Development and evaluation of digital resources for the appropriation of structural praxeologies in the transition from school to university mathematics
For mathematics at the university, so-called structural concepts or praxeologies (Hausberger, 2018) are particularly important. Mathematical practices linked to these concepts and praxeologies concern, among other things, justifications with reference to object sets, relationships between object sets and structure-invariant operations. With regard to such praxeologies in analysis and higher mathematics for engineers, concrete proposals for digital support measures in the transition from school to university and the first year of study will be developed and evaluated and optimized in a Design-Based-Research approach. The subject-specific analyses will be based on the institutional analyses in Hausberger (2018) and Hochmuth (2020). Linking the concept of structural praxeologies with Weber’s ideal type concept (Weber, 1904) should enable, for example against the background of approaches of methodological constructivism (Shubat, 2011), a methodical, object-adequate relationship between institutional and subject-related analyses in design-based-research cycles (cf. with regard to this research-methodological desideratum in didactics, for example (Hußmann & Prediger, 2016)). The digital learning environments to be developed should promote the acquisition of structural mathematical concepts of analysis with a view to advanced concepts in analysis as well as higher mathematics for engineers with a view to electrotechnical concepts.
Hausberger, T. (2018). Structuralist Praxeologies as a Research Program on the Teaching and Learning of Abstract Algebra. International Journal of Research in Undergraduate Mathematics Education, 4(1), 74-93.
Hochmuth, R. (2020) (Im Druck). A general scheme for a heterogeneous manifold of transitions.
Hußmann, S., & Prediger, S. (2016). Specifying and Structuring Mathematical Topics. Journal für Mathematik-Didaktik, 37(1), 33-67.
Shubat, A. H. (2011). Rationale Rekonstruktion und empirische Realität: ein Beitrag zur Sozialtheorie von Max Weber, insbesondere: zum” Idealtypus” (Dissertation, Humboldt Universität Berlin).Weber, M. (1904). Die” Objektivität” sozialwissenschaftlicher und sozialpolitischer Erkenntnis. Archiv für Sozialwissenschaft und Sozialpolitik, 19(1), 22–87.