Bruns, Julia; Erhorn, Jan (German Journal of Exercise and Sport Research)
The construct of noticing is considered to be of crucial importance for professional action of (prospective) physical education (PE) teachers in the context of (inclusive) PE. In order to implement the demands of inclusive PE teaching, noticingwith regard to processes of recognition proves to be particularly significant. Due to the relevance of physicality, the design of recognition relationships that encourage pupils' development results in specific requirements for the selective attention and the theory-based interpretation of processes of recognition and disregard in complex teaching situations. This facet of competence has hardly been studied so far, partly due to the lack of instruments for standardised assessment of this construct. In the context of this paper, the development and validation of a standardised, video vignette-based test instrument for the measurement of noticingwith regard to processes of recognition of prospective PE teachers is presented. The validation focuses on the content of the test and the internal structure of the instrument as well as on correlations with related constructs in terms of content. The results from three consecutive validation studies provide indications of the reliability and validity of the test score interpretation of the instrument ViProQiS_A. The findings so far indicate that the standardised measurement of noticingwith regard to processes of recognitionin inclusive PE could be realized on the basis of the test instrument developed here.
Keywords: Physical education teacher education; Competence modelling and; measurement; Inclusive physical education; Video-based items; Noticing

Einfluss der Berufserfahrung von Multiplikatorinnen und Multiplikatoren auf die Wirksamkeit von Fortbildungsmaßnahmen zur frühen mathematischen Bildung. Zeitschrift Für Erziehungswissenschaft - Hagena, Maike; Bruns, Julia; Gasteiger, Hedwig (Zeitschrift für Erziehungswissenschaft)
Teachers expect facilitators to have own teaching experience as a teacher in order to be able to carry out effective teacher professional development programs. As part of the project EmMa(M), it is investigated, to which extent the teaching experience of facilitators influences the development of early childhood teachers' (n = 83) mathematical pedagogical content knowledge (MPCK) and early childhood teachers' enjoyment of mathematics in the context of a teacher professional development program. It turns out that the teaching experience of the facilitators has no influence on the development of early childhood teachers' MPCK, but favors the development of early childhood teachers' enjoyment of mathematics. Controlling for this increased enjoyment an influence of teaching experience on the development of early childhood teachers' MPCK emerges, but in favor of the participating facilitators who have no teaching experience but have a university degree.
Keywords: Facilitator professional development; Early childhood teachers; Teaching; experience; Early mathematics education

Muster- und Strukturerkennungsprozesse bei potenziell mathematisch begabten Grundschulkindern untersuchen – Das Potenzial von Eye-Tracking und retrospektivem Interview im Vergleich - Reuter, Dinah; Bruns, Julia (Eye-Tracking in der Mathematik- und Naturwissenschaftsdidaktik)

Verstehensgrundlagen diagnostizieren - Diagnostisches Denken von drei Professionalisierungsgruppen - Dröse, Jennifer (Beiträge zum Mathematikunterricht)

Lernwege von fachfremd unterrichtenden Lehrkräften zur Ablösung vom zählenden Rechnen - Graf, Lara Marie; Häsel-Weide, Uta; Nührenbörger, Marcus; Höveler, Karina (Beiträge zum Mathematikunterricht 2022 - 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik)

Verdoppeln und Halbieren im 2. Schuljahr - Vorgehensweisen und Verständnis - Schwerin, Imke (Beiträge zum Mathematikunterricht 2022 - 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik)

Eye-Tracking Studie zu Textaufgaben in Klasse 5: Bemerken und Interpretieren syntaktischer Strukturen - Dröse, Jennifer; Neugebauer, P.; Delucchi Danhier, R.; Mertins, B. (Eye-Tracking in der Mathematik- und Naturwissenschaftsdidaktik. Forschung und Praxis)

Teacher expertise for fostering at-risk students’ understanding of basic concepts: conceptual model and evidence for growth - Prediger, S.; Dröse, Jennifer; Stahnke, R.; Ademmer, C. (Journal of Mathematics Teacher Education)

Prosepctive teachers‘ diagnostic judgements on students’ under- standing of conditional probabilities - Dröse, Jennifer; Griese, B.; Wessel, Lena (Twelfth Congress of the European Society for Research in Mathematics Education (CERME12))

