Computer Algebra Systems (CAS) have been changing the mathematics instruction requirements for many years. Since the tendency of using CAS in mathematics instruction has been rising for decades and reports have often been positive, the implementation of notebook classes seems to be the consequent next step of mathematics instruction supported by computers. Experiences that have been made with the use of CAS in PC-rooms can be transformed directly into the classroom. Hence the use of CAS is no longer limited to certain rooms. The permanent availability of the notebook with installed CAS offers the chance to realize these concepts that have already been approved with the use of CAS so far. The following speech shall show what these concepts could look like and that the use of notebooks is not only the further development of teaching in PC-classes. Examples from personal experience in teaching will especially show meanders and thought-provoking impulses in order to support teachers finding their way into teaching mathematics instruction in notebook classes successfully. Please allow me to point out two things in the beginning: (1) Yes, I am a vehement supporter of the use of notebooks (and the use of CAS in particular) in mathematics instruction. (2) No, I do not believe that teachers who have chosen another path (or at least partly) are teaching badly.

The main purpose of this workshop is to focus upon a complementary approach to the study of, and the investigation into, concepts related to Geometry- Space Strand. It ought to benefit educators especially those who prepare teachers for the primary/elementary schools. Participants in this workshop will initially learn the skills needed in Pop-Up Engineering to produce ‘hole’ 3- D paper models which illustrate some particular geometric concepts. The process of the construction of these models allows for building imagery, testing predictions, arousing and satisfying curiosity, connecting to Geometric concepts and most of all motivating and holding interest. It is envisaged that this approach to the teaching and learning of geometric concepts will provide grounds for discussion, enrichment, exploration, clarification of and ownership of ideas, and cross curriculum integration. It has the potential to reduce the apparent difficulty students experience with the study of geometric concepts.

The main purpose of this workshop is to focus upon a complementary approach to the study of, and the investigation into, concepts related to Geometry- Space Strand. It ought to benefit educators especially those who prepare teachers for the primary/elementary schools. Participants in this workshop will initially learn the skills needed in Pop-Up Engineering to produce ‘hole’ 3- D paper models which illustrate some particular geometric concepts. The process of the construction of these models allows for building imagery, testing predictions, arousing and satisfying curiosity, connecting to Geometric concepts and most of all motivating and holding interest. It is envisaged that this approach to the teaching and learning of geometric concepts will provide grounds for discussion, enrichment, exploration, clarification of and ownership of ideas, and cross curriculum integration. It has the potential to reduce the apparent difficulty students experience with the study of geometric concepts.

Computer Algebra Systems (CAS) have been changing the mathematics instruction requirements for many years. Since the tendency of using CAS in mathematics instruction has been rising for decades and reports have often been positive, the implementation of notebook classes seems to be the consequent next step of mathematics instruction supported by computers. Experiences that have been made with the use of CAS in PC-rooms can be transformed directly into the classroom. Hence the use of CAS is no longer limited to certain rooms. The permanent availability of the notebook with installed CAS offers the chance to realize these concepts that have already been approved with the use of CAS so far. The following speech shall show what these concepts could look like and that the use of notebooks is not only the further development of teaching in PC-classes. Examples from personal experience in teaching will especially show meanders and thought-provoking impulses in order to support teachers finding their way into teaching mathematics instruction in notebook classes successfully. Please allow me to point out two things in the beginning: (1) Yes, I am a vehement supporter of the use of notebooks (and the use of CAS in particular) in mathematics instruction. (2) No, I do not believe that teachers who have chosen another path (or at least partly) are teaching badly.

Der Umweltunterricht in Biologie befindet sich in der Orientierung zwischen Zwängen zur Reduktion auf naturwissenschaftliches Basiswissen (scientific literacy), den Kompetenzansprüchen der traditionellen Umweltbildung (environmental literacy) und der zuletzt implementierten Bildung für Nachhaltigkeit (BNE) mit dem Ziel Gestaltungskompetenz (sustainability literacy). Die hier präsentierte Studie diente neben der Bestimmung und Diskussion des Ist-Standes bei der Vermittlung umweltbezogener Gesichtspunkte im Rahmen des Faches Biologie auch der Entwicklung eines entsprechenden Instrumentes zur Erfassung der Unterrichtskonzepte von Lehrpersonen. Die Identifikation der Unterrichtskonzepte ging von Lehrkräften und deren Befragung in einem Ländervergleich zwischen Deutschland und Schweden aus. Methodisch wurde eine Kombination aus qualitativen und quantitativen Verfahren umgesetzt. Drei latente Erklärungsvariablen für die Antwortmuster der Lehrpersonen wurden faktorenanalytisch identifiziert und in verschiedenen Erhebungswellen validiert. Darauf basierend wurden drei kurze Testskalen gebildet. Ein zweites Auswertungsverfahren bestand in der Clusteranalyse der befragten Lehrkräfte. Indem die Cluster mit den Skalen in Beziehung gesetzt wurden, konnten anhand der Varianz der Gruppenmittelwerte verschiedene Profile identifiziert werden. Dies führte zur Beschreibung von je sechs qualitativ und quantitativ differenzierbaren Unterrichtskonzepten in Deutschland und Schweden als reservierte, minimalistische, traditionelle, neuorientierte, ambivalente und pluralistische Realisierung von Umweltbiologie. Während der reservierte Ansatz in Schweden nicht auftritt, kann dort „theoretische Umweltbiologie“ unterschieden werden. Beim derzeitigen Aus- und Fortbildungsstand der Lehrkräfte ist die Umsetzung von BNE in Deutschland nicht adäquat gewährleistet. Gründe dafür liegen im disziplinären Vermittlungsmodus, mit dem die Entwicklung überfachlicher Kompetenzen kaum vereinbar ist. / Environmental education has been implemented interdisciplinary at school in Germany. On the contrary, teacher training still remains emphasizing specific scientific subjects. Only recently, different initiatives towards education for sustainable development (ESD) are under way on state level, sub-state level and local level. However, common criteria for designing interdisciplinary teaching processes have not become obvious in Germany. There is a risk, therefore, that teachers will make decisions concerning aims, content and methods based solely on intuition. The study presented here identifies and discusses the existing state of concepts of environmental biology among biology teachers with respect to scientific literacy, environmental literacy and sustainability literacy. A wide range of different aspects of didactics in environmental biology was identified and gathered from biology teachers and scientists in Germany and Sweden. Following classical test theory, the diverse statements were eventually transformed into a closed Likert-scale questionnaire. In two preliminary studies and in the main study that was conducted across the whole of Germany, three dimensions were identified and validated by means of factor analysis. Using cluster analysis, six concepts can be distinguished: pluralistic, ambivalent, realigned, traditional, minimalist and reserved realisation of environmental biology. Biology teachers generally refer to a disciplinary science orientated teaching repertoire when addressing environmental education, which is not adequate to ESD theory. Following the investigation in Sweden, also six concepts can be distinguished. Instead of the reserved concept, a theoretic realisation exists in Sweden suitable for facilitation of sustainability literacy. In five types of realising environmental biology, a high degree of agreement was identified between perceptions of teachers in Germany and Sweden.