A proposal for the European Science Education Initiative
(FP6-2003-Science and Society-5)
Occasional Paper 187 October 2003

Science and Society
European Science Education Initiative – Call March 2003
Co-ordination Actions
SEE!
Date of preparation: October 8, 2003
List of participants: 1. Coordinator:
2. Austria:
3. Bulgaria:
4. Denmark:
5. France:
6. Germany:
7. Germany:
8. Hungary:
9. Israel:
Universität Bielefeld
Universität Klagenfurt
Sofia University
Danish University of Education
IUFM d’Aix-Marseille
Universität Frankfurt/Main
Leibniz-Institute for Science Education at the University of Kiel (IPN)
Eötvös Loránd Tudományegyetem
(ELTE)
Center for Educational Technology & Haifa University
10. Italy:
11. Lithuania:
12. Slovenia:
13. Spain:
Universita di Torino
Vilnius Pedagogical University
University of Maribor
Fundació EMI - Facultat d'Economia IQS - Universitat Ramon
14. Sweden:
Llull
Linköpings Universitet
15. Techn. Infrastruct.: BCS, Paderborn, Germany
16. Internet portal: Virtech Ltd., Sofia, Bulgaria
Name of the co-ordinating person Dr. habil. Michael H.G. Hoffmann e-mail: fax: michael.hoffmann@uni-bielefeld.de falk.seeger@uni-bielefeld.de
+49(0)521/106-2991
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Science and Society
European Science Education Initiative – Call March 2003
Co-ordination Actions
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Table of contents
B.1 Objectives of the project and state of the art........................................................................... 4
B.2 Relevance to the objectives of Science and Society ............................................................ 10
B.3 Potential impact ..................................................................................................................... 11
B.3.1 Contributions to standards .................................................................................................. 12
B.4 The consortium and project resources .................................................................................. 13
Ø Co-ordination (C) ............................................................................................................... 14
Ø Empirical research and video analysis (E)........................................................................ 15
Ø Theoretical analysis (T)..................................................................................................... 19
Ø Web presentation (W)....................................................................................................... 23
Ø
Networking (N) ................................................................................................................... 24
Ø Technical Infrastructure (TI) .............................................................................................. 28
B.5 Project management.............................................................................................................. 29
B.6 Workplan ................................................................................................................................ 30
Ø References ........................................................................................................................ 36
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Science and Society
European Science Education Initiative – Call March 2003
Co-ordination Actions
SEE!
Proposal summary page
Science Education across Europe (SEE!). A Project on Generalisation in Science:
Overcoming the Split between the Two Cultures
SEE!
Strategic objectives addressed:
SOCIETY-1.2
INNOVATION-3
COOR-1.1
SOCIETY-3.2
Proposal abstract
To encourage girls’ and boys’ enthusiasm for science, the project tries to improve Science
Education through international co-operation. The emphasis of the project is, first, on disseminating theoretical approaches and practical skills by organising a sequence of conferences, by translating research results, and by networking the existing networks through an public internet-portal “Science Education across Europe” (SEE!). The second principal aim is the improvement of science teaching by reflecting on videotaped classroom activities and on differences between classroom cultures within the enlarging EU. Last, but not least, the project will contribute through exemplary teaching units to curriculum development in science and mathematics teaching.
A short teaching unit will serve as a lens collecting the diverse aspects. This teaching unit will be about a historical example of generalising theories, i.e. the discovery of incommensurability in Ancient Greece. The unit will be conducted and videotaped in classrooms of the participating countries. It is supposed to be the start of a longer series of exemplary teaching units.
The theme of this teaching is supposed to motivate exchange on science education across
Europe: 1) By focussing on generalisation as a core idea of scientific thinking which is essential both in science and in the humanities, we offer a paradigm for curricula which stress a much deeper and more intensive reflection on general features of scientific thinking and its dependence on a self reflected integration of a variety of cultural traditions. 2) By concentrating attention on a paradigmatic case, a thorough analysis and comparison of different practices of teaching, learning, communication, argumentation, interactions, and activities in classrooms are possible. At the same time, applying different theories and methods of analysis to this concrete case allows an evaluation of these approaches.
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Science and Society
European Science Education Initiative – Call March 2003
Co-ordination Actions
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A closer look at the educational parts within the Science and Society Work Programme 2003 of the EU commission reveals a certain tension between two foci: On the one hand, there is a general focus on teaching girls and boys which can be summarised by the following points:
• to promote young people’s interest in science
• to encourage critical and creative ways of thinking
• to improve science education and the uptake of scientific careers
• to change the predominant perception of science as uninteresting and difficult
• to improve the “appeal” of study courses at school
Based on this emphasis on teaching, one purpose of the call for the Science Education Initiative is “to support actions that identify and disseminate methods, techniques and good practices aimed at enhancing science teaching in schools across Europe through activities and approaches that complement formal curricula.” (Guide for Proposers, European Science
Education Initiative, Co-ordination Actions, Call March 2003, p. 7)
On the other hand, there is a more specific focus on building up a network of networks . Thus, the Work Programme formulates with regard to the implementation of the Science Education
Initiative in 2003: “The focus will be on providing a mechanism for allowing science teachers, science professionals, education specialists and associated expertise from across Europe to exchange ideas, techniques, and methods to supplement existing science curricula and educational strategies in order to increase the attractiveness and relevance of science studies at schools. The action must involve existing science teachers networks and the use of internet resources to ensure the widest possible dissemination of the shared and newly acquired knowledge among the science teaching profession and associated professions. Proposals must provide an openly accessible resource infrastructure.” (Work Programme 2003, Science and
Society, section 4, 2. April 2003, p. 12)
A guiding idea, however, of our project proposal is that it will hardly be possible to building up a network between already existing networks if there are no concrete projects, no fascinating ideas of concrete teaching and of possible ways to improve the “appeal” of science education at school. As in any activity, networks are built up and kept alive by living human beings so that it is first of all necessary to find a motivation for researchers and teachers to engage in an abstract activity as network building is.
Based on this consideration, the main idea of our project is that networking in science education is possible only if it is combined with an intensive exchange on concrete teaching activities.
Thus, the “way” we have “found to mobilise of existing resources and networks, as well as all the professions that have a stake in the development and use of science skills” (Guide for
Proposers, European Science Education Initiative, Co-ordination Actions, Call March 2003, p.
7), is to combine both the foci mentioned above. We want to initiate networking across Europe on the basis of a dialogue about the question how science and mathematics education could be improved. To motivate such a dialogue, we have built up a group of proposers across the boundaries between different cultural and educational traditions within the enlarging EU and
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associated countries that plan to run a concrete project on “Generalisation in Science:
Overcoming the Split between the Two Cultures.”
There are two reasons for choosing this theme. The first is the assumption that the recent problems of science education – lack of interest in science, horrific ideas about what scientists are doing, lack of even elementary understanding science, dropping standards, etc. – can only be overcome by more global, more holistic attempts to introduce kids into the culture of science.
In particular, the old split between a culture based on literacy and literacy studies and a culture based on mathematics and the sciences at which C.P. Snow 1961 <1959> had pointed already more than forty years ago seems still to be an important obstacle. This became apparent, for example, during the recent discussion on the results of international assessment of scholastic achievement like, e.g., TIMSS or PISA, and in hot debates between an understanding of education in the literary tradition and education in the tradition of the mathematician and natural scientist (cf., e.g., Fischer 2002 <2001> versus Schwanitz 2001 <1999>). Also the famous
“science wars” of the last years give an illuminating example of a conflict that seems to be basic for modern societies (cf. “The Science Wars Homepage” at http://members.tripod. com/ScienceWars/ ).
In a situation, where science and the humanities often fight against each other to gain recognition in society, a most important task of science education should be to demonstrate that genuine scientific thinking does not know such a separation of clear-cut “cultures.” By focussing on processes of Generalisation in Science , we want to highlight, first, that there are specific forms of scientific thinking which are essential both in science and in the humanities.
Understanding how theories are generalised in ongoing processes of knowledge development is a prerequisite for a deeper understanding of all sciences, natural or human (cf. Otte and
Hoffmann 1996). Second, and even more important, by discussing an illuminating example of generalisation from the history of science , we will show how deeply interwoven the two cultures have mostly been in the critical phases of scientific development. Generalisation depends, in most cases, on a change of perspective which often has been suggested by ideas from very different fields of thinking. New cultural and conceptual paradigms, images from the arts, or terms from other areas of life that were used purely metaphorically at first, often have an important impact on the possibility of generalisation. From this follows that teaching
“Generalisation in Science” means to teach a truly interdisciplinary view of scientific thinking, in which also philosophical, aesthetic, and “humanistic” approaches, to put it most generally, play a central role.
The second reason for choosing “Generalisation in Science” as the project’s motivating idea is the consideration that science education should, first of all, focus on the most general features of scientific thinking . Generalising scientific theories is suc h a most basic feature. Teaching generalisation from the start cannot be understood within a “transmission” or “broadcast” metaphor. Teaching – and learning to use – generalisation must be reflective (cf. Gravemeijer et al. 2002). That amounts to saying that also the learners have to be aware of, e.g., the complementarity of social and content-related forms of generalisation and generalising (cf. Otte
1997b; Otte 1997a). Learning generalisation, as it were, does not only mean to learn something more general but also to learn how to generalise in social and content-related form.
Our starting point is defining the “generalisation” of theories by semiotic means as a process of restructuring the systems in which knowledge is represented (cf. Hoffmann 2003a, chap. 9).
Going beyond an idea of “generalisation” in the sense of formulating universal propositions on the basis of particular observations, as it is well-known as “inductive generalisation,” the concept of generalisation we have in mind emphasises the creation of new concepts and structures that allow the reorganisation of theories or the creation of new ones (cf. in philosophy of science Kuhn 1970 <1962>, Balzer and Moulines 1996) or, to put it more generally, the reorganisation of representational systems (because knowledge can be represented also in diagrammatic or iconic forms, or in models; cf. Hoffmann 2003b).
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The project’s centre will be a teaching unit on the discovery of incommensurability in Ancient
Greece. We have chosen this historical example because here our understanding of generalising scientific theories can be demonstrated most clearly. This example highlights, in particular, the need of going beyond the boundaries of scientific disciplines in processes of generalisation. Thus, it should be taught within a context that comprises not only mathematics but also philosophy, music theory, and semiotics.
It is our contention that the role mathematics can play on the effort to gain a new perspective on science teaching is far from being peripheral. We feel that mathematics plays an outstanding role in motivating kids for science education when the goal is to reach lasting and enduring effects of this interest in science that goes beyond a superficial attraction by science made colourful. Mathematics can be seen as providing a solid fundament for an understanding of generalisation in science. In turn, the understanding of mathematics can be deepened if it is experienced in the context of science education.