Prospective Teachers’ Diagnostic Thinking on Students’ Understanding of Multi-Digit Multiplication: A Content-Related Analysis on Unpacking of Knowledge Elements - Dröse, Jennifer; Prediger, Susanne (Journal für Mathematik-Didaktik)
Abstract Teachers’ in-depth diagnostic thinking has been shown to be crucial for student-centered teaching as they need to perceive and interpret students’ understanding for well-informed decision-making on adaptive teaching practices. The paper presents a content-related approach to analyzing diagnostic thinking processes with respect to the mathematical knowledge elements that prospective teachers identify as students’ resources and obstacles. Prospective teachers’ challenge is that some relevant knowledge elements first have to be unpacked, because compact concepts (such as the place value concept) or procedures (such as for multi-digit multiplication) comprise several smaller knowledge elements (such as the positional property) that have to be made explicit for students to foster their learning processes adequately. Our study examines what knowledge elements prospective teachers perceive and interpret in a transcript vignettes on multi-digit multiplication (of decimal and natural numbers) and its underlying basic arithmetic concepts (place value understanding and meaning of multiplication) in written diagnostic judgments on students’ resources and obstacles ( N = 196). A comparative design within the vignette is used to investigate how far the process of perceiving can be supported by thematic cues. The analysis reveals that those knowledge elements cued in the vignette by being already unpacked and explicitly addressed are perceived and interpreted more often (but with lower correctness) than those that are uncued and therefore have to be unpacked by the prospective teachers themselves. This confirms the need to prepare prospective teachers for unpacking mathematical concepts themselves.
Keywords: Education; General Mathematics

Prospective Teachers‘ Competence of Fostering Students’ Understanding in Script Writing Task - Dröse, Jennifer; Wessel, Lena (Proceedings of the 45th Conference of the International Group for the Psychology of Mathematics Education. PME)

Neue Wege im mathematischen Unterricht - Auf den Spuren Mathilde Vaertings - Werth, Gerda (Beiträge zum Mathematikunterricht)

Linguistic features of word problems that cause difficulties for learners across the curriculum: A literature review - Malik, Sara Naseem; Rezat, Sebastian (Proceedings on the Twelfth Congress on the European Society for research in Mathematics Education (CERME 12))

Scaffolding Close Reading of Mathematical Text in Pre-service Primary Teacher Education at the Tertiary Level: Design and Evaluation - Rezat, Sebastian; Malik, Sara Naseem; Leifeld, Markus (International Journal of Science and Mathematics Education)
Abstract Even in the digital age, learning mathematics at an academic level still requires much reading of mathematical text. Research has shown that reading mathematical text requires readers to engage with all the structures of the book and with its pedagogical voice, making connections, and plausible reasoning. Specific practices and strategies that support the close reading of mathematical text have been suggested; however, descriptions and empirical evaluations of materials designed to support these activities are rare. We present the design and first evaluation cycle of materials developed in a design research project that aims to scaffold close reading of mathematical text. The materials were designed and evaluated in a German university course on elementary geometry for first-year teacher education students who study mathematics to become primary teachers. The reading strategies were explained and modeled for students in reading-strategy videos. Additionally, close reading of mathematical text was scaffolded by close-reading tasks and homework tasks and problems that build on the reading strategies and were specifically designed to foster understanding of the mathematical text. Survey data were collected from 296 students to evaluate their use of and attitude toward the different materials. The quantitative results indicate that students used the materials and were generally able to learn the course content by themselves. From all provided materials, they found the close-reading tasks most helpful. A qualitative analysis of answers to open questions revealed issues with different materials, particularly with the script, and requests for additional materials. The issues with the script were categorized inductively. The categories are presented as a qualitative result of the study and discussed.
Keywords: General Mathematics; Education

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)

Facilitators’ Orientations Towards Learning Goals, Perceived Challenges, and Teaching Resources for a PD Course on Conditional Probability - Nieszporek, Ralf; Griese, Birgit; Biehler, Rolf (Bridging the Gap: Empowering and Educating Today’s Learners in Statistics. Proceedings of the Eleventh International Conference on Teaching Statistics)
The data age has led to curriculum developments promoting the relevance of stochastics in mathematics education. This has resulted in an increased demand for teacher professional development (PD) courses, and thus in a rising number of facilitators for this purpose. Their expertise, however, remains under-researched, even though facilitators are the crucial factor in PD success. Our study aims at revealing how one aspect of facilitator expertise, orientation, is connected to other aspects: views on content goals, perception of possible challenges, and attitude towards teaching resources. The explorations reveal differing orientations and learning goals with identical teaching resources for two facilitators who had also been working as a team for the re-design of the PD course for years.

