### Analysis and modelling of the fostering of mathematical enculturation in the transition from school to university through processes of informal learning

The specific challenges for beginners in MINT studies are attributed in particular to the ‘cultural break’ in the transition from school to university mathematics, which is constituted by various aspects. These aspects include, for example, new content, combined with a new theoretical approach and a changed conceptualisation of mathematical terms, the goals to be achieved, new means of presentation with an increased demand for formalisation, as well as new ways of argumentation and differences with regard to didactic-methodological aspects of teaching and learning (cf. Thomas et al. 2015, Hochmuth, Broley, Nardi 2020). The diversity of the necessary extension of the capacity to act and the qualitative learning steps associated with it (Holzkamp 1993) in the transition from school to university are conceptualized in socio-culturally oriented theories, among other things, as a process of “enculturation” (Pepin 2014). This addresses in particular the subject-related participation in so-called “authentic” activities of the new, university-mathematical culture. This includes the adoption of beliefs, values, goals, procedures and an adaptation of one’s own identity. Recent empirical surveys on the development of mathematical enculturation in the first year of study in the context of bridging lectures and their effects have shown rather negative results. Students did not seem to learn or apply the subject matter on their own. They also tended not to be willing to invest time in learning something new (Hochmuth et al. 2020).

In the intended dissertation project, funding opportunities for mathematical enculturation processes are to be analysed and modelled against the background of Bachelard’s (2002) concept of scientific experience, which integrates, analyses and models cognitive and affective-motivational aspects. According to this view, enculturation processes would not only be understood as continuous developmental steps based on school experience, but also as a (inevitable) break that contradicts it. Such steps in the development of scientific experience are also understood in the context of the subject scientific learning theory as an extension of possible horizons of meaning. The contribution of digital informal learning activities to mathematical enculturation and how related processes can be supported digitally has not yet been investigated, which is also due to a lack of data. Methods of Learning Analytics offer new possibilities for the analysis and modelling of relevant processes. After a first phase of the analysis of updated processes of informal learning with a view to the development of enculturation, a funding measure is to be developed, which will subsequently be researched with regard to its effects both qualitatively and quantitatively in a design-based study.

#### References

Bachelard, G. (2002). *The Formation of the Scientific Mind. A Contribution to a Psychoanalysis of Objective Knowledge*. Avon, UK: The Bath Press.

Hochmuth, R., Nardi, E., Broley, L. (2020) (Im Druck). Transitions to and across university.

Hochmuth, R., Biehler, R., Schaper, N., Kuklinski, C., Lankeit, E., Leis, E., Liebendörfer, M., Schürmann, M. (2020) (Im Druck). Wirkung und Gelingensbedingungen von Unterstützungsmaßnahmen für mathematikbezogenes Lernen in der Studieneingangsphase.

Holzkamp, K. (1993). *Lernen: Subjektwissenschaftliche Grundlegung*. Campus-Verlag.

Pepin, B. (2014). Student transition to university mathematics education: transformations of people, tools and practices. In *Transformation-A Fundamental Idea of Mathematics Education*(pp. 65-83). Springer, New York, NY.Thomas, M., de Freitas Druck, I., Huillet, D., Ju, M.K., Nardi, E., Rasmussen, C., Xie, J. (2015). Key mathematical concepts in the transition from secondary school to university. In S.J. Cho, The *Proceedings of 12*^{th}* International Congress on Mathematical Education*. (pp. 265-284). Cham: Springer.