The idea of our interdisciplinary teaching unit on an intuitively understandable and highly illuminating paradigm for generalisation was originally developed by Hoffmann and Plöger
2000, where also the necessary materials from the different disciplines are prepared. The example of the discovery of incommensurability is most illuminating because it can be shown here how traditional Pythagorean arithmetic which had known only rational numbers was generalised to a number system which included also irrational numbers. The important point of this step in the history of science is that this discovery depended, for the first time, on a new epistemological frame, namely the necessity of proofs in mathematics. Using this example, it can also be studied how this first important step to mathematics as a science was closely connected to a fundamental change in a philosophical debate on the role of numbers in “the
Great Book of Nature” (from divine to man-made entities as a basis for theories of measurement, for example). Overcoming the split between different cultures of thinking, thus, is the natural focus of this example.
It has to be said that the idea is not totally new to base science teaching on “generalisation” as a key concept. It has been done before, e.g., in the groundbreaking work of V. V. Davydov
1990. The specific thrust of the present project can be seen in that it contextualises generalisation through exemplary and data-rich cases and themes very much in the way that the idea of “anchored instruction” put forward by the Cognition and Technology Group at
Vanderbilt (see, e.g., Cognition and Technology Group 1990; Sherwood et al. 1998).
Embedding science learning into a context containing rich data can lead to highly motivated problem solving and ensuing authentic learning processes. Generally, putting generalisation into a rich context includes an emphasis on complex, open-ended problem solving, communications and reasoning, more connections from mathematics to other subjects and to the outside world, and more use of representational tools, such as spreadsheets and graphing programs, for exploring relationships.
Based on these considerations, we try to achieve the following objectives which might be grouped into the fields curriculum development , improving teaching practices , applying research results , and networking :
Objectives with regard to curriculum development :
1. To promote students’ interest in science by disseminating the idea that education in sciences is education in scientific thinking .
2. To foster understanding of science by focussing on the most general features of scientific thinking and its dependence on a self reflected integration of a variety of cultural traditions from philosophy and religion to music and mathematics.
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3. To disseminate new and innovative ideas for curricula of science and mathematics education which highlight these most basic features of scientific thinking and its interdisciplinary character.
4. To demonstrate by means of a concrete teaching unit how “Generalisation in Science” might be taught as an important aspect of scientific thinking (cf. Hoffmann and Plöger
2000 for these four points).
Objectives with regard to improve teaching :
1. To conduct this concrete teaching unit in a set of different countries and classes across
Europe and associated nations, and to videotape the classroom activities and interactions. (C. 6 classroom hours. To establish this method, a certain technical equipment has to be provided, as well as a specific training program to cope with technical and interpretational difficulties of this method. Teacher training will be provided by the project participants; there is NO request for financial support by the EU.)
2. To disseminate experiences of how to improve the quality of mathematics and science teaching by using the method of reflecting on videotaped classroom activities in order to support the development of teachers’ competence to critically assess their own performance. (Cf. Jungwirth and Stadler 2003, Stadler 2002, Pleskac 2002.)
3. To initiate a process of mutual learning across national boundaries about good practices of teaching, learning, and interacting, and about different classroom environments, by comparing the project’s videotapes. Comparing different classroom activities about the same theme is the best way to evaluate teaching and learning practices, and classroom cultures. (This methodological approach goes beyond the means developed for the great international studies that aimed at quantitative comparison of students’ skills and competencies. While even the innovative TIMSS 1995 and 1999 Video Studies focussed on quantifiable criteria for comparing different learning and classroom cultures – cf.
Stigler et al. 1999, Stigler and Hiebert 1999, Hiebert et al. 2003b, Hiebert et al. 2003a,
Reusser and Pauli 2003 –, our project’s explicit aim is to use qualitative comparison which, hopefully, reveals more than a surface analysis of classroom activities. The challenge of qualitative analysis should be met by a methodology that is far more oriented towards direct comparisons between only small numbers of video sequences from most distinct classroom cultures than it is the usual practice. The idea is that the obvious differences for themselves should suggest certain methods of interpretation, as
Grounded Theory puts it – cf. Glaser and Strauss 1967, Beck and Jungwirth 1999).
4. To build up a library of video tapes or DVDs that will be of greatest interest for lots of further research projects, e.g., with regard to long-term processes in classroom cultures, changes of teaching and learning cultures within the European Union, etc.
Objectives with regard to the application of research results :
1. To initiate a long-term exchange between professional science educators across the boundaries between different cultural and educational traditions within the enlarging EU and associated countries about the question: What are the most promising educational theories , practices of teaching , and methods of interpreting and analysing of what happens in classroom activities and in learning processes? The project’s focussing on a rather short and specific teaching unit has the primary function to motivate this exchange. It is a trivial fact that the methods of teaching are not the methods of the sciences that have to be taught. The methods of mathematics or physics education are not mathematical or physical methods but methods that stem mainly from the
Humanities. In a situation, however, where most of all professional science educators
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are first of all trained within their respective scientific disciplines, there is a continual need to consolidate theoretical foundations that are specific for the educational side of science education. That means, sustained efforts have to be made to disseminate the most important theories, methods, and reflections on good practices within the community of professional science educators and teachers.
2. To evaluate the applicability of those theoretical and methodological approaches which are renown today as most relevant by analysing and comparing the project’s videotapes in a joint endeavour. We have to apply what we consider as the standards of science education in order to perceive their limits, and to check out possibilities of their further development. (As most relevant for recent discussions, we will discuss, for example, the following approaches: Semiotics as a theoretical tool to understand the use, the construction, and interpretation of signs and representations in classrooms – cf. Whitson
1997, Cobb, Yackel, and McClain 2000, Radford 2000, Hoffmann 2001b, Gravemeijer et al. 2002, Hitt 2002, Roth and Lawless 2002b, Hoffmann 2003c, Hoffmann 2003d,
Hoffmann 2003b, Anderson et al. 2003, Roth 2003, Hoffmann, Lenhard, and Seeger
2003. Anthropological Theory of Didactics (ATD), which provides a methodology for the analysis and development of teaching and learning activities (Artaud and Chevallard
2002, Artaud 1998). Social interactionism as an instrument to understand social aspects of teaching and learning as the negotiation of meaning – cf. Voigt 1984, Bauersfeld
1988, Lawler 1990, Krummheuer 1992, Bauersfeld 1995, Cobb and Bauersfeld 1995,
Krummheuer 1997a, and Seeger, Voigt, and Waschescio 1998. Activity theory , in order to understand communication and interaction in classrooms – cf. Engeström 1987, Lave
1988, Cole 1990, Engeström 1991, Raeithel 1991, Lerman 1994, and Seeger et al.
1998, Roth 2003. Theory of argumentation as an instrument to understand the genesis of rationality in classroom interactions – c.f. Krummheuer 1997b, Krummheuer and
Brandt 2001. And finally, the complementary approaches of embodied cognition (Lakoff and Núñez 2000, Sinclair and Schiralli 2003, Arzarello and Robutti 2003) and the instrumental approach (Rabardel and Vérillon 1995, Artigue 2001, Lagrange 2003) which allow to describe the student’s mental dynamics between intuitive and concrete aspects of concept development on the one hand, and formal, abstract aspects on the other.
3. To overcome the theory-practice dichotomy by focussing on both the question how theoretical approaches make visible and communicable what happens in the videotaped classroom interactions, and the question how reflecting on the concrete practice of teaching and learning can direct the development of theories and methods.
Objectives with regard to networking :
1. To implement an internet portal “Science Education across Europe” (SEE!) which is supposed to function both as a fundament for the development of a European science education network and as a linkage between already existing national and international approaches.
2. To disseminate the project’s results by means of this internet portal, and to motivate scientific exchange also beyond the project’s limits to an ever-widening audience of science educators at schools across Europe.
3. To foster public understanding of science both by informing the public through press campaigns about the project’s objectives and results, and to invite interested scientists, teachers, students, parents, and educational institutions to using the internet portal
“Science Education across Europe” (SEE!) and to participate in exchange.
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4. To initiate a thinking process about possibilities of harmonising European curriculum development by promoting the idea of a holistic and interdisciplinary approach of science education as designed for the project.
Concerning the project’s web activities , there are already concrete plans: SEE! will be fully presented on the Internet. Also, the Internet is intended to serve as the primary communication/networking tool among partners throughout the project. These requirements will be met by a general web-design enabling two-level access for the most material as well as the inclusion of a database tool. The following main functions will be offered:
•
Information about the project and its phases, conferences, main activities and progress with unlimited access.
•
A public forum for world-wide communication about problems, activities, and perspectives of science education for researchers, teachers, students, parents, and other interested persons who will be invited to participate at this forum by two press campaigns and the other activities of the project.
•
In-depth information about project details, including in-work reports and activity details, non-public research plans and data, etc. for internal (password-protected) use only.
•
Database, containing curricula, learning modules, method descriptions as well as enhancements to different learning material with two-level access to offer unpublished data for internal use only.
•
A forum to discuss different topics for internal use by the project participants.
•
A “service box” for internal use to receive and discuss error reports and change suggestions concerning the web-service itself.
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Science and Society
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Within the 6 th
Framework Program of the European Commission, the program’s “Science and
Society” main objective is “developing structural links between institutions and activities concerned with the dialogue between the scientific community and society at large.” Following this general idea, Science and Society focuses on three main fields:
§ Bringing research closer to society
§ Responsible research and application of science and technology
§ Stepping up the science-society dialogue and women in science
“Science Education across Europe (SEE!). A Project on Generalisation in Science: Overcoming the Split between the Two Cultures” is concerned with the first and the third of these areas.
Being an application for the European Science Education Initiative (Call 5 within Science and
Society ), the project’s most general objective to improve science education across Europe is supposed to have an important impact upon the next generations’ possibilities to link science and society in an adequate manner. Understanding the general features of scientific thinking , as our project emphasizes as a core idea of teaching science by focusing on generalization as a central procedure of scientific thinking, is obviously an essential condition of the sciencesociety dialogue. Highlighting scientific thinking in this way might also be an important aspect with regard to Science and Society ’s goal of “promoting young people’s interest in science and scientific careers.”
A second dimension of influencing the dialogue between science and society will be addressed by our objective to building up an open, internet-based network for communication and exchange between researchers in science education, teachers, and students. In so far as parents and the public as well are invited to participate in that exchange, we hope to enhance an ongoing interaction between science and society – mediated by an open discourse about general ideas of science education.
A third dimension of contributing to the objectives of Science and Society will be realised by integrating “PUSH” elements (“Public Understanding of Science and Humanities”) in the project’s work plan. After a first conference, where a joint understanding of the project’s central ideas will be addressed, the participating groups are supposed to initiate press campaigns in their respective countries to inform the public about the project’s educational innovations and its internet activities. And again in the final phase of the project, the public should be informed about the results and possible continuations of the project’s approaches. Both activities should foster “public awareness of science and science communication” as formulated in the Science and Society descriptions.
