Edith Schneider

CAS in general mathematics education

A rational discussion of the use of Computer algebra systems (CAS) in mathematics teaching in general education needs an explicit image of (general) mathematics education, an explication of global perspectives and goals on mathematics teaching focusing on general education (chapter 1). The conception of general education according to the «ability of communication with experts» described in chapter 2 can be such an orientation for analysing, considering, classifying and assessing the didactical possibilities of using CAS. CAS are materialised mathematics allowing for more or less exhaustive outsourcing of operative (also symbolically) knowledge and skills to the machine. This frees up space of time as well as mental space for the development of those competences being in our view relevant for general mathematics education. In chapter 3 the idea of outsourcing and the role of CAS for it is discussed more detailed as well as consequences being possible for the CAS-supported teaching of mathematics. Beyond, CAS can be didactically used and reflected as a model of communication between (mathematical) experts and lay-persons (chapter 4). Chapter 5 outlines some research perspectives.

Professionalität von Lehrerinnen und Lehrern

A portable ultrasound diagnostic device dynamically collecting diagnostic data from a patient and, once the portable ultrasound diagnostic device determines that collecting the diagnostic data is complete, the portable ultrasound diagnostic device transmits the diagnostic data using a communication channel to a person at another location to analyze the diagnostic data.

CAS as a didactical challenge

The paper starts with the discussion of a concept of general mathematics education (mathematics education for everyone). This concept views the focus of teaching mathematics in the reduction of the demands in the field of operative knowledge and skills as well as in an increase of the demands in the fields of basic knowledge and reflection. The consequences of this concept are didactically challenging for the use of Computer Algebra Systems (CAS) in the teaching of mathematics. By reducing the operative work we reduce exactly that field in which the original potential of CAS lies. It is shown that in such maths classes the main focus of CAS is on their use as a pedagogical tool, namely as support for the development of basic knowledge and reflection as well as a model of communication with mathematical experts.

Mathematics and reflection

The notion of reflection is a broad one, which can be approached from various directions. The intention of this volume is to consider reflection from a (socio-)philosophical and education theoretical point of view and to offer insight into various approaches. Thus, at the centre of attention in this issue are orientations of reflection which concentrate on the discussion of mathematics and its role for, meaning to and effects on each individual, on the learning community, on societal collectives and on the world in the narrow or broader sense. The reference points are mathematics itself, one’s own relationship to mathematics and/or the effects of mathematics on systems, on the world. In the sense of being an opening for this focus, a glimpse above and beyond, in place of different approaches, a metacognitive view of reflection and mathematics will be introduced as an additional aspect, in which the learners reflect on their own position in the learning process and thus make mathematics an object of their own thinking.

Mathematische Bildung im Klagenfurter Doktorand(inn)enkolleg

In 2003 we set up a programme for PhD-studies (,,Doktorand(inn)enkolleg”) at the University of Klagenfurt which should promote and support PhD-studies in the field of mathematics education. Within this programme it is worked on the topic “general mathematics education” from different perspectives. In the first part of this paper intentions, the fields of work and the form of organisation are briefly demonstrated. The second and main part considers in detail the work in one of the four fields of work, and finally, the third and last part presents some experiences with regard to the contents as well as general ones.

Das Klagenfurter DokotrandInnenkolleg. 'Mathematische Bildung im informationstechnologischen Zeitalter'

der Austausch mit den anderen Promovenden schafft neue und erhält Kontakte. Neben den DoktorandInnenkolloquien, an denen Expertinnnen und Experten teilnahmen, trafen sich einige Nachwuchswissenschaftlerinnen und Nachwuchswissenschaftler auch regelmäßig unter sich, um ihre Forschungsprojekte zu diskutieren. Diese Initiative zeigt ebenfalls den Wunsch nach Austausch, der während der Promotionszeit so wichtig ist. Auf nationaler Ebene gibt es für Promovenden der GDM durch genannte Kolloquien sowie durch die jährlich stattfindende GDM-Tagung mit einem Doktorandentreffen Möglichkeiten, Kontakte aufzubauen. Doch nicht nur die Vernetzung auf nationaler Ebene, sondern auch die auf internationaler Ebene ist wichtig. Das Besuchen von internationalen Konferenzen zählt sicher zu den ersten Einstiegsmöglichkeiten, aber dort Kontakt zu anderen Promovenden zu finden, kann schwierig sein. Für einen guten Einstieg in die internationale Community halte ich die Teilnahme an der YERME Summer School für sinnvoll. YERME kommt von ” Young researchers in mathematics education“ und wurde von einigen Promovenden und Professoren auf einer der ersten ERMEKonferenzen (European Society for Research in Mathematics Education) gegründet. Die alle zwei Jahre stattfindende YERME Summer School mit internationalen Expertinnen und Experten und Teilnehmerinnen und Teilnehmer, nicht nur aus dem europäischem Raum, wird dieses Jahr in der Nähe von Prag stattfinden. Innerhalb dieser zwei Jahre finden jeweils die ERME-Konferenzen statt. Vor Konferenzbeginn gibt es einen sogenannten YERME-Tag, der nur den Doktorandinnen und Doktoranden gewidmet ist. Für diesen Tag kann man sich meist für thematische Working oder Discussion Groups anmelden, die wiederum von Expertinnen und Experten geleitet werden.