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This survey presents an overview of a German meta-discourse on theories and mathematics education as a scientific discipline from the 1970s to the 1990s. At that time Hans-Georg Steiner initiated the first of five international conferences on Theories of Mathematics Education (TME) to advance founding mathematics education as a scientific discipline. In the Post-TME era, German researchers still focused on TME topics but within various theory strands. Two theory strands will be presented: a semiotic view related to Peirce and Wittgenstein (presented by Willibald Dörfler), and the theory of learning activity by Joachim Lompscher (presented by Regina Bruder and Oliver Schmitt). While networking the two theoretical approaches in the case of learning fractions, we will clarify the nature of the two theories and how they can be related to inform practice and renew TME issues for mathematics education as a scientific discipline.

This first chapter of the survey addresses the historical situation of the community of mathematics education in German-speaking countries from the 1970s to the beginning 21st century and its discussion about the concept of theories related to mathematics education as a scientific discipline both in German-speaking countries and internationally.

The concept of activity is a psychological construct that connects man and his development to culture and society. This concept was shaped substantially by Vygotsky, Leontiev, and Luria and developed further in the German-speaking countries by Lompscher in particular.

It is obvious that mathematicians throughout history have used signs of various kinds, such as symbols, diagrams, graphs, and formulae, but they also occur in everyday language and scientific language.

During the last decade, the discussion on theory development has been reconsidered, for example, by Prediger (2010), in the networking of theories approach worked out by a group of European researchers coming from Germany, Italy, Spain, Israel, France, and (at the beginning also from) the UK.

A vivid discussion about the theory concepts and the role of theory in mathematics education began at the end of the 1970s. This was embedded into a broader discourse about the nature of the “” (“Didactics of Mathematics”/mathematics education) and its core subject: the mathematics to be learned and taught.