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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.
The steadily increasing usage of smart meters generates a valuable amount of high-resolution data about the individual energy consumption and production of local energy systems. Private households install more and more photovoltaic systems, battery storage and big consumers like heat pumps. Thus, our vision is to augment these collected smart meter time series of a complete system (e.g., a city, town or complex institutions like airports) with simulatively added previously named components. We, therefore, propose a novel digital twin of such an energy system based solely on a complete set of smart meter data including additional building data. Based on the additional geospatial data, the twin is intended to represent the addition of the abovementioned components as realistically as possible. Outputs of the twin can be used as a decision support for either system operators where to strengthen the system or for individual households where and how to install photovoltaic systems and batteries. Meanwhile, the first local energy system operators had such smart meter data of almost all residential consumers for several years. We acquire those of an exemplary operator and discuss a case study presenting some features of our digital twin and highlighting the value of the combination of smart meter and geospatial data.