This book discusses a significant area of mathematics education research in the last two decades and presents the types of semiotic theories that are employed in mathematics education. Following on the summary of significant issues presented in the Topical Survey, Semiotics in Mathematics Education, this book not only introduces readers to semiotics as the science of signs, but it also elaborates on issues that were highlighted in the Topical Survey. In addition to an introduction and a closing chapter, it presents 17 chapters based on presentations from Topic Study Group 54 at the ICME-13 (13th International Congress on Mathematical Education). The chapters are divided into four major sections, each of which has a distinct focus. After a brief introduction, each section starts with a chapter or chapters of a theoretical nature, followed by others that highlight the significance and usefulness of the relevant theory in empirical research.

This book discusses a significant area of mathematics education research in the last two decades and presents the types of semiotic theories that are employed in mathematics education. Following on the summary of significant issues presented in the Topical Survey, Semiotics in Mathematics Education, this book not only introduces readers to semiotics as the science of signs, but it also elaborates on issues that were highlighted in the Topical Survey. In addition to an introduction and a closing chapter, it presents 17 chapters based on presentations from Topic Study Group 54 at the ICME-13 (13th International Congress on Mathematical Education). The chapters are divided into four major sections, each of which has a distinct focus. After a brief introduction, each section starts with a chapter or chapters of a theoretical nature, followed by others that highlight the significance and usefulness of the relevant theory in empirical research.

This volume discusses semiotics in mathematics education as an activity with a formal sign system, in which each sign represents something else. Theories presented by Saussure, Peirce, Vygotsky and other writers on semiotics are summarized in their relevance to the teaching and learning of mathematics. The significance of signs for mathematics education lies in their ubiquitous use in every branch of mathematics. Such use involves seeing the general in the particular, a process that is not always clear to learners. Therefore, in several traditional frameworks, semiotics has the potential to serve as a powerful conceptual lens in investigating diverse topics in mathematics education research. Topics that are implicated include (but are not limited to): the birth of signs; embodiment, gestures and artifacts; segmentation and communicative fields; cultural mediation; social semiotics; linguistic theories; chains of signification; semiotic bundles; relationships among various sign systems; intersubjectivity; diagrammatic and inferential reasoning; and semiotics as the focus of innovative learning and teaching materials.

Einleitung.- Teil I. Theoretische UEberlegungen.- 1. Theorematische Deduktion als kreative Verwendung von Inskriptionen.- 2. Zeichen statt Metaphysik.- Teil II. Semiotik in der Praxis, das Sichtbare ordnen.- 1. Diagrammatisches Schliessen lehren und lernen.- 2. UEber Darstellungen reflektieren.- 3. Rekonstruktion diagrammatischen Schliessens beim Erlernen der Subtraktion negativer Zahlen.- Teil III. Zeichen hoeren und Zeichen sehen.- 1. Translanguaging im Matheunterricht.- 2. Semiotische Perspektiven auf das Erklaren von Mathematik in Laut- und Gebardensprache.- 3. Mathematische Gebarden der OEsterreichischen Gebardensprache aus semiotischer Sicht.- 4. Modusschnittstellen in mathematischen Lernprozessen.

Die fortschreitende Entwicklung der Mathematikdidaktik als Wissenschaft begrundet sich unter anderem in der fruchtbaren Anwendung unterschiedlicher allgemeiner Ansatze zur Beschreibung des Lernens und zur Organisation des Lehrens von Mathematik. Seit mehr als einem Jahrzehnt nimmt unter diesen Ansatzen die Semiotik, also die Theorie der Zeichen, einen Platz von zunehmender Bedeutung ein. Der vorliegende Band tragt dieser Entwicklung Rechnung und entwirft in einer Reihe von Beitragen Perspektiven auf die Mathematikdidaktik. Dazu zahlen unter anderem UEberlegungen zu ontologischen und historischen Fragestellungen, Texte zur Visualisierung von Mathematik oder Ausfuhrungen zum Verhaltnis von Sprache und Verstehen von Mathematik.