Promoting adaptive intervention competence for teaching simulations and mathematical modelling with digital tools: theoretical background and empirical analysis of a university course in teacher education - Gerber, Sebastian; Quarder, Jascha; Greefrath, Gilbert; Siller, Hans-Stefan (Frontiers in Education, 2023)
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 the digital tool. These challenges need to be closely examined and diagnosed, and might – if necessary – have to be overcome through an intervention in such a way that the students can subsequently continue working independently. An ideal-typical diagnosis-based intervention is described by Klock und Siller (2020b) in a process model based on Leiss (2007): According to this model, if a difficulty arises in the working process, two knowledge dimensions are necessary in order to provide adapted support to students. Previously, we concretised these knowledge dimensions for simulations and mathematical modelling with digital tools as follows (Gerber and Quarder, 2022): pedagogical content knowledge about simulation and modelling processes supported by digital tools (this specifically 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. We concretise the process model of Klock and Siller (2020b) with simulations and digital tools and distinguish different types of teacher interventions. Then, we focus on promoting this domain-specific professional adaptive intervention competence. University courses in the first phase of teacher education are considered to have a crucial influence on the development of the corresponding professional competence (Kunter et al., 2013b). Thus, we describe the design and content of a university course at two German universities with the aim of promoting this competence, among others. In a study using a quasi-experimental pre-post design, the effectiveness of the course is examined and confirmed quantitatively (N = 146).