Revisiting Fundamental Ideas for Statistics Education From the Perspective of Machine Learning and Its Applications - Biehler, Rolf (Bridging the Gap: Empowering and Educating Today’s Learners in Statistics. Proceedings of the Eleventh International Conference on Teaching Statistics)
Fundamental ideas (Burrill & Biehler, 2011) have been specified to structure the curriculum across different age levels and to focus on and revisit the most important ideas. Such ideas must be based on an epistemological analysis of the scientific domain of statistics and its applications. Because these domains are changing, fundamental ideas have to be revisited from time to time. In particular, data science and machine learning have led to new methods and applications in society that must be considered for updating fundamental ideas.

Editorial: Research on Data Science Education - Biehler, Rolf; De Veaux, Richard; Engel, Joachim; Kazak, Sibel; Frischemeier, Daniel (Statistics Education Research Journal)
A very warm welcome to this Special Issue of the Statistics Education Research Journal (SERJ) on data science education. Our hope is to give an overview of selected theoretical thoughts and empirical studies on data science education from a statistics education research perspective. Data science education is rapidly developing but research into data science education is still in its infancy. The current issue presents a snapshot of this developing field.
Keywords: Education; Statistics and Probability

Alles normal?! Daten auf Normalverteilung prüfen–mit schulischen Mitteln - Biehler, Rolf; Langlotz, Hubert; Zappe, Wilfried (mathematik lehren)

Modellieren im Stochastikunterricht: Annahmen hinterfragen, Ergebnisse validieren - Biehler, Rolf; Griese, Birgit (mathematik lehren)

Teaching and Learning Data-Driven Machine Learning with Educationally Designed Jupyter Notebooks - Fleischer, Yannik; Biehler, Rolf; Schulte, Carsten (Statistics Education Research Journal)
This study examines modelling with machine learning. In the context of a yearlong data science course, the study explores how upper secondary students apply machine learning with Jupyter Notebooks and document the modelling process as a computational essay incorporating the different steps of the CRISP-DM cycle. The students’ work is based on a teaching module about decision trees in machine learning and a worked example of such a modelling process. The study outlines the students’ performance in carrying out the machine learning technically and reasoning about bias in the data, different data preparation steps, the application context, and the resulting decision model. Furthermore, the context of the study and the theoretical backgrounds are presented.
Keywords: Education; Statistics and Probability

Facilitators’ views on content goals, learning obstacles, and teaching resources in reference to conditional probability - Griese, Birgit; Nieszporek, Ralf; Biehler, Rolf

Mathematik-Vorkurse zur Vorbereitung auf das Studium – Zielsetzungen und didaktische Konzepte - Lankeit, Elisa; Biehler, Rolf (Unterstützungsmaßnahmen in mathematikbezogenen Studiengängen - Konzepte, Praxisbeispiele und Untersuchungsergebnisse)

The role of learning strategies for performance in mathematics courses for engineers - Liebendörfer, Michael; Göller, Robin; Gildehaus, Lara; Kortemeyer, Jörg; Biehler, Rolf; Hochmuth, Reinhard; Ostsieker, Laura; Rode, Jana; Schaper, Niclas (International Journal of Mathematical Education in Science and Technology)
Keywords: Applied Mathematics; Education; Mathematics (miscellaneous)

Unterstützungsmaßnahmen in mathematikbezogenen Studiengängen - Konzepte, Praxisbeispiele und Untersuchungsergebnisse

Data Science, Statistics, and Civic Statistics: Education for a Fast Changing World - Ridgway, Jim; Campos, Pedro; Biehler, Rolf (Statistics for Empowerment and Social Engagement)

Mini-Aufgaben in mathematischen Übungsgruppen zur Analysis: Charakteristika von Aufgaben und Abstimmungsverhalten von Studierenden - Bauer, Thomas; Biehler, Rolf; Lankeit, Elisa (Unterstützungsmaßnahmen in mathematikbezogenen Studiengängen - Konzepte, Praxisbeispiele und Untersuchungsergebnisse)

Vorkurse und ihre Wirkungen im Übergang Schule – Hochschule - Lankeit, Elisa; Biehler, Rolf (Unterstützungsmaßnahmen in mathematikbezogenen Studiengängen - Konzepte, Praxisbeispiele und Untersuchungsergebnisse)

Enriching videos with interactive questions to enhance students’ cognitive activity: concept and implementation - Liebendörfer, Michael; Profeta, Angelo; Krämer, Sandra; Schlüter, Sarah; Becher, Silvia; Biehler, Rolf; Mai, Tobias; Schmitz, Angela

Dokumentation der Erhebungsinstrumente des Projekts WiGeMath - Schürmann, Mirko; Büdenbender-Kuklinski, C.; Lankeit, Elisa; Liebendörfer, Michael; Hochmuth, R.; Biehler, Rolf; Schaper, N.