Regarding Science and Society ’s special interest in the problem “women and science” we do not expect any relevant outcomes. We would like to observe, however, whether there are any gender specific differences concerning interest in our project’s emphasis on “overcoming the split between the two cultures,” and on understanding science from an interdisciplinary and holistic point of view. If there are any such differences to observe, that would be a fascinating starting point for further research.
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The outcome of our proposed Co-ordination Action should be an improvement of science educations at all its levels. What we want to achieve is
§ an improvement of curriculum development by disseminating the idea of interdisciplinary teaching, and by focussing on core ideas of scientific thinking, both on the basis of the teaching unit on “generalisation” sketched above in B.1;
§ an improvement of young people’s ability to think critical and creative, and the promotion of a personally involved interest in scientific thinking by a much deeper and more intensive reflection on general features of scientific thinking and its dependence on a self reflected integration of a variety of cultural traditions;
§ an improvement of teaching methodologies in didactical activities, using different teaching environments (paper and pencil, low and high level technology), different fields of experience (historical, social, physical, economical) and different mediating tools
(spreadsheets, CAS);
§ an improvement of teaching practice by disseminating the method of using videotaping as an instrument to reflect on ones own teaching activities, and by comparing different cultures of teaching, learning, communicating, and interacting within the enlarging EU
(and associated countries);
§ and an improvement of possibilities to exchange theoretical approaches, ideas on teaching, and a variety of resources from research and from practice between the different partners involved in science education, between the different educational cultures across Europe, and between already existing networks. Our instrument for doing this will be providing an openly accessible internet-portal “Science Education across Europe” (SEE!).
A plan for disseminating the project’s results will be described in greater detail below in section
B.6 Workplan . Dissemination is a central idea of the proposed project itself so that listing the relevant activities and evaluating their adequacy should be discussed within this context.
However, by what is said above with regard to an openly accessible internet-portal “Science
Education across Europe” (SEE!), it should be clear already that we expect a dissemination and exploitation of the project’s results “beyond the participants.” The very project is designed to impact already existing networks, co-operations, and discussions across Europe.
The added-value in carrying out the work at a European level is obvious: The very idea of the project’s focus on learning from different classroom cultures, and on building up a “network of networks” presupposes a variety of participators as great as possible.
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We expect to contribute to long-term curriculum development in the participating nations, but also in those nations who will engage in the proposed “Science Education across Europe”
(SEE!) initiative. As described in greater detail in B.1 Objectives , these contributions concern mainly supplementing existing curricula by stressing general features of scientific thinking, and by enhancing holistic and interdisciplinary forms of Science Education.
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The key idea of the proposal is to combine six types of necessary competencies which are either represented by the project’s participants or which have to be integrated by specific subcontracts. Because our workplan in B.6
below is structured according to these competencies, we will distinguish them in a first step, and relate all the participants, in a second step, to these types of competence.
First, there is a group of participants who are trained in empirical research and who represent experiences with curricula development, implementing new teaching ideas, videotaping classroom activities, transcribing interaction sequences, and/or analysing teaching, communication, and learning processes. Participants belonging to this group will conduct the proposed teaching unit in co-operation with teachers and classes they will choose within their countries, respectively.
Second, there is a group of theoretical researchers who represent the most relevant theoretical approaches and methodological standards within science and mathematics education. Their primary task will be to introduce the consortium to theories and methods necessary for developing the teaching unit, for analysing what happens in classes, and for evaluating the project’s results.
Third, there is a business participant whose special competencies are: designing a standard equipment for video-taping, and for preparing DVD records of exemplary classroom sequences; buying the necessary components to the best possible conditions; implementing the technical equipment in place of the empirical research projects.
Forth, there are the project’s co-ordinators who link together the project components, provide support for the participating groups, care about quality management, and maintain communication with the EU-commission. In our case, the project’s guiding ideas were developed as a continuation of the co-ordinators research results of the last years so that this group will provide also the setting of the project’s framework.
The fifth type of competence concerns designing and providing the internet portal “Science
Education across Europe” (SEE!). To accomplish this task, two competent partners having the relevant experience will join and share work in a way that also ensures professional quality management. After implementation of the internet portal, they will organise the maintenance of the web service, also beyond the limits of the project.
And finally, there is the competence of networking that is represented by each of the academic consortium partners due to their already given integration in existing networks.
Most of the participants represent at least two of the competencies listed so far, so that they are added to different groups in the lists below. We signify, in the following, the participants constantly by the numbers used at the front page of this Proposal Part B, and the types of competencies they represent by the letters C (co-ordination), E (empirical research), T
(theoretical analysis), W (web presentation), N (networking), and TI (technical infrastructure).
The same number attached to different competencies means that a group of participants takes over different tasks.
It should be noted, however, that we plan to invite for each of our conferences some specialists.
These specialists are, on the one hand, scientists who can inform us about results of their
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research according to the usual procedures of scientific exchange, but they are also specialists for certain techniques as, e.g., interpretative video analysis. These have to be paid as subcontractors. Their respective tasks are described in greater detail in the Workpackage descriptions of B.6
.
The following table shows the structure of our project consortium according to the six competencies mentioned above. The particular entries, that is the participating groups with their respective competencies, are described below in competence groups.
Co-ord. Emp. Theor. Web Netw. Techn.
1. Co-ordinator
2. Austria
3. Bulgaria
4. Denmark
1.C
2.E
3.E
4.E
1.T
2.T
3.T
1.N
2.N
3.N
4.N
5. France
6. Germany, Ffm.
7. Germany, Kiel
8. Hungary
9. Israel
10. Italy
11. Lithuania
12. Slovenia
13. Spain
14. Sweden
15. Techn. Infrastr.
16. Web-portal
11.E
12.E
13.E
14.E
7.E
8.E
9.E
10.E
13.T
14.T
5.T
6.T
7.T
9.T
10.T
16.W
8.W
11.N
12.N
13.N
14.N
5.N
6.N
7.N
8.N
9.N
10.N
15.TI
Ø
The responsibility of co-ordinating, managing and supporting the diverse activities in the respective national groups rests with Dr. habil. Michael Hoffmann and Dr. Falk Seeger from the interdisciplinary Research Institute for Mathematics Education (IDM) at the University of
Bielefeld. This co-ordinating group is also responsible for communication with the EU and for all technical question having to do with the proposal and its implementation.
Michael Hoffmann’s organisational skills are proven by his activities as the founder and recent director of an internationally oriented working group “Semiotik in der Mathematikdidaktik”
(Semiotics in Mathematics Education). Falk Seeger has organised lots of activities within the
International Society for Cultural an Activity Research (ISCAR) and within the AERA (American
Educational Research Association).
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The IDM at the university of Bielefeld has been able in the past to collect expertise in fields pertinent to the present proposal as the organisation of international cooperation in the realm of mathematics education, semiotics, epistemology, and history of science. Another outstanding area of work has been the study of classroom interaction with video and transcript analysis.
Finally, Bielefeld is internationally renowned for the grounding of mathematics education in the matrix of a multitude of scientific disciplines.
Resources provided by the IDM in Bielefeld are – besides the man power given by an interdisciplinary structured collegium of well-known scientists – an internationally renowned
Documentation Centre for research literature, school text books and curricula for mathematics from all around the world, and an Advisory Centre for Learning Problems in Mathematics which is connected with a multimedia lab for videotaping, recording, and analysing both children’s behaviour in working with mathematical tasks and the activities of future teachers.
Ø
The research group for mathematics education in Klagenfurt, directed by Prof. Willi Dörfler, is supervising a special program for PhD students (mainly teachers) in mathematics education.
One of those students is specializing on the teaching and learning of notions related to incommensurability and irrational numbers. This constitutes an ideal context for the empirical investigation of the viability of certain already developed theoretical notions. Besides this W.
Dörfler is member of a large Austrian project on teacher professionalisation which covers all science subjects and mathematics. Within this project, teachers are supported with their investigations for implementing innovative teaching methods. Some of those activities can be related to the topic of generalisation as well.
Ø
The Bulgarian participant – the Centre of Information Society Technologies (CIST) at the Sofia
University – is an interdisciplinary research and training institution of Sofia University “St.
Kliment Ohridski” (SU). It is motivated by the challenge to support the development, introduction and wide use of Information Society Technologies ( http://www-it.fmi.uni-sofia.bg/cist ). CIST was initially born as part of, and now works in close cooperation with, the Faculty of Mathematics and Informatics (FMI) at SU. CIST has strong technological and educational design and delivery expertise. For example, in cooperation with the Faculty of Behavioural Sciences, The
University of Twente, The Netherlands, CIST delivers the international MSc. Programme
“Educational and Training Systems Design,” which has a strong focus on finding effective and efficient design solutions to management, curriculum, instructional, media, evaluation, and learning problems in educational and training settings, by utilizing the new technologies to their fullest extent ( http://www-it.fmi.uni-sofia.bg/etsd/ ). Alongside with its educational, learning and technology expertise, CIST will be the operational and management core of the Bulgarian group of the project researchers – scientists and educators, consisting of 15 members from CIST,
Sofia University in general, and the Faculty of Mathematics and Informatics (FMI) in particular,
The Institute of Mathematics and Informatics, and The Institute of Mechanics of the Bulgarian
Academy of Science (BAS). All the group experts and the institutions, which they represent are an active part of the Union of Bulgarian Mathematicians (UMB) – a very influential and respectable network, with more than 100 years of history, which is the backbone of the
Bulgarian Mathematical research and Mathematical school and university education in the country. Thus, the CIST, the FMI – as a national institution for pre-service and in-service teacher education –, and the UMB as a network of Mathematics teachers and researchers will assure not only the research and technological expertise, necessary for the project, but also the
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teachers/schools/classrooms network, necessary to successfully design, conduct and analyse the empirical research project. Dr. Roumen Nikolov, Director of CIST and Vice-dean for international cooperation of the FMI will supervise the empirical research group.
Ø
The Danish group, directed by Dr. Helene Sørensen, consists of 4 persons. All in the group have documented theoretical skills in the field, and three are experienced in empirical research
(cf. Andersen and Sørensen 1995b, Andersen and Sørensen 1995a, Allerup 1998, Allerup
2003). They have studied science classrooms for several years, partly with a focus on gender issues (cf. Sørensen 1991, Allerup 2002). Video recording was used as a tool in research and development processes. With regard to the project’s empirical part, there exist already excellent connections to teachers who can conduct the teaching unit in corporation with the group.
One member of the group, Peter Allerup, has a background in mathematical statistics. He has been a member of national and international steering committees in reading and mathematics/science studies over the past 15 years. His professional field covers modern psychometrics, especially the development of scaling procedures, which are used for assessment of student characteristics (cf. Allerup 1994). He has been engaged in methods for statistical analyses of gender differences (cf. Allerup 2002).
