Doing mathematics. Substantive learning environments in the classroom

Doing mathematics. Substantive learning environments in the classroom.

The project focuses on the learning environment of "structured packets". The concept of the substantial learning environment as a possibility of natural differentiation offers the opportunity for all children to learn together according to their individual learning level within the same subject framework. The mathematical didactic principles of learning through discovery and productive practice are made possible by making the inherent patterns and structures of mathematical content tangible. (cf. Hirt, Wälti 2010)

The learning environment is implemented and evaluated in mathematics lessons together with primary school teachers. This task format is intended to make the ways in which teachers and learners deal with substantial learning environments visible.

Both phases of introduction by the teacher and (group) work phases of the students will be videotaped. Quantitative analysis of the work phases (learning time used, number and type of questions asked by the learners) and qualitative analysis of the learners' communication with each other and with the teachers will be used to identify the following aspects:

• In what way do teachers introduce substantial learning environments?
• What is the quality of substantial learning environments in the students' work phases?
• What influence does the introduction of the learning environment have on the students' work phases?
• To what extent does a discourse about the inherent patterns and structures take place among the learners?

Further collaborators: Elisa Wagner, Maria Wendt

Previous publications:

- Wagner , Elisa / Beier, Frank (2025, in print), "das ist das Einfachste was ich je gerechnet habe" -Ergebnisorientierte Konkurrenzpraktiken in der Arbeit an Strukturierten Päckchen im Mathematikunterricht. In: Leicht, J. & Schreyer, P. & Breidenstein, G. & Heinzel, F. (eds.), Interaction and professionalism in the classroom: concepts and research approaches. Waxmann Publishers.

- Wagner, E. & Beier, F. (2024). From arithmetic to algebra. Examining structured parcels. teaching mathematics, 246/2024, 8 - 13.

- Beier, Frank / Wagner, Elisa / Stern, Julia (2024), Learning environments for the mathematically weak to the highly gifted? A videographic study on the constitution of subject-specific modes of participation in substantial learning environments. In: Wilm, Gianna et al. (eds.), Videographic research on inclusive teaching: educational science and didactic perspectives. Klinkhardt Verlag, pp. 101-118.

- Wagner, Elisa & Wendt, Maria (2022): The importance of opening phases for the processing of substantial learning environments. (56th annual conference of the Society for Mathematics Didactics in Frankfurt)

- Beier, Frank (2021), Between "What discoveries have you made?" and "First say what you have calculated" - Paradoxical interaction constellations in the presentation phases of Substantial Learning Environments. In: Binder, Ulrich / Krönig, Franz K. (eds.), Paradoxes (in) Pedagogy. Beltz Verlag. S. 212-232. open access

- Wagner, E. (2020). Solution behavior and error types of primary school students in structured packets. In GDM conference proceedings

- Beier, F.; Wyßuwa, F. ;Wagner, E. (2020). Case interpretations between theory and application. On the practical use of scientific knowledge using the example of qualitative course and teaching research. In debate. Contributions to adult education, Vol. 3, Issue 1.

- Beier / Wagner (2019): Letting children do mathematics - What does a qualitative intervention study achieve? (11th ZSM junior research conference, Magdeburg)