Einführung in das WiGeMath-Projekt: Wirkung und Gelingensbedingungen von Unterstützungsmaßnahmen für mathematikbezogenes Lernen in der Studieneingangsphase - Hochmuth, Reinhard; Biehler, Rolf; Schaper, Niclas; Liebendörfer, Michael; Büdenbender-Kuklinski, Christiane; Lankeit, Elisa; Ruge, Johanna; Schürmann, Mirko (Unterstützungsmaßnahmen in mathematikbezogenen Studiengängen - Konzepte, Praxisbeispiele und Untersuchungsergebnisse)

Ein Rahmenmodell für hochschuldidaktische Maßnahmen in der Mathematik - Liebendörfer, Michael; Hochmuth, Reinhard; Biehler, Rolf; Schaper, Niclas; Büdenbender-Kuklinski, Christiane; Lankeit, Elisa; Ruge, Johanna; Schürmann, Mirko (Unterstützungsmaßnahmen in mathematikbezogenen Studiengängen - Konzepte, Praxisbeispiele und Untersuchungsergebnisse)

Jupyter Notebooks for Teaching, Learning, and Doing Data Science - Fleischer, Yannik; Hüsing, Sven; Biehler, Rolf; Podworny, Susanne; Schulte, Carsten (Bridging the Gap: Empowering and Educating Today’s Learners in Statistics. Proceedings of the Eleventh International Conference on Teaching Statistics)
We report on our work with students in our data science courses, focusing on the analysis of students’ results. This study represents an in-depth analysis of students’ creation and documentation of machine learning models. The students were supported by educationally designed Jupyter Notebooks, which are used as worked examples. Using the worked example, students document their results in a so-called computational essay. We examine which aspects of creating computational essays are difficult for students to find out how worked examples should be designed to support students without being too prescriptive. We analyze the computational essays produced by students and draw consequences for redesigning our worked example.

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)

Civic Statistics for Prospective Teachers: Developing Content and Pedagogical Content Knowledge Through Project Work - Podworny, Susanne; Frischemeier, Daniel; Biehler, Rolf (Statistics for Empowerment and Social Engagement)

Data Visualization Packages for Non-inferential Civic Statistics in High School Classrooms - Frischemeier, Daniel; Podworny, Susanne; Biehler, Rolf (Statistics for Empowerment and Social Engagement)

An example of rich, real and multivariate survey data for use in school - Podworny, Susanne; Fleischer, Yannik; Stroop, Dietlinde; Biehler, Rolf

Self-regulated learning in a mathematics course for engineers in the first semester: insights into students reported resource management and cognitive strategies - Kolbe, Tim; Wessel, Lena (Fourth conference of the International Network for Didactic Research in University Mathematics)

Evaluation von Unterstützungsmaßnahmen in mathematikbezogenen Studiengängen - Schürmann, Mirko; Liebendörfer, Michael; Büdenbender-Kuklinski, Christiane; Lankeit, Elisa; Ruge, Johanna; Schaper, Niclas; Biehler, Rolf; Hochmuth, Reinhard (Unterstützungsmaßnahmen in mathematikbezogenen Studiengängen - Konzepte, Praxisbeispiele und Untersuchungsergebnisse)

Effects of drawing instructions and strategic knowledge on mathematical modeling performance: Mediated by the use of the drawing strategy - Schönherr, Johanna; Schukajlow, S.; Blomberg, J.; Leopold, C. (Applied Cognitive Psychology, ac3930)

Drawing instructions, strategic knowledge, strategy-based motivation, and students' use of drawings - Schönherr, Johanna; Schukajlow, S.; Leopold, C. (Proceedings of the 45th PME Conference)

Inklusive Praktiken im Mathematikunterricht. Empirische Analysen von Unterrichtsdiskursen in Einführungsphasen. - Häsel-Weide, Uta; Nührenbürger, Marcus (Zeitschrift für Grundschulforschung (ZfG))

Das Dezimalsystem verstehen – Bedeutung, Erkenntnisse, Anregungen - Häsel-Weide, Uta; Schöttler, Christian (Zeitschrift für Mathematikdidaktik in Forschung & Praxis (ZMFP))