Ø
The group from Kiel around Wilhelm Walgenbach is located at the Leibniz-Institute for Science
Education (IPN). The IPN’s main task is to develop and promote science education through research on questions concerning teaching and learning in the sciences. For that purpose, teams of scientists, experts in science didactics, educationalists, and psychologists work together. Wilhelm Walgenbach has got lots of experience in developing outdoor teaching and in videotaping interactive processes in classes and groups of children.
Ø
The Hungarian Group, directed by Prof. Julianna Szendrei, includes approx. 15 researchers in
Didactics of Mathematics belonging to 5 Hungarian universities and institutions. These include primary and secondary schools, in-service and pre-service teachers training and a scientific research institute. The group consists of teachers of all educational levels of Hungary. Members of this group perform significant work in the János Bolyai Mathematical Society and maintain close co-operation with the Hungarian Academy of Sciences.
The group can contribute experiences in:
1. Empirical research in co-operation with teachers (including videotaping of teaching sessions);
2. Introduction to and development of theoretical frameworks and methodological tools for developing teaching units and their evaluation.
The efforts in the framework of the project described in this proposal meet optimally with current activities of the Hungarian education to generally renew national curricula. Members of the project group actively participate in these efforts. The project gives an excellent opportunity to undertake an international test and to compare curricula in an international field and against other’s experiences.
Ø
In co-operation with Pearla Nesher, who will be responsible for the Israeli group, Beba
Sternberg and Ilana Arnon from the Center for Educational Technology (CET) will organize the
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empirical study. CET is a non-profit institution that specializes in writing curriculum materials and disseminating them among teachers.
Beba Sternberg and Ilana Arnon both are experts in performing experiments with videotaping and making a qualitative analysis. Sternberg has performed several video studies with children working in a computerized environment.
Their studies with Video involve videotaping and analyzing samples of classroom lessons and of interviews with students, teachers or with educators. In each study they usually concentrate on a specific issue, for instance: “A computerized mathematical class – proceedings for a math teacher,” “Discussions in mathematics classrooms,” “From arithmetic to algebra: A model for working with teachers on implementation of guided inquiry in pre-algebra classes,” “’Time is always here’ – a case study of bridging modeling to algebra.”
From these experiences it became evident that video enables analysing from multiple perspectives, allows different analyses of an issue and analyses of varied issues by several researches (not necessarily in parallel), integrates qualitative and quantitative information, and encourages communication about the data and about the researching results.
Ø
The Italian group around Ferdinando Arzarello, Ornella Robutti and Mariolina Bartolini Bussi represents special competence in observing and analysing processes of interaction, among students and between students and teacher as concerns the production of metaphors, and student-tool interactions as concerns the instrumental genesis.
In previous research small group activities, whole class discussions (Bartolini Bussi 1996), and teacher’s institutionalisation of knowledge has been analysed, using video and audio recording of the lessons as well as students’ written protocols. Particular attention has been paid at the analysis of gestures, words and rhythms that are part of the social construction of knowledge
(Arzarello 2000, Radford 2000, Radford 2002, Nemirovsky, Tierney, and Wright 1998; Roth and
Lawless 2002a).
The here developed methodology represents an innovation in the usual teaching practices in the school: in fact, generally the focus of teachers is on the products, not on pupils’ processes, which may be a stumbling block for a friendly teaching of Science and specifically of
Mathematics.
Ø
The content of education in Lithuanian comprehensive schools is realized in a number of disciplines, so the learners have to acquire notions and regulations referring to one and the same phenomenon discussed in lessons of different disciplines. Science classes also deal with different aspects of a certain phenomenon employing the necessary means of expression and terminology. Teachers are expected to realise the complex content in a harmonious system, disclosing the interactional relationships within the discussed phenomenon. With this aim in view, the teaching materials are rearranged and put into a system, and the teaching principle based on the methods is called an interdisciplinary relationship.
Nowadays, the understanding of interdisciplinary relationships is determined by holistic pedagogy, whose representatives claim that everything exists in interrelation and interaction and that the principal mission of education is development of spirituality. The content of teaching is not a storehouse of disciplines and knowledge but a system of existential meanings which learners are supposed to find out, understand, and interpret under the guidance of their teachers. Thus, educational practice lays great emphasis on the principle of interdisciplinary integral relationships, whose purpose is to form an integral outlook of the world in the learner.
The formation of the outlook is based not only on the content of the studied disciplines but also on the universal programmes ethics, civility, ecology, etc. offering socio-cultural integration.
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Lithuania’s education experts and subject teachers are greatly interested in this kind of integration implemented in three levels: inner, interdisciplinary, and socio-cultural.
Interdisciplinary integrational relationships are a new teaching principle, being already implemented in primary schools with an integrated science subjects course, which is continued in the fifth and sixth forms. With the purpose of retaining the introduced integral science subjects outlook, the seventh-twelfth form subjects content calls for the discussion of the theoretical and practical aspects of integral relationships.
From an educological point of view, in dealing with interdisciplinary integral relationships in the reformed Lithuanian comprehensive school, the following themes should deserve the researcher’s attention:
1. Application of interdisciplinary integral relationships in teaching physics in comprehensive secondary schools.
2. Preconditions of interdisciplinary integral relationships in the content of science school disciplines.
3. Socio-cultural integration in the school science subjects development on the basis of methods and teaching content.
4. Preparation of study programmes and teachers for the integrated studies of science subjects in schools.
The research findings in the above-mentioned fields could be of great importance to educologists both in Lithuania and abroad, who deal with integration in teaching practice, as well as school teachers, pedagogical university and college instructors, writers and publishers of new teaching aids, such as textbooks, workbooks, etc.
Ø
The Slovenian group comprises of two researchers in Didactics of Mathematics working at two
Slovenian universities: Vlasta Kokol-Voljc at the University of Maribor and Zlatan Magajna at the University of Ljubljana. They are located at the two most important Faculties of Education responsible for mathematics teachers education in Slovenia. These faculties in Ljubljana and
Maribor organise pre- and in-service mathematics teachers training for mathematics teachers on all levels of education. Both researchers are in contact with other researchers and authorities (Ministry of education) involved in teacher education in Slovenia as well as with mathematics teachers.
The group is, in particular, competent in videotaping teaching sequences and in analysing empirical results in the frame of constructivists concept development theory. For the project’s teaching unit on “Generalisation in Science,” a co-operation with teachers and with the teachers coordination institute “Zavod za solstvo Republike Slovenije” (National Institute of Education ) is prepared.
Ø
The Spanish Group, directed by Dr. Marianna Bosch, includes 12 researchers in Didactics of
Mathematics belonging to 7 Spanish universities and working in two main institutions: preservice teachers training and mathematics teaching at secondary school and university levels.
The group is therefore in close contact with teachers of all educational levels and of different regions of Spain.
Based on these experiences, the group will organise an empirical research project on
“Generalisation in Science” in co-operation with teachers.
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Ø
The Swedish group, directed by Dr. Christer Bergsten, includes four researchers in the didactics of mathematics at two universities, Linköpings universitet in the south of Sweden, and
Luleå tekniska universitet in the north. By being involved in teacher education for a long time the group is in close contact with teachers of all educational levels in Sweden. Two members are engaged as supervisors at the Swedish National Graduate School in Mathematics
Education with its network of researchers and doctoral students. Members of the group are also involved in the renewal of the mathematics education curriculum and practices taking place in
Sweden’s compulsory and upper secondary school at present, initiated by the government through “Matematikdelegationen” (see www.matematikdelegationen.gov.se
). A key issue in the development of this reform program is to increase the joy of learning mathematics as well as the general interest in mathematics and science.
The Swedish group is best prepared to conduct, in co-operation with teachers, the teaching unit and its video study (including methodology development).
In the group, Eva Riesbeck is well experienced in class room video studies. The discrepancy between metaphors used for describing practice and the practice itself (Wyndhamn, Riesbeck, and Schoultz 2000) being one important study outcome with importance for the development of the present project. Magnus Österholm is also experienced in the analysis of video tapes, with a focus on learning mathematics from reading mathematical texts (Österholm 2003).
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In the coordinating two person group Dr. habil. Michael Hoffmann is primarily interested in the conceptual questions of grounding mathematics education, the questions of how semiotics could be applied to research in mathematics and science education and in the history of philosophical thinking. Most recent publications are concerned with the role representations play in learning processes (“diagrammatic reasoning”, Hoffmann 2001b, Hoffmann 2003b,
Hoffmann 2003d, Hoffmann 2003e), with the question how hypotheses can be created in learning processes and in qualitative research (Hoffmann 1999; Hoffmann 2000; Hoffmann
2001c), with semiotics in general (Hoffmann 2003c, Hoffmann 2001a), and with the concept of generalisation (Hoffmann and Plöger 2000; Hoffmann 2003a).
Dr. Falk Seeger is qualified in video analysis, semiotics, and in educational psychology. Since years, he is internationally renowned as a proponent of cultural-historical theory in the field of education and of its linkage with semiotics (cf. Seeger et al. 1998, Seeger 2000, Seeger 2002,
Seeger 2003). He has worked also about the educational relevance of Davydov’s theory of generalisation (Seeger 1989). Within the project consortium, there exists already long-term cooperation with the groups from Austria (2.T) and from Frankfurt, Germany (6.T).
Ø
Willi Dörfler, director of the Klagenfurt group, since many years has investigated processes of generalisation in mathematics learning. A main outcome of this is a model for generalising in the learning process which emphasizes the role of student actions and their symbolic and diagrammatic presentations. In a way, this research tries to merge the strengths of ideas of
Piaget (like reflective abstraction) with semiotic approaches like that of Peirce (diagrammatic thinking; cf. 1.T). The main features of this work can be seen for instance in the papers: Dörfler
1991, Dörfler 2000, and Dörfler 2002.
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Ø
During the last 2 years, a group of 5 researchers from the Institute of Mathematics and
Informatics and the Institute of Mechanics of the Bulgarian Academy of sciences chaired by
Prof. Dr. Habil. Sava Grozdev studies the potential of students as a function of their abilities.
This group has developed a theory of declarative and algorithmic knowledge and has modelled the speed of problem solving. Using some basic notions from mechanics, Prof. Grozdev proposed a model for problem solving (Grozdev 2002b). He has studied the organisation and self-organisation of knowledge, abilities, and reflection in learning from the point of view of
Synergetics (Grozdev 2002c). Also, he has developed a mathematical model of the learning process and has applied it in the evaluation of the perception level (Grozdev 2002a). Some of the theoretical results concerning the interdisciplinary approach to both teaching and learning processes have been applied during the preparation of the Bulgarian students for the
International math Olympiads. Perhaps, having in mind that Prof. Grozdev is the scientific leader and main trainer of the team, this could be also one of the reasons for the continuing success of the Bulgarian school students teams at the International Mathematics Olympiads, culminating with the success at the last International Olympiad in Japan, 2003.
