This survey provides an overview of German meta-discourse on theories and mathematics education as a scientific discipline, from the 1970s to the 1990s. Two theory strands are offered: a semiotic view related to Peirce and Wittgenstein (presented by Willibald Doerfler), and the theory of learning activity by Joachim Lompscher (presented by Regina Bruder and Oliver Schmitt). By networking the two theoretical approaches in a case study of learning fractions, it clarifies the nature of the two theories, how they can be related to inform practice and renew TME-issues for mathematics education as a scientific discipline. Hans-Georg Steiner initiated the first of five international conferences on Theories of Mathematics Education (TME) to advance the founding of mathematics education as a scientific discipline, and subsequently German researchers have continued to focus on TME topics but within various theory strands.

This survey book reviews four interrelated areas: (i) the relevance of heuristics in problem-solving approaches - why they are important and what research tells us about their use; (ii) the need to characterize and foster creative problem-solving approaches - what type of heuristics helps learners devise and practice creative solutions; (iii) the importance that learners formulate and pursue their own problems; and iv) the role played by the use of both multiple-purpose and ad hoc mathematical action types of technologies in problem-solving contexts - what ways of reasoning learners construct when they rely on the use of digital technologies, and how technology and technology approaches can be reconciled.

Der Tagungsband gibt einen breiten Uberblick uber Ziele, Kursszenarien und Lehr-Lernkonzepte, Unterstutzungsmassnahmen in der Studieneingangsphase, Moglichkeiten des Assessments und der Diagnostik sowie einen Ausblick zur Zukunft von mathematischen Vor- und Bruckenkursen. Zudem werden aktuelle Vor- und Bruckenkursprojekte vorgestellt und der aktuelle empirische und theoretisch-konzeptionelle didaktische Forschungsstand in diesem Bereich abgebildet. "