An overview over the current state of research reports and ongoing projects about the integration of graphic tools and computeralgebra in mathematics teaching was the aim of this bibliography report

An overview over the current state of research reports and ongoing projects about the integration of graphic tools and computeralgebra in mathematics teaching was the aim of this bibliography report. To understand the German situation in this field it is helpful to give a glimpse view on historical specifics in Germany.

Graphic calculators (GC) and computer algebra systems (CAS) in mathematics education - there used to be two different ways of facing these new technologies when looking at different countries (Barzel 2006). On one hand, the development went from scientific calculators towards GCs until CAS was finally reached. This way was mainly broken by the USA, Australia and in Europe, the UK, Netherlands, all Scandinavian countries as well as the eastern German counties. In the newly-formed German states the GC is an inherent part since the 1990’s. Long-term studies started, such as Hentschel/ Pruzina (1995), in different counties and analysed the integration of a GC from grade 9 until A-levels from 1991 onwards. This way, going from scientific calculators to GC and just then to CAS, is much more straightforward for the teachers then going from the scientific calculator directly to a CAS. This second way was mainly broken by Austria, Switzerland and the West German counties. It is more difficult for the teachers to integrate the graphical abilities of the calculator as well as the algebraic functions at the same time than one after another.
According to Weigand (2006) the discussion of the importance of CAS in maths classes can be divided into three main phases. The first phase began in 1988 when the CAS “Derive” was introduced on “personal computers”. Lots of discussions followed arguing about the meaning of basic mathematical skills when knowledge and skills could be passed from the head to the technology. That way a lot of complicated calculations such as polynomial long division, trigonometric calculations or transformation of terms could be facilitated. Unfortunately, there was very little research done in this time.
The second phase started in December 1998 when the first handheld calculator TI-92 was introduced. Suddenly, it was no more necessary to go to the computer lab. Pupils could just take their calculator wherever they went. The discussion of how content and examination in maths classes should be changed started. Many suggestions of lesson designs were published by teachers and also first research projects were carried out.
In the third and last phase which started at the beginning of the century the awareness appears along that GC and CAS only achieved partial of acceptance. Weigand names four different, possible reasons for the non-acceptance in Germany:
1) teachers’ attitudes: lack of familiarity with the tool, sorrow of losing important, mathematical basic skills, great importance to the traditional “paper-pencil-mathematics”
2) syllabuses and curricula: lack of integration of handheld calculators into the existing syllabuses, lack of change of learning content in respect of the use of handheld calculators
3) institutional demands: problem of various designs, fast change of versions, high price and social balance
4) construction of the tool: complicated handling, insufficient resolution of the screen, absence of development towards a pedagogical tool, high price, different types

Unfortunately, we could not include all existing German publications in this field because many of them were published already in the early 1990’s. There have been esp. reports about various official projects initiated and oragnized by ministries of education in German counties such as Saxony, Baden-Wuerttemberg, Lower Saxony, North Rhine-Westfalia, Saxony Anhalt and Thuringia. These reports were published and dissiminated by the local ministries or their institutes for teaching training.
The focus of this bibliography report is on official publications after the year 2000 and the ones that were not explicitly linked to a county government.

The main aim of this report is to give an overview of the existing researches concerning the integration of technology into mathematics education. We, basically, divided our report into four main parts. First, we explain the design of the chapters. In the second part, we list all relevant researches just to give an overview. The third part presents a summary and an analysis of all included projects. As there are different kinds of researches concerning the integration of technology in maths classes, we subdivided this chapter into four sections. There is first of all, research projects which means that these ones have already finished and are serious researches. The following part presents research projects still in progress and where we can only present first results. We are looking forward to the final results. The third section includes case studies and projects without a clear research design, mainly just focussing on few lessons or special short-time sequences. In the fourth part of the third chapter, we give a list of the lately published ressources for maths lessons using CAS. All of them are designed and tried at school, so they base on experience.

Beside a lot of papers concerning studies we have involved two position papers. One of these is by Schneider/Peschek (2002) that presents ideas and aspects for a theoretical framework coming from a communication theory (i.e. Fischer 2000). Schneider and Peschek declare the calculator an expert. Hence, the use of a graphic calculator is the training of communication with an expert.
Another position paper is published by Barzel (2004) discussing the question whether integration of new media and opening up of processes in teaching and learning mathematics presuppose each other. She differentiates “new learning” into two main branches. First, the “interior method” is mentioned, saying that the teacher could open up the task. Beside, there is the “exterior method” with means that the way of teaching, the classroom organisation could be disclosed.
Finally, we want to, of course, thank all authors who helped us to find the relevant papers and checked our summary for their own publications. Additionally, our thanks go to Texas Instruments for giving us the opportunity to write this report.