In addition, an educational model was designed jointly by researchers and educators from the
Faculty of Mathematics and Informatics (FMI), Sofia University, and the Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, and has been experimented since 1979 in the
Bulgarian school system. In this experiment the curriculum has been changed so as to make the use of computers a natural part of the teaching/learning process. After the conclusion of the project, the outcomes were widely applied within the school sub-system of so called
Mathematics and Science Schools in the country. This model is in harmony with the idea that the computer revolution consists in the way we think and in the way we express what we think
(Sussman 1999). This has already had an impact on the way we teach mathematics, science, art, music and literature. These domains deal with symbols, images, transformations and operations – thus the modelling of phenomena in each of them become natural within appropriate computer environments, purposefully developed to facilitate experimentation, hypothesis generation, testing and open-ended exploration. For example, one can look at the
Bulgarian “Elica” system, developed under the leadership of Assoc. Prof. Dr. Bojidar Sendov from FMI, which is now distributed in the USA ( http://www.elica.net
). Such environments are called microworlds . Evgenia Sendova has been involved in this project with developing teaching materials and Logo microworlds tuned to various knowledge domains while retaining the full programmability (Sendova 2001). In these exploratory microworlds, it is easy to experiment with ideas to gain more insight into the problem being modelled, thus adding an “ you experiment – you invent” fourth part to the well known saying “ You hear – you forget, you see – you remember, you do – you understand .” Our experience shows that the formalisation of a certain idea in terms of a programme may bring out further insights, proving a real understanding, which in turn provides for a new formalisation and new theory. In making problems concrete, deciding what is essential and what is not, and moving knowledge and understanding from being implicit to being explicit, problems become objects that facilitate thinking about them. As
Hofstadter 1985 states, pattern perception, exploration, and generalisation are the crux of creativity, and one can come to an understanding of these fundamental cognitive processes only by modelling them in the most carefully designed and restricted microdomains .
Ø
For many years now, mathematics teaching and learning activities have been studied in France within the theoretical framework of Anthropological Theory of Didactics (ATD) as created by
Yves Chevallard. In this approach, two main aspects are considered. The first one regards to what is learnt and taught and is modelled in terms of mathematical praxeologies . The second one concerns learning and teaching activities as such and is modelled in terms of didactic praxeologies . The concept of praxeology allows one to describe and analyse the gist of human
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activity, be it mathematical or not. More precisely, a praxeology consists of four main components: a number of types of tasks , that is what one has to do (e.g. solve quadratic equations, teach Pythagoras’ theorem, etc.); with each type of tasks, a technique which provides a way to achieve tasks of the given type (e.g. a way to solve effectively quadratic equations); for every technique, a technology , that is a “discourse
∗
” able to justify, explain, and
“generate” the technique; and finally, a theory , that is a discourse that plays the same role towards technology that technology does towards technique, and makes it possible to interpret techniques and set up technological descriptions and proofs.
This theoretical framework provides a methodology for the analysis and development of teaching and learning activities (Artaud and Chevallard 2002, Artaud 1998). A product of fundamental research in mathematics education, it has been developed and used in pre- and in-service teachers training programs, especially for the observation and assessment of classroom practices (Artaud 2003). When used to describe and to analyse mathematical activities, the notion of praxeology constitutes an appropriate epistemological model that can help to analyse “generalisation” in mathematics, including the constitution of technological environments, reorganisation of theories and integration of more powerful forms of knowledge.
Based on previous research on the Anthropological Theory of Didactics (ATD), the French group – directed by Dr. Michele Artaud – will represent, together with the Spanish group (13.T), this theoretical approach with the project consortium.
Ø
Prof. Götz Krummheuer, the director of the Frankfurt group, developed an interactionistic theory of mathematics learning, which is based on the concept of “collective argumentation”
(Krummheuer 1995, Krummheuer 2000a, Krummheuer 2000c, Krummheuer 2000b). His approach refers to micro-sociological approaches, such as ethnomethodology and symbolic interactionism. With regard to the aspects of argumentation there is also a closer relation to semiotics (cf. 1.T) and to approaches of the use and function of inscriptions in mathematical classroom interaction. His work is empirically oriented, videotaping everyday mathematics classroom situations and analyzing them by means of the analysis of interaction and the analysis of argumentation. Krummheuer uses these analytical tools in a variety of seminars of student and teacher education in mathematics (cf. Krummheuer 1999, Krummheuer and Naujok
1999, Krummheuer 2002).
Ø
The second German group is directed by Priv. Doz. Dr. Wilhelm Walgenbach who is Senior
Researcher at the Leibniz-Institute for Science Education (IPN) at the University of Kiel,
Lecturer for General Didactics at the University of Hamburg, Department of Education, and
Initiator and Organizer of the i nterdisciplinary and intercultural network “Interdisciplinary Self-
System Design (INSYDE) e.V.” The theoretical approach represented by INSYDE is centred around the programs Synthesis of Educational theory (based on the German Idealism), Activity theory (Vygotsky, Leontjev, Davydov, Engeström), Systems Theory, and Aesthetics/Art. The theoretical ideas find applications in field of science education which have to do with a concept of nature, natural resources and forces informed by an evolutionary understanding of physical nature and of humans situated within that physical nature. The works include theoretical foundations, educational experiments, empirical research and the organisation of an interdisciplinary and intercultural research and development network.
For further informations about INSYDE e.V. see:
∗
The meaning of « discourse » here is akin to Descartes’ use of the word in his Discourse on method
(1637).
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http://www.ipn.uni-kiel.de/persons/walgenbach.htm
and http://www.systembildung.de/
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Prof. Pearla Nesher, the director of the Israeli group, will continuing her well-documented theoretical research on semiotic aspects involved in the transition from natural language to formal, scientific language and the use of models in the teaching of mathematics, in particular solving word problems (Nesher, Greeno, and Riley 1982b; Nesher 1980; Nesher 1982a; Nesher
1988; Nesher 1989; Nesher and Hershkovitz 1994; Nesher and Katriel 1977; Nesher and
Sukenik 1991). In discussing semiotics from this point of view, the group expects, in particular, new insights concerning the role of language and models in the teaching of science. Other aspects that were emphasized by Nesher's and Sternberg's research in recent years were computerized environments serving as interactive models in the teaching of Algebra and Word
Problems (Hershkovitz and Nesher 1996; Hershkovitz, Nesher, and Yerushalmy 1990;
Hershkovitz and Nesher 1997; Nesher and Hershkovitz 1994).
Ø
Regarding theoretical approaches, the Italian group is best qualified for describing and analysing:
1. the relationship between intuitive, concrete and formal, abstract aspects of mathematical concepts.
The former aspects are codified in various analogic forms which the subjects reconstruct on the basis of perceptual, anticipatory and numerical elaborations (e. g. Dehaene 1997, Berthoz
1997, Butterworth 1999). The latter aspects are codified into symbolical languages that subjects manipulate according to appropriate syntactic rules (e.g. Sfard 1991). Such fertile relationship between the two is at the basis of a mathematical understanding that is not a pure adaptation to rules (Cobb, Yackel, and Wood 1992).
2. the students’ mental dynamics in this double polarity (intuitive/formal).
With regard to this point, the group represents in particular the competence to analyse the ways students usually try to overcome the epistemological and cognitive discontinuity in the passage from commensurability to incommensurability. Such mental dynamics reveal a process of conceptualisation marked by different stages, that can be interpreted using complementary theoretical frameworks. Namely, the embodied cognition approach (Lakoff and Núñez 2000,
Sinclair and Schiralli 2003, Arzarello and Robutti 2003) and the instrumental approach
(Rabardel and Vérillon 1995, Artigue 2001, Lagrange 2003) in the use of artefacts.
Taking these points together, the approach represented by the Italian group allows, first, to describe the students' mental processes while exploring or constructing mathematical objects, second, to produce conjectures, models and justifications for describing these activities, and third, to interpret them within the theoretical frameworks mentioned above.
Ø
The Spanish group, directed by Dr. Marianna Bosch, has been working as a research group for more than 5 years within the theoretical framework of Anthropological Theory of Didactics
(ATD), in close relation with the French group (cf. 5.T) headed by Yves Chevallard and Michèle
Artaud at the IUFM d’Aix-Marseille (Chevallard, Bosch, and Gascón 1997, Bosch and
Chevallard 1999).
Within the proposed project “Generalisation in Science,” the group will develop an introduction to the anthropological approach as a theoretical framework and as a methodological tool for developing teaching units and their evaluation (Bosch and Gascón 2002, Bosch, Espinoza, and
Gascón 2003).
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For the time being, the group’s main research project centres on the integration of the main mathematical praxeologies that make up the current Spanish secondary curriculum. Roughly speaking, the problem can be formulated thus: How can one design didactic praxeologies that facilitate the integration of the mathematical curriculum, both between topics and areas at one educational level and between different educational levels? And, more particularly, which specific characteristics should a didactic organization have in order to allow one to resume study of topics previously studied, even at prior educational stages, and to question, develop and integrate them into larger and more complex mathematical praxeologies?
In this context, we postulate that generalization activities in mathematics relate to the process of integrating the practical and theoretical tools that mathematical activity builds up in order to provide answers to questions or sets of questions. It therefore seems better to approach these activities through a more extensive notion of study – pertaining to the concept of didactic praxeology – than the one traditionally used in classical research on mathematical problem solving.
Ø
The Swedish group represents within the consortium theoretical frameworks with regard to
• the conception of artefacts in mathematics education, including semiotic/representational aspects of mathematics and computer based work
• the relation between intuitive and formal aspects of understanding, learning, and doing mathematics
With his work in research methodology and the role of artifacts in the didactics of mathematics
(e.g. Dorier 2003; Straesser 2001, Straesser 2003; Straesser and Blomhoj 2002), Rudolf
Straesser will contribute to the development of the research methodology and theoretical framework of the project. Christer Bergsten has developed and investigated empirically a theoretical framework for the analysis of the relation between form and content in mathematics, based on the operational/structural categories and a notion of mathematical form related to core ideas within embodied cognition (Bergsten 1990, Bergsten 1999), well apt to contribute to the development of the teaching unit and objectives of the project. Studies in visualisation, algebra, and assessment (Presmeg and Bergsten 1995; Bergsten 2002, Bergsten 2003) also highlight important aspects of the generalisation process in mathematics.
Ø
The project’s web-related activities will be managed by the Hungarian Group. Part of this group is the Computer and Automation Research Institute of the Hungarian Academy of Sciences.
This institute has 40+-years traditions in cutting-edge computer technology research and applications development. It houses the Hungarian Web-Office and runs one of the central “.hu” servers thus having optimal professional prerequisites to perform this part of the project.