Conceptualising and measuring domain-specific content knowledge of early childhood educators: A systematic review - Bruns, Julia; Gasteiger, Hedwig; Strahl, Carolin (Review of Education)
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.
Keywords: content knowledge; domain-specific learning; early childhood education; teacher knowledge

Eine mustergültige Wissenschaft - Bruns, Julia; Schopferer, T. (. TPS – Theorie und Praxis der Sozialpädagogik)

Place value and regrouping as seperate constructs of place value understanding - Jensen, Solveig; Gasteiger, Hedwig; Bruns, Julia (Proceedings of the 44th Conference of the International Group for the Psychology of Mathematics Education)

Context and Implications Document for: Conceptualising and measuring domain-specific content knowledge of early childhood educators: A systematic review - Bruns, Julia; Gasteiger, Hedwig; Strahl, Carolin (Review of Education)

Stellenwertverständnis: Verständnis von Stellenwertprinzip und Bündelungsprinzip als separate Konstrukte - Jensen, Solveig; Gasteiger, Hedwig; Bruns, Julia (Beiträge zum Mathematikunterricht 2021)

Investigating students' processes of noticing and interpreting syntactic language features in word problem solving through eye-tracking - Dröse, Jennifer; Prediger, S.; Neugebauer, P.; Danhier, R. D.; Mertins, B. (International Electronic Journal of Mathematics Education, 16(1), em0625)

Identifying obstacles is not enough for everybody – Differential efficacy of an intervention fostering fifth graders’ comprehension for word problems - Dröse, Jennifer; Prediger, S. (Studies in Educational Evaluation, 68 (100953))

Mit Aufgaben im inklusiven Mathematikunterricht professionell umgehen - Erkenntnisse einer Interviewstudie mit Lehrpersonen der Sekundarstufe - Häsel-Weide, Uta; Seitz, Simone; Wallner, Melina; Wilke, Yannik; Heckmann, Lara (QfI - Qualifizierung für Inklusion. Online-Zeitschrift zur Forschung über Aus-, Fort- und Weiterbildung pädagogischer Fachkräfte)

Conceptualiziation processes of 6th graders for rotational symmetry - Hattermann, Mathias; Häsel-Weide, Uta; Wallner, Melina (Proceedings of the 44th Conference of the International Group for the Psychology of Mathematics Education)

Geometrisches Begriffsverständnis in der Grundschule am Beispiel der Begriffe Viereck, Rechteck und Quadrat - Bruns, Julia; Unterhauser, Elisabeth; Gasteiger, Hedwig (Journal für Mathematik-Didaktik)
Zusammenfassung Zu den ersten geometrischen Begriffen, die Kinder bereits im Elementar- und Primarbereich lernen, zählen u. a. Viereck, Rechteck und Quadrat. Studien zeigen, dass Lernende bereits früh individuelle Vorstellungen, sog. individuelle Begriffskonzepte, zu diesen Begriffen aufbauen. Zwar wird die Entwicklung von Begriffsverständnis in verschiedenen mathematikdidaktischen Stufenmodellen dargestellt, diese sind jedoch generisch und beschreiben nicht explizit die Entwicklung der ersten individuellen Begriffskonzepte von Lernenden zu Viereck, Rechteck und Quadrat. Aus empirischer Sicht liegen verschiedene Studien vor, die einzelne Aspekte der individuellen Begriffskonzepte von Lernenden unterschiedlicher Altersgruppen zu diesen Begriffen ausleuchten. Um Begriffsbildungsprozesse aus empirischer Sicht detaillierter entlang der jeweils vorherrschenden individuellen Begriffskonzepte zu beschreiben, fehlen insbesondere Studien in der Grundschule, die alle vier Klassenstufen betrachten und dabei differenzierte Erkenntnisse zu verschiedenen theoretischen Indikatoren des Begriffsverständnisses liefern. Daher geht die vorliegende Studie der Frage nach, welches Verständnis der Begriffe Viereck, Rechteck und Quadrat Schülerinnen und Schüler der Jahrgangsstufen 1, 2, 3 und 4 zeigen. Dazu wurde eine Quasi-Längsschnittstudie mit N = 456 Grundschulkindern (ca. 100 pro Jahrgangsstufe) durchgeführt. Die Ergebnisse geben detaillierte Einblicke in die individuellen Begriffskonzepte der Lernenden und zeigen, dass Lernende zunehmend Eigenschaften der Figuren berücksichtigen, jedoch individuelle Begriffskonzepte über lange Zeit auch prototypisch geprägt sind. Implikationen dieser Ergebnisse für Forschung und Praxis werden diskutiert.
Keywords: Education; General Mathematics

