Bildung im Mathematikunterricht. Lehrkunst im Dialog mit Heymann. Komposition, Erprobung und Interpretation von zwei Lehrstücken mit Blick auf ihre Bildungsqualität: "Das Nichtabbrechen der Primzahlfolge" und "Mit Tartaglia die kubische Gleichung lösen".

Die Verwendung der Bildungsbegriffe, die im Bestreben um eine differenzierte Beurteilung des Beitrags eines Faches oder einer Domäne an die Bildung eines Menschen herbeigezogen werden, ist oft uneinheitlich. Im ersten Teil dieser Arbeit werden deshalb die Bildungsbegriffe «Bildung», «Allgemeinbildun...

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Bibliographic Details
Main Author: Spindler, Philipp
Contributors: Berg, Hans Christoph (Prof. Dr.) (Thesis advisor)
Format: Doctoral Thesis
Published: Philipps-Universität Marburg 2022
Online Access:PDF Full Text
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The use of educational terms, which are invoked in an effort to make a differentiated assessment of the contribution of a subject or domain to a person's education, is often varying. In the first part of this work, the educational concepts "education" (Bildung), "general education" (Allgemeinbildung), “educational potential” (Bildungspotential), "educational content" (Bildungsgehalt) and "educational value" (Bildungswert) are differentiated, taking into account the work of Wolfgang Klafki, Hans Werner Heymann and Otto Willmann, and assigned to different focal points of the educational process. In the following, the focus is on mathematics teaching. In order to create a test criterion for authentic mathematics teaching that does justice to the subject matter, a model is presented for the first time with the “Mathemaion” sketch, which describes mathematics as a set of core areas that are processed with specific tools and brought into a form that is characteristic of mathematics, always serving a purpose. With this model, the educational potential and content of mathematics education can be made the subject of a rational discourse. In order to be able to assess the educational content of a mathematical unit, the categorial planning table by Hans Christoph Berg and Wolfgang Klafki as well as a specially developed catalogue of basic experiences and insights are used. On the level of the educational potential of mathematics, the seven tasks of a general education school by Hans Werner Heymann (2013) are useful. Didactic concepts, however, must have a more concrete learner approach in the form of educational processes. It is therefore crucial to examine specific teaching units with regard to their educational effect. The “Lehrkunst” didactics pursues the goal of bringing essential achievements and breakthroughs of science and culture into the classroom by staging lessons (“Lehrstücke”), while keeping focused on categorial enlightenment, educational content and educational value in the tradition of Klafki. It therefore makes sense to examine such teaching examples in consideration of their educational effect. In the second part of the present work, the concept of “Lehrkunst” didactics is developed and explained in detail. Two staging lessons - carefully prepared, explained in terms of composition, described in lesson reports and analysed with regard to their conformity to the “Lehrkunst” concept - form the middle part of the work. This is the unit «The non-cessation of the prime number sequence», which draws on lesson sequences by Wagenschein (1949), Werner (1995), Brüngger (2004) and Gerwig (2013) and is presented in a new version after an optimisation process. The newly composed unit «Solving the cubic equation with Tartaglia» re-enacts the mathematical duel between Nicolo Tartaglia and Antoniomaria Fior in Venice in 1535 and, with the solution formula for a special type of cubic equation and the later invention of complex numbers, makes two great moments in the history of mathematics come to life. In the last part this work, the presented and newly developed instruments and models are applied. Heymann's tasks for general schools, supplemented by the task "Enabling aesthetic perception experiences", help to assess the educational potential and the educational content of mathematics teaching and of staging lessons in general and the two staging lesson units in particular. It is shown that staging lessons are particularly effective in the dimension of "development of the human being" and can also satisfy the dimension of "empowerment for knowledge". In addition, the two staging lesson units presented provide a wide range of opportunities for aesthetic perception experiences and make numerous characteristics of mathematics transparent, as a comparison with the “Mathemaion” model shows. On the level of educational content, the catalogue of basic experiences and insights in mathematics is able to highlight the richness of the fundamental experiences promoted by two staging lesson units. It also becomes apparent that the two staging lesson units offer a manifold categorial enlightenment. A small study carried out on the prime number unit provides evidence of a particular impact of the lesson on those tasks that contribute to the development of humanity.