We have identified three poles of research 3 following the readings of work relative to our study:

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1 The integration of ICT in the teaching of mathematics seen from the side of the teacher. The case of the dynamic geometry in ordinary classes of junior high school 1 There have been researches centered on the use of the ICT (The Information and Communication Technology) in the teaching of mathematics for more than twenty years, but primarily on the pupils and the trainings. According to Meta-analyzes, on researches completed between 1994 and 1998, there were few researches on the practices of the teachers regarding this subject (Lagrange&Grugeon, 2003). Since then, we have noted a growing interest and numerous works concerning the teacher and TICE 2. Our thesis work concentrate on this last particular field of research. We have identified three poles of research 3 following the readings of work relative to our study: The first pole of research relates to "the integration of the ICT in the teaching of mathematics" in which complexities of this integration are highlighted (Artigue, 1998; Lagrange, 2001; Monaghan, 1998; Schneider, 1998; Stacey, 2001). This research shows that the question of the ICT integration has no simple answer, since the teacher-student-knowledge relationship is completely transformed in the ITC environment. The second pole of research gathers works on "the training of teachers". According to the research of Abboud-Blanchard (undertaken during his thesis in 1995), the nature of training (or precisely the absence of real training) completed by teachers in new technologies constitutes the principal cause of non-integration of ICT tools in teaching. From the same point of view, other researches (Assude&Gélis, 2001; Assude&Grugeon, 2003) are centered on the strategies and the engineering of training methods, which lead to a successful integration, and therefore an evolution of teaching using of the TICE. Training is seen like a long course. In addition, currently, certain research in progress reveals a growth in studies relative to this pole (theses and projects in progress). In the third and last pole, we consider research which relates to "the analysis of teachers practices". The purpose of this research is to contribute to the analytical works on teachers 1 First level of secondary education in the French education system. The teaching followed by pupils of years during 4 years. 2 Technologies de l'information et de la Communication pour l'enseignement : Communication and Information Technologies for Teaching. 3 These three poles of research were defined thanks to elements found in research on the teaching of mathematics with TICE. These elements are in relation to the teacher and the TICE. It is important to announce that all quoted research does not carry in a direct way on the subject of the pole given. 1

2 practices using of the TICE by providing adapted tools. In this prospect, Ruthven and Hennessy (2002) take into account the point of view of the teachers on successful use of the TICE in order to elaborate teaching methods for teachers using the TICE. Monaghan (2003) proposes a model of analysis borrowed from Saxe (1991) to examine the influences of certain factors on the activity of the teachers and to include/understand complexities of the practices. Problematic of research Questioning The double approach of Robert&Rogalski (2002) highlighted the complexity and the coherence of the system of the practices of teachers. We make the assumption that the use of TICE influences on decisive elements related to the teaching of mathematics and brings new complexities in the practices. Indeed, the constraints of the ICT environment are different from those of the usual environment and impose on teachers specific constraints to its utilization at several levels. Consequently, we are interested, in particular, in the reactions of the teachers to these changes and in the way they adapt to these new phenomena. As illustrated in the research of Lagrange (2003), Monaghan (2001) and of Stacey (2001), the study on teachers practices is likely to provide knowledge on the real contribution of the ICT to teaching and learning. Therefore, we seek to know on the one hand the functions attributed by teachers to the TICE and the means engaged (or wish to engage) to fulfill these functions, and on the other hand the effective realization of these functions in the practices as well as the a posteriori opinion of the teacher. The work of Ruthven&Hennessy (2002) relates, in some way, to the first two points (functions of the TICE). Indeed, they propose a model which takes in account the way a teacher can conceive the use of the TICE in the teaching and the learning of mathematics. The various topics of which the model is made up can be seen as "functions" assigned by the teachers to the ICT. In the same manner, we try to identify the topics present in the declarations of the teachers. Then, through observations, we will be able to see whether the model may apply in real situation, i.e. in classrooms, or whether it is mainly made up of ideological preferences, with little chance of success in practice. Mathematical topic: dynamic geometry in junior high school We are limiting our research topic to the teaching of the geometry in junior high school with the assistance of the software of dynamic geometry. We chose this topic, because there are growing 2

