Winsløw and Grønbæk (2014) showed that the “double discontinuity” (Klein, 2016/1924) is still a relevant problem in our current education system. One of the main problems is the different appearance of mathematics at school and at university resulting in students difficulties to relate them to each other. As a consequence the intention of university courses in mathematics teacher education to make mathematical and didactical insights relevant for future teaching at school threatens to fail.
The "Digital Interactive Mathematical Maps" can be accessed on their Homepage.
Nodes in space represent mathematical content. Edges symbolize historical developments that highlight mathematics as an evolving science. Further details can be displayed using the "Vertical Cut" and "Horizontal Cut" functionalities, where only one of the features is examined.
The DIMMs have already been used and empirically examined at the University of Karlstad in Sweden (cf. e.g. Przybilla, Brandl, Vinerean & Liljekvist, 2022).
Currently the languages German and English as well as the areas Geometry, Algebra and Calculus are available. In the course of further development, additional languages as well as interdisciplinary application possibilities of the maps in other subject areas are envisaged. At the moment the area of Stochastics and additional languages Spanish and Ukranian are in implementation progress.
In the context of the „Quality Offensive in Teacher Education” ("Qualitätsoffensive Lehrerbildung") of the Federal Ministry of Education and Research (BMBF), the project SKILL or SKILL.de, respectively, of teacher education at the University of Passau, which has been funded in its second phase since 2016, responds to deficits in teacher education that are discussed under the keywords "segmentation", "marginalization" and "fragmentation".
SKILL an abbreviation for "Strategien zur Kompetenzentwicklung: Innovative Lehrformate in der Lehrerbildung" (engl.: "Strategies for Competence Development: Innovative teaching formats in teacher education") or SKILL.de for "SKILL, digitally enhanced". In one of the largest individual inter-faculty projects at the University of Passau, specialists from didactics, sciences and educational sciences together do research in education.
Details about the general project can be accessed at the project homepage.
Brandl, M. (2009). The vibrating string – an initial problem for modern mathematics; historical and didactical aspects. In I. Witzke (Ed.), Mathematical Practice and Development throughout History: Proceedings of the 18th Novembertagung on the History, Philosophy and Didactics of Mathematics. Logos Verlag, 95–114.
Klein, F. (2016/1924). Elementary Mathematics from higher standpoint. Volume I: Arithmetik Algebra Analysis. (G. Schubring, Trans.) Berlin, Heidelberg: Springer. (Original work published 1924). doi: 10.1007/978-3-662-49442-4
Przybilla, J., Brandl, M., Vinerean, M., & Liljekvist, Y. (2022). Digital mathematical maps – results from iterative research cycles. In J. Hodgen, E. Geraniou, G. Bolondi & F. Ferretti. (Eds.), Proceedings of the Twelfth Congress of the European Society for Research in Mathematics Education (CERME12) (pp. 4793–4800). Free University of Bozen-Bolzano and ERME. https://hal.archives-ouvertes.fr/hal-03754749/
Przybilla, J., Brandl, M., Vinerean, M., & Liljekvist, Y. (2021). Interactive Mathematical Maps – A contextualized way of meaningful Learning. In G. A. Nortvedt, N. F. Buchholtz, J. Fauskanger, F. Hreinsdóttir, M. Hähkiöniemi, B. E. Jessen, J. Kurvits, Y. Liljekvist, M. Misfeldt, M. Naalsund, H. K. Nilsen, G. Pálsdóttir, P. Portaankorva-Koivisto, J. Radišić & A. Wernberg (Eds.), Bringing Nordic mathematics education into the future. Preceedings of NORMA 20. The ninth Nordic Conference on Mathematics Education. Oslo, 2021 (pp. 209–216). (Skrifter från Svensk Förening för MatematikDidaktisk Forskning; No. 14). Svensk förening för matematikdidaktisk forskning (SMDF). http://matematikdidaktik.org/wp-content/uploads/2021/04/NORMA_20_preceedings.pdf
Winsløw, C., & Grønbæk, N. (2014). Klein's double discontinuity revisited: contemporary challenges for universities preparing teachers to teach calculus. Recherches en Didactique des Mathématiques, 34(1), 59–86. https://revue-rdm.com/2014/kleins-double-discontinuity-revisited/