ABSTRACT
The Bewegungsgeometrie (geometry of motion) as a way to make static, rigid figures movable and to interpret curves as locus curves of movements has emerged as a teaching topic in German mathematics teaching over the past 150 years in various contexts: as an idea of the reform of geometry teaching “Neuere Geometrie” (Newer Geometry) to enrich the teaching of deductive rigid representations in the Books of Euclid through movements, as a teaching subject of the technical colleges and universities founded in the 19th century, as implementation of the educational goals of the “Meraner Reform”, and also as a reform idea of the German teaching reform “Neue Mathematik” (New Math). The emergence of Bewegungsgeometrie in the context of the New Math Reform, which aimed to introduce structural mathematics and set theory through the axiomatic teaching method, is surprising at first glance. The consideration of relationships and changeability would rather be assigned to the Meraner Reform and traditional mathematics (Lenné, 1969). The analysis of the Bewegungsgeometrie in the context of New Math allows a differentiated view of various tendencies of this western German teaching reform and its educational goals. We investigate the ideas of motion geometry from Otto Botsch (Botsch, 1955), an invited speaker to the Royaumont seminar. Otto Botsch presented his ideas for reforming geometry teaching at the seminar. We examine the implementation of his ideas in the Nuremberg curriculum (Damerow, 1977). Thereby, we are especially interested in which extent the curricular realizations of Bewegungsgeometrie supported the main educational goals of the Western German New Math Reform. The popularity of the Bewegungsgeometrie is also evident in the fact that Hans-Georg Steiner, one of the main protagonists of the German New Math Reform, published on this topic (Steiner, 1956). A second question that we are interested in are similarities and differences between Bewegungsgeometrie and the Abbildungsgeometrie (transformation geometry). The latter is of interest, since the Abbildungsgeometrie can also be found in the reform plans of geometry teaching in other countries. Isaak Moissejewitsch Yaglom’s problem-oriented approach to geometrical transformation (Яглом, 1956) was one of the standard works of Soviet Union “New Math”.
The investigation of these connections is of particular interest, since this topic reveals contradictions between the intended and implemented reform goals and thus also enables a better understanding of the failure of the German New Math Reform as a curricular reform of mathematics for upper secondary schools.
SELECTED BIBLIOGRAPHY
Botsch, O. (1955) Die Bewegung als methodisches Prinzip im Geometrie-Unterricht de Mittelstufe [Motion as a methological pinciple to teach geometry in lower secundary school]. Frankfurt, Germany: Diesterweg.
Damerow, P. (1977). Die Reform des Mathematikunterrichts in der Sekundarstufe I. Band 1: Reformziele, Reform der Lehrpläne. Max-Planck-Institut für Bildungsforschung [The reform of mathematics education in lower secondary schools. Vol. 1: Reform goals, reform of curricula. Max Planck Institute for Human Development]. Stuttgart, Germany: Klett-Kotta.
Lenné, H. (1969). Analyse der Mathematikdidaktik in Deutschland [Analysis of didactics of mathematics in Germany]. Stuttgart, Germany: Ernst Klett Verlag.
Steiner, H.G. (1956). Bewegungsgeometrische Lösung einer Dreieckskonstruktion. Math. Phys. Semesterber., 5, pp. 132–137.
Яглом, И.М. (1956). Геометрические преобразования. Серия Библиотека математического кружка, выпуск 8.