At the school-university interface, problems often occur, especially in mathematics, which among other things traditionally lead to significantly high dropout rates (cf. Dieter, 2012). This difficulty - which belongs to the context of Klein's first discontinuity (Klein, 2016/1924) - is ultimately based on different ideas about or views of "mathematics" (cf. also, for example, the "three-world approach" by D. Tall, 2008).

On the one hand, qualitative cross-sectional and longitudinal studies were conducted for this purpose - with the aim of sensitizing both sides to the present discrepancy and appropriate didactic support measures - which in part resulted in the development of appropriate didactic teaching-learning elements (Pfeffer, 2017; Pfeffer & Brandl, 2015, 2016); on the other hand, the overall phenomenon of Klein's double discontinuity is being addressed in the context of Interconnectedness and defragmentation by means of digital and narrative tools in the DIMM project.

References:

Dieter, M. (2012). Studienabbruch und Studienfachwechsel in der Mathematik: Quantitative Bezifferung und empirische Untersuchung von Bedingungsfaktoren. Universität Duisburg-Essen.

Klein, F. (2016/1924). Elementary Mathematics from higher standpoint. Volume I: Arithmetik Algebra Analysis. (G. Schubring, Trans.) Berlin, Heidelberg: Springer. (Original work published 1924). https://doi.org/10.1007/978-3-662-49442-4

Pfeffer, W. (2017). Qualitative Entwicklung der Begriffsbildung im Fach Mathematik in der Studieneingangsphase. Dissertation. https://doi.org/10.13140/RG.2.2.10408.06403

Pfeffer, W., & Brandl, M. (2016). Mentales Modell zum Abbildungsbegriff bei Studienanfängerinnen und Studienanfängern. In Institut für Mathematik und Informatik der Pädagogischen Hochschule Heidelberg (Hrsg.), Beiträge zum Mathematikunterricht 2016 (S. 1423–1426). WTM. https://doi.org/10.17877/DE290R-17647

Pfeffer, W., & Brandl, M. (2015). Schwierigkeiten beim Übergang Schule – Hochschule in Mathematik. Eine qualitative Längsschnittstudie. In F. Caluori, H. Linneweber-Lammerskitten & C. Streit (Hrsg.), Beiträge zum Mathematikunterricht 2015 (S. 1089–1092). WTM. https://doi.org/10.17877/DE290R-16835

Tall, D. (2008). The Transition to Formal Thinking in Mathematics. Mathematics Education Research Journal, 20(2), 5–24.