Concerning the internet portal of SEE!, the following activities will be performed:
•
Conception and specification of the Web-services and the management of software maintenance after operation has begun (hotfix control, release planning, etc.),
•
Quality management of the Web-service development (which will be carried out by
Virtech Ltd., Bulgaria, cf. 16.W) including progress control, reviews and acceptance of the software deliveries,
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•
Provision of the Web-service by running it on an appropriate server, processor and storage capacity and with a reasonable error recovery service in case of service degradation,
•
On-going site management including also the editorial management of the Web-site contents.
Ø
The project’s web-related activities with respect to the design and development of the internet portal itself will be carried out by Virtech Ltd., Bulgaria (standing for Virtual Technologies).
Virtech Ltd. is a SME (Small or Medium Sized Enterprise) created by the Faculty of
Mathematics and Informatics, Sofia University, on the base of the science incubators under the motto “Bringing the scientific research into practice.” Virtech participates successfully in a number of European and other international projects ( http://www.virtech-bg.com
) and has excellent professional expertise and reputation in the areas of Flexible Working Training and
Support, Information Systems Development, Web Design and Maintenance, Business on the
Internet Support, Multimedia Software, and WWW Based Training. Recently, in the frames of the international project “WWW in Education,” Virtech developed and now maintains a webportal called Web Teacher Database (WTD), where researchers, educators, teachers, and students from different countries can store their products and search for interesting materials with regards to the project themes ( http://www.virtech-bg.com/demos/wtd/ ).
Ø
In the coordinating group, Michael Hoffmann represents, first of all, networks concerning semiotics: He is the founder and recent director of an internationally oriented working group
“Semiotik in der Mathematikdidaktik” (Semiotics in Mathematics Education) within the German
Society of Mathematics Education (GDM), and he is member of the Advisory Committee of the
German Society for Semiotic DGS – Deutsche Gesellschaft für Semiotik e.V.
(since 1999), responsible for the field of mathematics education. He is member of The American
Philosophical Association (APA), of the Gesellschaft für Philosophie in Deutschland e.V.
(GPhD), the Gesellschaft für Analytische Philosophie e.V. (GAP), the International Association for Semiotic Studies – Association Internationale de la Sémiotique (IASS-AIS), and of the
Deutsche Gesellschaft für Erziehungswissenschaften (DGfE). There are contacts to the IPN,
Kiel, and to the Max Planck Institute for Human Development, Berlin.
Falk Seeger is a member of the German Society for Mathematics Educ ation (GDM –
Gesellschaft für Didaktik der Mathematik) – and also a member of its working Group Semiotik in der Mathematik-Didaktik (Semiotics in Math Education). He is a member of the International
Society for Cultural an Activity Research (ISCAR) which is a multinational group of researchers in the tradition of the cultural-historical school of psychology and activity theory. He is affiliated with the AERA (American Educational Research Association) and EARLI (European
Association for Research in Learning and Instruction). He is also a frequent visitor of the international conferences organized each year by the PME-group (Psychology of Mathematics
Education).
Ø
The research group on mathematics education at the University of Klagenfurt is a centre of excellence in its field and constitutes the largest unit of this sort in Austria. As such it is widely connected to other institutions in Europe and worldwide. Within Austria, it is mainly part of
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projects for teacher in-service training (PFL) and teacher professionalisation (IMST). Research co-operations exist among others with groups in Bielefeld, Darmstadt, Nashville, Stockholm.
Members of the group have been and are active as editors of international journals and book series and as officers of professional organizations.
Ø
The members of the Bulgarian group represent the following research, teaching, and education networks:
•
The CIST, FMI, and the Bulgarian Academy of Science (Institute for Mathematics and
Informatics – IMI, and Institute for Mechanics) represent a strong national research network of scientists in Mathematics and Mathematics education, and form an influential core group within the frames of the Union of Bulgarian Mathematicians
•
The Union of Bulgarian Mathematicians, which has branches in all country regions and clubs in literally all towns with more than 10,000 inhabitants in the country. In practice, all Mathematics teachers in the country, all university teachers and researchers in
Mathematics, and all the state experts, inspectors, and authorities in Mathematics education are members of the Union and respect its decisions. Under its auspices the
Bulgarian Mathematics educators and educational authorities organise and conduct a number of national and international competitions, the systems of national and
International Olympiads in Mathematics and Informatics
( http://www.math.bas.bg/bcmi/ ). UMB supports methodologically a network of more than 40 specialised Mathematics and Science profile schools, and more than 300 special Mathematics and Science classes in other schools throughout the country, which have very high ranking and special advanced curricula in Mathematics and
Science education.
•
The International Federation for Information Processing (IFIP), especially its Technical
Committee 3 (TC3) – “Education”, and the UNESCO educational network
Ø
The members of the French group are involved in the following national and international research and professional networks:
§
European Society for Research in Mathematics Education ( www.erme.uniosnabrueck.de/ )
§ Association pour la Recherche en Didactique des Mathématiques ( www.ardm -asso.fr
)
§ Unité Mixte de Recherche (UMR) ADEF (the web site is under construction)
§ Équipe de mathématiques de l’IUFM d’Aix-Marseille ( www.aixmrs.iufm.fr/formations/filieres/mat/index.html
)
Ø
Götz Krummheuer from the German group in Frankfurt is
§ Constant Member of Thematic Group “Social interaction in mathematical learning situations” of the European Society for Research in Mathematics Education (ERME)
§ Constant Member of Working Group “Interpretative classroom research in mathematics education” of the German Society of Mathematics Education (GDM)
In addition, he is involved in long-term scientific cooperation with:
§ Terry Wood, Purdue University, West-Lafayette, In (USA)
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§ David Clarke, University of Melbourne, Melbourne (Australia)
§ Patty Barber; Institute of Education, University of London (UK)
Ø
The group from Kiel around Wilhelm Walgenbach represents due to its location at the Leibniz-
Institute for Science Education (IPN) lots of national and international projects and networks in the field of science education. The IPN is a member of the Wissenschaftsgemeinschaft
Gottfried Wilhelm Leibniz, and it is closely affiliated to the University of Kiel/Germany.
Ø
The members of the Hungarian Group are involved in national and international research and in professional networks as:
•
János Bolyai Mathematical Society ( www.bolyai.hu
)
•
CIEAEM, Commission Internationale pour l'Étude et l'Améliorisation de l'Enseignement des Mathématiques (International Commission for the Study and Improvement of
Mathematics Education)
•
ERME, European Society for Research in Mathematics Education ( www.erme.uniosnabrueck.de
)
Ø
The Center for Educational Technology (CET) which will organize the Israeli empirical study is located at a set of important cutting points between different networks. By its specialisation in writing curriculum materials, CET has experiences, first of all, in disseminating concrete suggestions and theoretical approaches among teachers. Of special relevance for our project is the group’s experience in providing these materials on a special website (see http://www.cet.ac.il).
In addition, CET has a connection on a regular basis with Haifa University, and usually initiates connections with the Tel-Aviv University, the Weizmann Institute, and the Technion, each of them has a net of electronical connections with teachers who come regularly to in-service meetings.
The group in Haifa (which works closely with the CET) is a part of the govermnental Center for
Science Teaching. The center at Haifa University also publishes a math journal for all school teachers in mamtematics that appears 4 times a year. The Math Center at Haifa University organizes once a year a math teachers conference for all levels of schooling.
Ø
The group’s particular attention will be given to the dissemination of the new methodology within the community of the Italian teachers of mathematics and physics at secondary school level.
For this aim, Prof. Ferdinando Arzarello, the person in charge in Turin, has many opportunities.
In fact he is currently in charge of scientific duties: President of the Italian Committee for
Mathematics Education (CIIM), Coordinator for the National Curriculum in Mathematics on behalf of CIIM (UMI), Head of the Teacher Training School in Piemonte. As such, he and his team have many official contacts and interactions with in-service and pre-service teachers, both at the National and at a local level. Moreover, F. Arzarello can possibly disseminate the results of this research through e-learning, within the official network of the Italian Ministry of
Education.
The main network connections of our group are:
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§ CINECA, which is the central network of the Italian Ministry of Education, to which all
Italian schools are connected (http://www.cineca.it/),
§ the Site of UMI (Italian Mathematical Society), to which are connected most of math researchers and teachers in Italy,
§ the Italian Teacher Training Schools (Scuola di Specializzazione per la Formazione degli Insegnanti), where the future teachers are trained.
Ø
The members of the Lithuanian group are engaged in the following national networks:
§ Vilnius Pedagogical University,
§ Secondary schools of Lithuania
§ Shiauliai University.
Ø
The members of the Slovenian group are involved in the following national and international networks:
§
Drustvo matematikov, fizikov in astronomov Republike Slovenije (DMFA, Mathematics,
Physics and Astronomy Society of Slovenia)
§ Skupina Didaktikov Matematike Slovenije (Group of Slovenian Researchers in
Mathematics Education)
§ Gesellschaft für Didaktik der Mathematik (GDM)
§ European Society for Research in Mathematics Education (ERME)
§ National Council of Teachers of Mathematics (NCTM)
Ø
The members of the Spanish group are involved in the national and international research and professional networks mentioned below:
1. Inter-university Seminar of Research in Didactics of Mathematics SIIDM
( www.ugr.es/local/jgodino/siidm/): assembling a group of 30 Spanish researchers in
Didactics of Mathematics
2. Spanish Society for Research in Mathematics Education ( www.ugr.es/local/seiem )
3. Spanish Federation of Societies of Mathematics Teachers ( www.fespm.es.org
)
4. Spanish Royal Society of Mathematics ( www.rsme.es
)
5. Association pour la Recherche en Didactique des Mathématiques ( www.ardm -asso.fr
)
6. European Society for Research in Mathematics Education ( www.erme.uniosnabrueck.de/ )
Ø
Members of the Swedish group are engaged in the following national and international research and professional networks:
•
Swedish Society for Research in Mathematics Education ( www.mai.liu.se/SMDF )
•
National Graduate School of Mathematics Education ( www.maths.lth.se/Forskarskolan/ )
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•
European Society for Research in Mathematics Education ( www.erme.uniosnabrueck.de
)
•
Gesellschaft für Didaktik der Mathematik (GDM; www.rsem.es
)
•
Association pour la Recherche en Didactique des Mathématiques ( www.ardm -asso.fr
)
Ø
The extent of experience offered by the provider of the technical infrastructure, the Beverungen
Company, Paderborn, can be seen from a long list of recent references, from which we render
10 here to document their regional, national and international experience:
§
Siemens AG Paderborn (Computer Technology and Software producer): Providing a
Complete Video Studio BetaCam SP
§ University of Bielefeld (24.000 students, 320.000 inhabitants): Digital video technology for Audiovisual and Media Centre with; giant projector for largest auditorium seating
2.000, media technology for 12 smaller lecture halls
§ Herzzentrum Bad Oeynhausen (North-Rhine-Westphalia’s largest and most renowned centre for cardiovascular conditions and heart transplants): Media technology for training centre including a large-scale projector and video technology for surgery theatres
§
Bertelsmann, Gütersloh (seat of world’s largest media corporation): Media and PC presentation technology
§ Bethel, Bielefeld (Europe’s largest Clinical Centre with a staff of 9.000): Complete video studio, emergency call system, linkage of video and audio signals for distance supervision of three large parking docks
§ Miele, Gütersloh (seat of Europe’s prime producer of kitchen appliances): Video studio containing BetaCam SP, video information system linking separate corporation facilities.