Fehlerbearbeitung bei mathematischen Textaufgaben – Sprachliche und strategische Fehlerursachen und ihre Bearbeitung - Prediger, Susanne; Dröse, Jennifer (Lernen und Lernstörungen, 10(2))

Mathematics textbooks and curriculum resources as instruments for change - Rezat, Sebastian; Fan, Lianghuo; Pepin, Birgit (ZDM – Mathematics Education)
Abstract In this survey paper we aim to provide an overview of research on mathematics textbooks and, more broadly, curriculum resources as instruments for change related to mathematical content, instructional goals and practices, and student learning of mathematics. In particular, we elaborate on the following themes: (1) The role of curriculum resources as instruments for change from a theoretical perspective; (2) The design of curriculum resources to mediate the implementation of reform ideas and innovative practice; (3) Teachers’ influence on the implementation of change through curriculum resources; (4) Students’ influence on the implementation of change through curriculum resources; and (5) Evidence of curriculum resources yielding changes in student-related factors or variables. We claim that, whilst textbooks and curriculum resources are influential, they alone cannot change teachers’ teaching nor students’ learning practices in times of curricular change. Moreover, more knowledge is needed about features of curriculum resources that support the implementation of change. We contend that curriculum innovations are likely to be successful, if teachers and students are supported to co- and re-design the relevant curriculum trajectories and materials in line with the reform efforts and their own individual needs.
Keywords: General Mathematics; Education

Challenges of making sense of tasks and automated feedback in digital mathematics textbooks - Rezat, Sebastian; Schacht, Florian; Häsel-Weide, Uta (Mathematics Education in the Digital Age. Learning, Practice and Theory)

How automated feedback from a digital mathematics textbook affects primary students’ conceptual development: two case studies - Rezat, Sebastian (ZDM Mathematics Education)
Abstract One of the most prevalent features of digital mathematics textbooks, compared to traditional ones, is the provision of automated feedback on students’ solutions. Since feedback is regarded as an important factor that influences learning, this is often seen as an affordance of digital mathematics textbooks. While there is a large body of mainly quantitative research on the effectiveness of feedback in general, very little is known about how feedback actually affects students’ individual content specific learning processes and conceptual development. A theoretical framework based on Rabardel’s theory of the instrument and Vergnaud’s theory of conceptual fields is developed to study qualitatively how feedback actually functions in the learning process. This framework was applied in a case study of two elementary school students’ learning processes when working on a probability task from a German 3rd grade digital textbook. The analysis allowed detailed reconstruction of how students made sense of the information provided by the feedback and adjusted their behavior accordingly. This in-depth analysis unveiled that feedback does not necessarily foster conceptual development in the desired way, and a correct solution does not always coincide with conceptual understanding. The results point to some obstacles that students face when working individually on tasks from digital mathematics textbooks with automated feedback, and indicate that feedback needs to be developed in design-based research cycles in order to yield the desired effects.
Keywords: General Mathematics; Education

Fachwissen zur Arithmetik bei Grundschullehramtsstudierenden – Entwicklung im ersten Semester und Veränderungen durch eine Lehrinnovation - Hochmuth, Reinhard; Biehler, Rolf; Blum, Werner; Achmetli, Kay; Rode, Jana; Krawitz, Janina; Schukajlow, Stanislaw; Bender, Peter; Haase, Jürgen (Lehrinnovationen in der Hochschulmathematik . Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik)

Integration digitaler Lernmaterialien in die Präsenzlehre am Beispiel des Mathematikvorkurses für Ingenieure an der Universität Paderborn - Fleischmann, Yael; Biehler, Rolf; Gold, Alexander; Mai, Tobias (Lehrinnovationen in der Hochschulmathematik . Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik)

Die Online-Lernmaterialien im Online-Mathematikvorkurs studiVEMINT: Konzeption und Ergebnisse von Nutzer- und Evaluationsstudien - Gold, Alexander; Fleischmann, Yael; Mai, Tobias; Biehler, Rolf; Kempen, Leander (Lehrinnovationen in der Hochschulmathematik . Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik)

Einführung: Lehrinnovationen in der Hochschulmathematik – praxisrelevant – didaktisch fundiert – forschungsbasiert - Biehler, Rolf; Eichler, Andreas; Hochmuth, Reinhard; Rach, Stefanie; Schaper, Niclas (Lehrinnovationen in der Hochschulmathematik . Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik)