Denken mit dem Stift?! Digitale Visualisierungsprozesse als Zugang zu komplexen wirtschafts- und berufspädagogischen Themenfeldern - Kückmann, Marie-Ann; Kundisch, Heike (bwp@ Berufs- und Wirtschaftspädagogik – online)

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)

Mathematikvorkurse als Brücke in das Studium–Einführung - Biehler, Rolf (Lehrinnovationen in der Hochschulmathematik . Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik)

Introducing students to machine learning with decision trees using CODAP and Jupyter Notebooks - Biehler, Rolf; Fleischer, Yannik (Teaching Statistics)
Keywords: Education; Statistics and Probability

Lehrinnovationen in der Hochschulmathematik

3D-Geometrie–virtuell und real - Biehler, Rolf; Weigand, Hans-Georg (mathematik lehren)

Mathematics in Engineering Education: a Review of the Recent Literature with a View towards Innovative Practices - Pepin, Birgit; Biehler, Rolf; Gueudet, Ghislaine (International Journal of Research in Undergraduate Mathematics Education)
Abstract The 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.
Keywords: Education; Mathematics (miscellaneous)

Design-Based Research in der Hochschullehre am Beispiel der Lehrveranstaltung „Einführung in die Kultur der Mathematik“ - Kempen, Leander; Biehler, Rolf (Lehrinnovationen in der Hochschulmathematik . Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik)

Education and professional development of university mathematics teachers - Winsløw, Carl; Biehler, Rolf; Jaworski, Barbara; Rønning, Frode; Wawro, Megan (Research and Development in University Mathematics Education)

Schatten von 3D-Objekten: Modellierung mit GeoGebra 3D und Anwendungen in der Computergrafik - Höper, Lukas; Malin, Leah; Biehler, Rolf (mathematik lehren)

Faszination 3D-Film: Entwicklung einer 3D-Konstruktion - Hüsing, Sven; Weiser, Niklas; Biehler, Rolf (mathematik lehren)

Consultation Phases in Mathematics Learning and Support Centres - Schürmann, Mirko; Panse, Anja; Shaikh, Zain; Biehler, Rolf; Schaper, Niclas; Liebendörfer, Michael; Hilgert, Joachim (International Journal of Research in Undergraduate Mathematics Education)
Abstract Mathematics Learning Support Centres are becoming more and more common in higher education both internationally and in Germany. Whereas it is clear that their quality largely depends on a functioning interaction in consultations, little is known about how such consultations proceed in detail. On the basis of models from the literature and recorded support sessions (N = 36), we constructed a process model that divides consultations into four ideal–typical phases. In the individual consultations, forward or backward leaps occur, but overall the model seems to describe the data well. A high intercoder reliability shows that it can be applied consistently on real data by different researchers. An analysis of the consultations between students and tutors shows that both mainly work on past attempts or thoughts of the students to solve the exercise or problems and on concrete strategies to solve a problem within the session. In contrast, very little time is dedicated to summarizing and reflecting the solution. The data allows for a more in-depth discussion of what constitutes quality in advising processes and how it might be further explored. Practically, the model may structure support sessions and help in focussing on different goals in different phases.
Keywords: Education; Mathematics (miscellaneous)

The process of actively building a model for a randomization test – insights into learners’ modeling activities based on a case study - Podworny, Susanne; Biehler, Rolf (Mathematical Thinking and Learning)
Keywords: Developmental and Educational Psychology; Education; General Mathematics

A first introduction to data science education in secondary schools: Teaching and learning about data exploration withCODAPusing survey data - Frischemeier, Daniel; Biehler, Rolf; Podworny, Susanne; Budde, Lea (Teaching Statistics)
Keywords: Education; Statistics and Probability