Beliefs-oriented subject-matter didactics

Design of a seminar and a book on calculus education

Authors

DOI:

https://doi.org/10.31129/LUMAT.12.1.2125

Keywords:

Belief Systems, Calculus Education, Pre-service Teacher Training, Subject-Matter Didactics

Abstract

This paper presents a modified approach to subject-matter didactics, in which the focus is not on the content itself, but on the students' view of the content. The introduction deals with an overview of subject-matter didactics and the notion of beliefs used in this paper. The main portion of the paper deals with presenting the concepts of a book and a seminar based on the student-centered subject-matter didactics approach. For the first qualitative evaluation, selected reflections of students are analyzed. Finally, initial findings are summarized and an outlook is provided.

References

Bauersfeld, H. (1983). Subjektive Erfahrungsbereiche als Grundlage einer Interaktionstheorie des Mathematiklernens und -lehrens. In H. Bauersfeld, H. Bussmann, G. Krummheuer, J. H. Lorenz, & J. Voigt (Eds.), Lernen und Lehren von Mathematik. Analysen zum Unterrichtshandeln II (pp. 1–56). Aulis.

Blum, W., & Törner, G. (1983). Didaktik der Analysis. Vandenhoeck & Ruprecht.

Conference of the German Ministers of Education and Cultural Affairs (2015). Bildungsstandards im Fach Mathematik für die allgemeine Hochschulreife. Beschluss der Kultusministerkonferenz vom 18.10.2012. KMK.

Danckwerts, R., & Vogel, D. (2006). Analysis verständlich unterrichten. Springer.

Goldin, G., Rösken, B., & Törner, G. (2009). Beliefs – No longer a hidden variable in mathematical teaching and learning processes. In J. Maaß, & W. Schlöglmann (Eds.), Beliefs and attitudes in mathematics education: New research results (pp. 1–18). Sense Publishers.

Greefrath, G., Oldenburg, R., Siller, H.-S., Ulm, V., & Weigand, H.-G. (2016). Didaktik der Analysis: Aspekte und Grundvorstellungen zentraler Begriffe. Springer. http://dx.doi.org/10.1007/978-3-662-48877-5

Green, T. F. (1971). The activities of teaching. McGraw-Hill.

Grigutsch, S., Raatz, U., & Törner, G. (1998). Einstellungen gegenüber Mathematik bei Mathematiklehrern. Journal für Mathematik-Didaktik, 19(1), 3–45. https://doi.org/10.1007/BF03338859

Hefendehl-Hebeker, L. (2016). Subject-matter didactics in German traditions. Journal für Mathematik-Didaktik, 37(1), 11–31. https://doi.org/10.1007/s13138-016-0103-7

Hefendehl-Hebeker, L., vom Hofe, R., Büchter, A., Humenberger, H., Schulz, A., & Wartha, S. (2019). Subject-matter didactics. In H. N. Jahnke, & L. Hefendehl-Hebeker (Eds.), Traditions in German-speaking mathematics education research (pp. 25–60). Springer. https://doi.org/10.1007/978-3-030-11069-7_2

Hußmann, S., Rezat, S., & Sträßer, R. (2016). Subject matter didactics in mathematics education. Journal für Mathematik-Didaktik, 37(1), 1–9. https://doi.org/10.1007/s13138-016-0105-5

Klein, F. (2016). Elementary mathematics from a higher standpoint. Volume I: Arithmetic, algebra, analysis. Springer. https://doi.org/10.1007/978-3-662-49442-4

Pajares, M. F. (1992). Teachers’ beliefs and educational research: Cleaning up a messy construct. Review of Educational Research, 62(3), 307–332. https://doi.org/10.3102%2F00346543062003307

Schoenfeld, A. H. (1985). Mathematical problem solving. Academic Press.

Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics. In D. A. Grouws (Eds.), Handbook of research on mathematics teaching and learning (pp. 334–370). Macmillan.

Stoffels, G. (2020). (Re-)Konstruktion von Erfahrungsbereichen bei Übergängen von empirisch-gegenständlichen zu formal-abstrakten Auffassungen. Universi.

Tall, D. (2013). How humans learn to think mathematically. Exploring the three worlds of mathematics. Cambridge University Press.

Thompson, A. G. (1992). Teachers’ beliefs and conceptions: A synthesis of the research. In D. A. Grouws (Eds.), Handbook of research on mathematics teaching and learning (pp. 127–146). National Council of Teachers of Mathematics.

Vom Hofe, R., & Blum, W. (2016). “Grundvorstellungen” as a category of subject-matter didactics. Journal für Mathematik-Didaktik, 37(1), 225–154. https://doi.org/10.1007/s13138-016-0107-3

Witzke, I., & Spies, S. (2016). Domain-specific beliefs of school calculus. Journal für Mathematik-Didaktik, 37(1), 131–161. https://doi.org/10.1007/s13138-016-0106-4

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Published

2024-02-01

How to Cite

Dilling, F., Stoffels, G., & Witzke, I. (2024). Beliefs-oriented subject-matter didactics: Design of a seminar and a book on calculus education. LUMAT: International Journal on Math, Science and Technology Education, 12(1), 4–14. https://doi.org/10.31129/LUMAT.12.1.2125