§ National Museum, Barcelona (Catalonia, Spain): Large-scale image projector driven by hard disk recorders and media control
§
National Museum, Brescia (Italy): Large-scale image projector driven by hard disk recorders and media control
§ National Museum, Split (Croatia): Large-scale image projector driven by hard disk recorders and media control
§ E.on Nuclear Power Plant, Würgassen (Germany): Modern media technology (Info centre for control by media technology).
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After the overall structure of the project has been agreed upon by the participant project groups in the respective countries, all organisational, managerial matters and decisions as regards the realization of the case study have to be taken care of by the local groups. This includes preparing the plan for the teaching unit, recording the classroom sessions and transcribing them into English.
As regards the sequence of conferences, the responsibility will be shared by the local organising committee and the coordinating committee in Bielefeld. It would be most effective if the preparation of the conferences could be monitored by a fulltime networker. This person would translate the general outline of theme and organisation of the conference onto the local conditions, she or he could would be in time at the disposal of the local organizing committee thus accumulating wisdom with how those meetings have to be run.
As regards the continuing tasks of organising, managing and monitoring the overall progress of the project, it will rest within the responsibility of the Bielefeld team.
Beneath the usual organisational and managerial tasks, the coordinating committee in Bielefeld will have to take care of four main tasks:
§ the task to select and prepare material for inclusion in the public part of the database containing also video clips and texts from classroom episode sticking out as best practices
§ the task to moderate communication between the different national sites about what seem to be key concepts in their case studies
§ the task to look for further exemplary teaching units and promote their elaboration
§ the task to maintain continuity over the total period of the project through an already existing mailing list (mailto:eu-science@lists.uni-bielefeld.de), discussion, papers and other communication.
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The central idea of the project’s workplan is to combine two complementary activities: concentration and dissemination , exemplariness and generalisation. On the one hand, we will bring together in a series of conferences the most relevant positions which describe both in theory and in practice / methodology the “state of the art” in science and mathematics education. These positions will not be presented one after the other, but they will be compared in a continuous competition with regard to their applicability at a variety of questions arising from the implementation and analysis of the concrete teaching unit we want to conduct in a set of European classrooms. At the same time, all these positions will be integrated in an ongoing discussion over the whole series of conferences, so that permanent evaluation of their applicability is possible, and substantial developments of theoretical approaches and reflections on practice can be expected. Concentrating theory and practice in this way should set free enough energy to promote the project’s objectives.
On the other hand, we want to build up an infrastructure that is supposed, firstly, to disseminate the project’s results and generated innovations, and secondly, that should become a basis for exchange regarding Science Education in a most general and long-term sense. This infrastructure has three central parts: First, we want to advertise a full-time position for a scientist whose main task will be to disseminate the project’s idea and reports about its results and observations at conferences and on networks as extensive as possible. For doing this, this scientist will keep in intensive contact with the participating groups and will visit them at least once. Second, we plan to implement and to maintain the openly accessible internet-portal
“Science Education across Europe” (SEE!). Finally, all participants will be engaged in networking. As mentioned above in B.4 Consortium , the participating groups represent already a great variety of existing networks, and have influence at various governmental and scientific institutions. Thus, one of their main tasks will be to link these connections with the proposed new network “Science Education across Europe” (SEE!), and to integrate here what already exists in the field.
The general structure of our workplan as presented in greatest possible clarity in the enclosed
Gantt-Diagram “Science Education across Europe (SEE!) – Workplan” (cf. the next two pages) mirrors this intertwining of concentration and dissemination. The pillars of the diagram – and of the project as well – are a series of nine conferences (C-1 to C-9) which rest on two central cooperation activities – web presentation and networking (workpackages WP-27, WP-28) – which accompany the sequence of activities described in the main body of the diagram (WP-2 to WP-
24) in an ongoing process.
All activities are mediated and discussed during these conferences, whose additional function is to supervise mutually what happens within the participating groups. Thus, there will be a permanent self-control regarding the objectives formulated in this proposal. The only significant risk for the project might be that groups stop their participation due to reasons from outside the project. However, intended as a growing and networks integrating activity, the project as a whole should be able to substitute those participants by new ones.
Describing in greater detail the work planned, we have to distinguish at first management activities and co-ordination activities (cf. also the enclosed Workpackage description forms).
There are only three genuine management activities :
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1. advertising the networker position (4 months before the proposed starting point of the project), and appointing the best qualified candidate for this position (WP-1, conducted by 1.C);
2. some of the activities around the Internet portal “Science Education across Europe”
(SEE!). The Computer and Automation Research Institute of the Hungarian Academy of
Sciences (8.W) will – in co-operation with all participants (co-ordination activity!) define the web-portal requirements (WP-25) and co-ordinate the content management (WP-
27). Genuine management activities are monitoring the quality of the portal design and development and hosting and maintaining the web-portal (part of WP-27. As a part of our co-ordination activities again, Virtech Ltd. – 16.W – will design and develop the webportal, according to the agreed specifications and requirements, WP-26, and will care for technical maintenance, WP-27);
3. the definition (by 1.C) of the technical infrastructure that is in need for videotaping classroom activities and for preparing DVD records for their further analysis (WP-29).
The much greater part of what the project plans to do can be counted as co-ordination activities . Here, the series of nine conferences plays the central role for initiating networking between professional science educators across the boundaries between different cultural and educational traditions within the enlarging EU and associated countries. As we have argued already above, the guiding idea of our project proposal is that networking needs a motivation which we want to provide by focusing on a concrete project for improving the “appeal” of science education at school. Our project concentrates, with regard to that, on a teaching unit on
“generalisation” as a paradigm for curricula that emphasise the most general features of scientific thinking, as described above (see B.1 Objectives ).
Thus, the genuine centre of the project’s activities is a teaching unit (c. six classroom hours;
WP-15). The first year of the project’s proposed time-span, one can say in short, serves for preparing this teaching unit, and the third year for analysing and interpreting it. For the teaching unit itself, we have reserved the second year, because the national empirical researchers and the teachers of the chosen classes need a certain freedom to decide when this additional teaching unit can be integrated at best in the very different existing curricula.
To describe now the sequence of those workpackages that form in a step-by-step order the main body of the proposed co-ordination activities (WP-2 to WP-24), we will begin by distinguishing the necessary preparation steps for our central teaching unit (WP-2 to WP-14).
The project is supposed to start with two introductory conferences (WP-5, WP-6). Their first task is to build up a “co-operation climate” between participating scientists and teachers (we expect during the project’s whole time-span an average number of c. 50 persons).
The first conference will introduce and discuss the general scheme of what is planned and, in particular, it will set the framework by preparing the necessary fundaments in philosophy of science and semiotics with regard both to the concept of “generalisation” and to the representational means for generalising theories (“diagrammatic reasoning”). A further important theme will be discussing the question how the planned teaching unit and the whole project can contribute to overcome “the split between the two cultures” of science and humanities (WP-5 = C-1).
Due to the fact that the planned teaching unit most probably will be situated in the mathematics classroom – although that is not necessary –, and due to the fact that the project participants work in rather different theoretical contexts, there should be an intensive preparation concerning primarily the philosophical perspective of the project. The problem of “generalising” scientific theories traditionally is a theme within philosophy of science, but there are also important relations to hot topics in psychology, cognitive science, sociology, etc. Thus, there should be a common effort of the participants to develop an appropriate theoretical framework
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for the project that, afterwards, has also to be shared with the teachers who are supposed to conduct the teaching unit.
During this first conference, the Beverungen Communications GmbH, Paderborn, Germany
(15.TI), will introduce also all participants to the technical standard equipment necessary for videotaping the teaching unit (WP-15). So, modifications of the configuration are still possible before the system will be installed eventually at the places of the empirical projects (WP-30).
At this point, we would like to formulate some general remarks concerning the proposed conferences: All our conferences will take place in the participating countries, organised by the respective national groups. The themes of the conferences, however, will be prepared by those groups of participants who are listed under the heading of “Theoretical analysis” in B.4
Consortium . Thus, the specialists in the relevant theoretical and methodological fields will introduce all the others to their research areas. In order to make clear which groups will be responsible for which theme, these preparation activities are put down in the Gantt-Diagram and in the Workpackage description forms as autonomous activities. As a rule, however, we do not request any EU support for these preparation units. At this point, we will profit from the resources of the participants. It will be necessary, however, to invite specialists from all over the world for fields we cannot represent by our own means.
The second conference, to continue our list of co-operation activities, is supposed to discuss, on the one hand, perspectives and problems of curriculum development in general and with regard to the planned teaching unit, and it should also formulate ideas and suggestions for the project’s networking activities (WP-6 = C-2). First of all, we have to prepare here in a joint endeavour what must happen in the next step (WP-7): The several national groups which will conduct the classroom activities (participants 2.E, 3.E, 4.E, 7.E to 14.E) have to develop a concrete plan of how the teaching unit on incommensurability might be integrated in existing curricula of their respective countries. It seems fair to assume that the project’s topic – the discovery of incommensurability within its cultural and philosophical context – is not part of existing curricula in the participating countries. Thus, it is a genuine pedagogical challenge to develop the concrete form of the teaching unit’s general idea on the basis of the best educational practice of the participating countries. To gain deeper insights into cultural and educational differences of the participating nations, and in order to get empirical data for a comparison between different styles of teaching and of learning, the participating groups should have great freedoms concerning the concrete realisation of the project’s general framework.
They will receive shared classroom materials, a standard list of classroom objectives, and a catalogue of evaluation criteria, but remain responsible for the project’s concrete implementation and evaluation.
To support the preparation of the teaching unit, there will be an introduction to the
Anthropological Approach of Didactics (ATD, cf. 5.T, 13.T). A further theme of the conference will be designing and organising the consortium’s network activities and of its internet portal
SEE!.
