Changed views on mathematical knowledge in the course of didactical theory development—independent corpus of scientific knowledge or result of social constructions?

Abstract

The study tries to show one line of how the German didactical tradition has evolved in response to new theoretical ideas and new-empirical-research approaches in mathematics education. First, the classical mathematical didactics, notably 'stoffdidaktik' as one (besides other) specific German tradition are described. The critiques raised against 'stoffdidaktik' concepts [for example, forms of 'progressive mathematisation', 'actively discovering learning processes' and 'guided reinvention' (cf. Freudenthal, Wittmann)] changed the basic views on the roles that 'mathematical knowledge', 'teacher' and 'student' have to play in teaching-learning processes; this conceptual change was supported by empirical studies on the professional knowledge and activities of mathematics teachers [for example, empirical studies of teacher thinking (cf. Bromme)] and of students' conceptions and misconceptions (for example, psychological research on students' mathematical thinking). With the interpretative empirical research on everyday mathematical teaching-learning situations (for example, the work of the research group around Bauersfeld) a new research paradigm for mathematics education was constituted: the cultural system of mathematical interaction (for instance, in the classroom) between teacher and students.