@article{GreefrathSillerKlocketal.2022,
  author    = {Greefrath, Gilbert and Siller, Hans-Stefan and Klock, Heiner and Wess, Raphael},
  title     = {Pre-service secondary teachers' pedagogical content knowledge for the teaching of mathematical modelling},
  series = {Educational Studies in Mathematics},
  volume    = {109},
  journal   = {Educational Studies in Mathematics},
  number    = {2},
  issn      = {0013-1954},
  doi       = {10.1007/s10649-021-10038-z},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-308259},
  pages     = {383-407},
  year      = {2022},
  abstract  = {The article deals with the pedagogical content knowledge of mathematical modelling as part of the professional competence of pre-service teachers. With the help of a test developed for this purpose from a conceptual model, we examine whether this pedagogical content knowledge can be promoted in its different facets—especially knowledge about modelling tasks and about interventions—by suitable university seminars. For this purpose, the test was administered to three groups in a seminar for the teaching of mathematical modelling: (1) to those respondents who created their own modelling tasks for use with students, (2) to those trained to intervene in mathematical modelling processes, and (3) participating students who are not required to address mathematical modelling. The findings of the study—based on variance analysis—indicate that certain facets (knowledge of modelling tasks, modelling processes, and interventions) have increased significantly in both experimental groups but to varying degrees. By contrast, pre-service teachers in the control group demonstrated no significant change to their level of pedagogical content knowledge.},
  language  = {en}
}
@article{GerberQuarderGreefrathetal.2023,
  author    = {Gerber, Sebastian and Quarder, Jascha and Greefrath, Gilbert and Siller, Hans-Stefan},
  title     = {Promoting adaptive intervention competence for teaching simulations and mathematical modelling with digital tools},
  series = {Frontiers in Education},
  volume    = {8},
  journal   = {Frontiers in Education},
  issn      = {2504-284X},
  doi       = {10.3389/feduc.2023.1141063},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-323701},
  year      = {2023},
  abstract  = {Providing adaptive, independence-preserving and theory-guided support to students in dealing with real-world problems in mathematics lessons is a major challenge for teachers in their professional practice. This paper examines this challenge in the context of simulations and mathematical modelling with digital tools: in addition to mathematical difficulties when autonomously working out individual solutions, students may also experience challenges when using digital tools. These challenges need to be closely examined and diagnosed, and might - if necessary - have to be overcome by intervention in such a way that the students can subsequently continue working independently. Thus, if a difficulty arises in the working process, two knowledge dimensions are necessary in order to provide adapted support to students. For teaching simulations and mathematical modelling with digital tools, more specifically, these knowledge dimensions are: pedagogical content knowledge about simulation and modelling processes supported by digital tools (this includes knowledge about phases and difficulties in the working process) and pedagogical content knowledge about interventions during the mentioned processes (focussing on characteristics of suitable interventions as well as their implementation and effects on the students' working process). The two knowledge dimensions represent cognitive dispositions as the basis for the conceptualisation and operationalisation of a so-called adaptive intervention competence for teaching simulations and mathematical modelling with digital tools. In our article, we present a domain-specific process model and distinguish different types of teacher interventions. Then we describe the design and content of a university course at two German universities aiming to promote this domain-specific professional adaptive intervention competence, among others. In a study using a quasi-experimental pre-post design (N = 146), we confirm that the structure of cognitive dispositions of adaptive intervention competence for teaching simulations and mathematical modelling with digital tools can be described empirically by a two-dimensional model. In addition, the effectiveness of the course is examined and confirmed quantitatively. Finally, the results are discussed, especially against the background of the sample and the research design, and conclusions are derived for possibilities of promoting professional adaptive intervention competence in university courses.},
  language  = {en}
}
@article{SillerElschenbroichGreefrathetal.2023,
  author    = {Siller, Hans-Stefan and Elschenbroich, Hans-J{\"u}rgen and Greefrath, Gilbert and Vorh{\"o}lter, Katrin},
  title     = {Mathematical modelling of exponential growth as a rich learning environment for mathematics classrooms},
  series = {ZDM Mathematics Education},
  volume    = {55},
  journal   = {ZDM Mathematics Education},
  number    = {1},
  issn      = {1863-9690},
  doi       = {10.1007/s11858-022-01433-8},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-324393},
  pages     = {17-33},
  year      = {2023},
  abstract  = {Mathematical concepts are regularly used in media reports concerning the Covid-19 pandemic. These include growth models, which attempt to explain or predict the effectiveness of interventions and developments, as well as the reproductive factor. Our contribution has the aim of showing that basic mental models about exponential growth are important for understanding media reports of Covid-19. Furthermore, we highlight how the coronavirus pandemic can be used as a context in mathematics classrooms to help students understand that they can and should question media reports on their own, using their mathematical knowledge. Therefore, we first present the role of mathematical modelling in achieving these goals in general. The same relevance applies to the necessary basic mental models of exponential growth. Following this description, based on three topics, namely, investigating the type of growth, questioning given course models, and determining exponential factors at different times, we show how the presented theoretical aspects manifest themselves in teaching examples when students are given the task of reflecting critically on existing media reports. Finally, the value of the three topics regarding the intended goals is discussed and conclusions concerning the possibilities and limits of their use in schools are drawn.},
  language  = {en}
}