After curriculum development within the respective empirical research groups (WP-7), a third conference will take place which will reflect on problems and on new perspectives resulting from these activities (WP-8 = C-3). A second point of this conference will be to prepare a press campaign (WP-9) by which the groups from the participating countries are supposed to inform the public on the project and its central ideas. This initiative is part of the recent world wide activities concerning “Public Understanding of Science and Humanities” (PUSH). For preparing this press campaign, a joint discussion again about the project’s objectives and ways to realise them is necessary – as well as continuing the exchange about the relevant theoretical approaches that will accompany the whole series of conferences. Through hinting at the project’s internet-portal SEE!, teachers, students, parents, and other interested persons should be invited to participate in an European communication about science education.
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The forth conference (WP-10), after the press campaign (WP-9), will, on the one hand, reflect on experiences concerning “Public Understanding of Science and Humanities” (PUSH), and it will prepare, on the other, the project’s next important step: To introduce the teachers chosen to conduct the teaching unit in their classes in the project’s objectives and methods, and in technical questions concerning videotaping of classroom activities (WP-11). At the preparing conference, the participating researchers – as far as necessary – have to be introduced firstly in these techniques, quasi in an act of “training the trainers.” For this part of the conference, we plan to hire a professional adviser who will conduct a workshop at the conference.
Up to this conference, the necessary technical infrastructure should already be implemented at the research centres which will conduct the empirical studies (WP-30).
After reflecting on the experiences of teacher instruction (WP-11) at the fifth conference, the essential point at this conference (WP-14) will be an introduction to three important theoretical approaches which are relevant in particularly for conducting the now following teaching unit
(WP-15): The theory of Social Interactionism that highlights, for example, the “negotiation of meaning” as a core idea of socially mediated learning processes, Activity Theory which stresses the relevance of culturally mediated processes of behaviour control, “frames” of social and individual activities, and culture defining sign systems and, finally, the Theory of
Embodiment. Embodiment theory, within the constructivistic approach developed recently by N.
Sinclair, allows an important analysis of the mathematical concepts’ genesis and of the approach to generalisation. It is particularly interesting when used to study pupils while using instruments: in fact it allows a companion approach to the semiotic machinery, which is part of this study.
With regard to this, the conference WP-13 will focus the interaction between the embodied, intuitive side and the conceptual, abstract one in generalisation processes in science and particularly in mathematics. More precisely, starting from the data elaborated in WP-12, it will be developed a theoretical frame suitable for analysing the processes of generalisation. This frame, together with the results got in other WP’s (WP-15, WP-16, WP-17, WP-19, WP-21) will contribute to define scientifically a frame for didactical interventions with the general aim of this project.
The next activity – the heart of the project – is conducting the interdisciplinary teaching unit on the discovery of incommensurability (WP-15). In order to get the greatest possible variety of styles of teaching, learning, and acting in classrooms, specialists in empirical research from different Eastern and Western European countries will organise this teaching unit in three somewhat different classes, respectively. There is no need for trying hard to be
“representative,” for the project’s scope is qualitative comparison, not quantitative. The classroom activities are followed by a test with defined standards but a free formulation of the concrete questions. The hours of classroom work will be videotaped.
After this teaching unit, the project’s final phase of interpreting and analysing will begin.
At the sixth conference (WP-17) central themes will be discussing problems of videotaping classroom activities, methods of transcription, the methodology of qualitative research and of
Grounded Theory, and the theory of argumentation in order to understand how the rationality of communication and interaction will be generated.
The main purpose of this conference will be to prepare the analysis of videotapes conducted in the following WP-18 by each empirical research group. The respective participants are supposed to evaluate what has happened in classrooms. This evaluation should take place on two levels: At the first level, each national subgroup writes an evaluation report in which the following questions are discussed:
§ How successful was teaching with regard to the objectives of our project “Generalisation in Science”?
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§ Which difficulties can be identified, what might be the reasons for these problems?
§ Which kinds of learning processes can be identified?
§ To which previously given knowledge do boys and girls refer back in order to understand the phenomenon of incommensurable lengths?
§ What kinds of creative hypotheses are formulated?
§ What is the role of representational means for understanding, for communicating, and for solving problems?
§ In which way are social interaction, cultural and social backgrounds, the gender problematic, and group dynamical influences relevant for learning processes?
§ What might be a “creative classroom atmosphere”?
§ Do young people have a language for describing what they are doing in mathematics?
§ How do they cope with the duality of natural language and formal language in science?
§ What kinds of argumentative structures can be observed?
§ What is necessary for someone to be convinced by a mathematical proof, how are different kinds of “evidence” treated?
§ How can learning processes be fostered?
§ Does the teaching unit fit to the normal curriculum?
§
At which point the normal curriculum or the teaching unit should be changed in order to get better homogeneity?
§ Are there any effects observable regarding the student’s interest in science?
§ Are there any differences between boys’ and girls’ interest in science?
§ How could science education be improved on the basis of these observations?
In addition to answering these questions, each national subgroup produces a presentation of their results, including parts of the video tapes on DVD and further interesting material. For this presentation, relevant parts of the classroom videotapes have to be transcribed and to translate into English by a native speaker. These presentations should be published as soon as possible on the project’s website “Science Education across Europe” (SEE!), and they will be the starting point for a joint discussion to be held at the project’s seventh conference.
This conference (WP-19 = C-7) will mainly focus on criteria for comparing the various classroom activities. Basis of discussion will be the classroom videotapes, their English transcriptions, and the answers formulated by the empirical research groups to the questions listed above. The possibility of answering these questions demands a methodology which goes beyond the means developed for the great international studies that aimed at quantitative comparison of students’ skills and competencies. Our project’s explicit aim is to do qualitative research which, hopefully, reveals more than a surface analysis of classroom activities. To disseminate methods and theoretical approaches which are necessary for this task will be at the centre of this seventh conference. Our project’s advantage is that comparing only a few hours in quite a lot of rather different classroom situations on the same theme allows a much more intensive comparison between various classroom cultures than usually. The idea is that the obvious differences for themselves should suggest certain methods of interpretation, as
Grounded Theory puts it (cf. Glaser and Strauss 1967, Beck and Jungwirth 1999).
At the conference, all transcripts and videotapes will be exchanged between the participants, so that the local groups, in the project’s next step (WP-20), can conduct the comparative analysis which was prepared by the conference before. The focus of this analysis is on differences between classroom cultures in the participating nations, on conditions and possibilities of
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different teaching strategies and habits of interacting, and on the question what could be learnt from other cultures.
The considerations and results of these discussions form the starting point for the eighth conference (WP-21). Here the project’s intercultural analysis is the main topic. Besides discussing how science education could be improved by comparing different teaching, learning, and communication cultures, there are two further goals: On the one hand, a theoretical and methodological exchange about new directions for developing methods in qualitative research is planned, and on the other hand, the next work package which will be conducted in the respective countries has to be prepared:
In this work package (WP-22), our empirical research groups are supposed to conduct some workshops together with the teachers whose classroom activities were videotaped. The objective here is to answer the question whether the method of reflecting on videotaped teaching can support the development of teachers’ competence to critically assess their own performance, and can thus improve the quality of teaching.
This question, then, will be a first topic of our final conference (WP-23 = C-9). At this conference, all the project’s issues – improving science education by focussing on most general features of scientific thinking, learning from other classroom cultures, networking – will be back on stage. In particular, perspectives of future networking and considering further possibilities of continuing what should have been initiated by our project will be a centre of discussion.
The project in whole will be finished with a final press campaign organised by the groups from the participating countries in order to foster public understanding of science by reporting on the project and its central results (WP-24). At the same time, publications of the project results are planned.
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The Ethnographie of Argumentation
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Bauersfeld, Heinrich:
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Hoffmann, Michael:
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Peirce und das Wechselverhältnis von Abduktion und Vergegenständlichung
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(September 1997)
Nr. 165
Tätigkeitsbericht des Instituts für Didaktik der Mathematik für den Senat der Universität Bielefeld
Berichtszeitraum Juni 1992 bis Juni 1997
(Oktober 1997)
Nr. 166
Meder, Norbert:
Mathematik für die Allgemeinheit.
Kritische Reflexionen aus Anlaß von Hypertext -Lern-

umgebungen
(Januar 1998)
Nr. 167
Winkelmann, Bernard:
Funktionen von Multimedia-Elementen beim Lernen von Mathematik
Theorie und Beispiele aus dem Bereich der Analysis
Mai 1998
Nr. 168
Seeger, Falk:
The complementarity of theory and praxis in the cultural-historical approach: From self-application to self-regulation
Juni 1998
Nr. 169
Horsmann, Sven:
A Three-Dimensional Model of Communicative
Activity Applied to a Hypertext Learning Environment
Juni 1998
Nr. 170
Otte, Michael:
Mathematik in der Philosophie I - Naturalisierte
Erkenntnistheorie
November 1998
Nr. 171
Winkelmann, Bernard:
Mathematikdidaktische Unternehmungen anhand der Betrachtung des Lernens von Mathematik mit
Hypermedia
November 1998
Nr. 172
Radu, Mircea:
The Concept of Construction in Justus Grassmann's
Mathematical Writings: Between Kant and Schelling
November 1998
Nr. 173
Otte, Micheal:
Mathematik in der Philosophie II - Repräsentation und Möglichkeitsgedanke
Dezember 1998
Nr. 174
Abendroth-Bussmann, Doris / Schubring, Gert /
Thiemann, Andreas:
Dokumentation: Die aktuellen Mathematik -Lehrpläne der allgemeinbildendenSchulen der deutschen
Bundesländer
Dezember 1998
Nr. 175
Sträßer, Rudolf:
Mathematical Means and Models from Vocational
Context - A German Perspective
Januar 1999
Nr. 176
Otte, Michael:
Proof and Perception
Januar 1999
Nr. 177
Horsmann, Sven:
GENRES
Juli 1999
Nr. 178
Otte, Michael
Mathematik als Prozeß
Januar 2000
Nr. 179
Otte, Michael:
Bertrand Russell: Einführung in die mathematische
Philosophie
April 2001
Nr. 180
Otte, Michael / Lenhard, Johannes:
Analyse und Synthese oder: Wie ist reine
Mathematik möglich?
April 2001
Nr. 181
Otte, Michael:
Konstruktion und Existenz in Mathematik und
Philosophie
April 2001
Nr. 182
Schipper, Wilhelm:
Thesen und Empfehlungen zum schulischen und außerschulischen Umgang mit Rechenstörungen
Dezember 2001
Nr. 183
Schubring, Gert:
Mathematics between Propaedeutics and professional use: A Comparison of institutional developments
Juli 2002
Nr. 184
Gawlick, Thomas:
Dynamische Linealkonstruktionen
Februar 2003
Nr. 185
Gawlick, Thomas:
Über die Mächtigkeit dynamischer Konstruktionen mit verschiedenen Werkzeugen
Februar 2003
Nr. 186
Otte, Michael:
A = B - Darstellen und Erklären in den formalen
Wissenschaften
Februar 2003