3 researches on dynamic geometry and its use is encouraged by the curricula. This should enable us to study the transposition of this research and the curriculum towards the classroom. First, we studied the transposition of the uses of the ICT tools 4. This study consisted in knowing what occurs around our topic on the researchers side as well as the institutional side. Researchers in didactic of mathematics, among whom are Laborde&Capponi (1994) and Pratt&Ainley (1997), were centered on the contribution of the software to the learning of mathematics and showed that the software of dynamic geometry (here Cabri-géomètre) facilitate the learning of the distinction drawing/figure, in particular to exceed the framework spatio-graph. In the last curricula of junior high school, we constated the same tendency in encouraging the utilization of software in the learning of geometry. Indeed, our analysis of last curricula and textbooks revealed encouragement in using of ITC tools in some subjects; however, surprisingly, we noticed a gap between the curricula and the textbooks. Second, we made a preliminary study on teachers practices concerning `the place of TICE in the professional dissertations of IUFM' 5 (C-Dedeoglu&Erdogan, 2003) to have a global idea of the extent to which the TICE is used by new teachers. In this study `the dynamic geometry in junior high school seemed a dominating type of TICE 6. This result is linked to the contents of the curriculum which seems rather easily compatible with the use of the dynamic geometry. We could also identify in the problematic of the professional dissertations, the impact of the material resources related to the dynamic geometry. Our assumption is that the models of activities made available to the teachers (in the handbooks, on Internet, in books of use of the software, etc.) generate the ideas of using this software in the study of the mathematical concepts and help the trainee teachers to be centered on objectives of their teaching. Following these two previous studies and the assumption that the effective practices should allow us to better understand the utilization of TICE by teachers, as well as to answer to our questions of research, we decided to observe practices of the ordinary teachers. 4 They are the ICT tools relative to the teaching of the geometry in junior high school 5 It acts of a quantitative study of the professional dissertations of the trainee teachers on the Web sites of IUFM (University Teacher Training Institutes), on the level of secondary education. 6 We indicate by ` type of TICE' the use of a tool given to a given level. 3

4 Methodology of observation In order to carry out our experimentation, we contacted teachers of junior high school, who use TICE in their classrooms. In our observations, while we are interested by the motivation behind the choice of the teachers, we did not limit ourselves to a topic or a level of study. Moreover, the teachers were not always able to tell us in advance in which topics they were going to use TICE and for which period. Therefore, the non-limitation of the topics enabled us to observe classes each time the opportunity arose. Our data consist with 14 sessions of observation, carried out in the classrooms of four teachers during year 2OO2-2OO3. We recorded the speech of the teacher during the classes thanks to a tape recorder and we remained in the classroom to take notes in order to supplement the audio recording. Before and after each session (insofar as it is possible) they shared with us their remark on the envisaged and the effective courses of the sessions. Teachers observed Teachers 7 X1 X2 X3 teach in junior high school C x, the teacher Y teaches in the C y junior high school. The attended establishments have the satisfactory material mean at the ICT level. In addition, let us specify that the four schools visited are not situated in difficult areas, i.e. not classified in ZEP 8. The concerned teachers have taught in those junior high schools for at least ten years. They have more or less learned by themselves how to use TICE and have already made use of TICE in their teaching for a few years. That is to say, they are beginner neither in their profession of teacher, nor in the use of the TICE. Functions of the TICE according to declarations Based on the first interview during our first meeting, we sought to identify the reasons for which the teachers use the TICE in their teaching. We grouped the terms pronounced by the teachers during this interview. It is quite difficult to take into account these declarations independently one from another. We identified three categories of reasons. The first reason, which includes: dynamic activity, variety of the figures, large, clean and beautiful figure, faster access to the concept of infinite, is related to the learning process as well as the time savings opportunities. The second reason, relating to comfort and management, is directly linked to the teaching activity. Finally, 7 8 Priority Zone of Education 4

5 the third and last reason, society tool and evolution of the teaching, is in connection with a will to change the current pedagogy. These declarations appear necessary to better understand the choices carried out by teachers at the time we analyze our observations. Analyze observed sessions We proceeded with the transcription of the recordings in order to conceive a protocol of each session observed. We, then, supplemented it by other data available during the following sessions. This collection of data led us to establish a grid of analysis according to our research questions. This grid is more or less adapted to our sessions. First, we observe the position of the pupils regarding the use of TICE, which is undoubtedly in relation with the teacher s project. The objectives of the teacher, the materials used and their respective role, the analysis of the activity using TICE, and the analysis of the course of the sessions, enabled us to identify the elements which would be used to establish our synthesis. In this synthesis, we compared the pre-session view of the teacher concerning the course of the session with the teacher s posteriori view following the effective session. This enabled us to answer to our questions of research. The analysis of the sessions, which is under in progress, illustrates, at first glance, that there is a variety of the practices regarding the utilization of TICE. At this stage of this work, we continue to fill our grid with our analysis and unfortunately, we do not have the synthetic results yet to be able to quote them here. Furthermore, we still need to adapt theoretical tools to our analyses. The variety of the observations (differences on the level of organization in class, mathematical topic, level of teaching, technology) signifies that it is rather difficult to apply a model of analysis, such as that proposed by Robert&Rogalski (2003) or Monaghan (2003). References ABBOUD BLANCHARD M. (1995), Dix ans après, l outil informatique a-t-il trouvé son chemin vers la classe de mathématiques?, Fascicule de didactique des mathématiques et de l E.I.A.O., 19 pp, Institut de Recherche Mathématique de Rennes. ARTIGUE M. (1998), Teacher training as a key issue for the integration of computer technologies, in D.Tinsley & D.C.Johnson (eds), Information and Communication Technologies in School Mathematics, , Chapman & Hall, London. ASSUDE T. & GRUGEON B. (20-22 juin 2003), Enjeux et développements d ingénieries de formation des enseignants pour l intégration des TICE, in ITEM : Intégration des Technologies dans l'enseignement des Mathématiques, IUFM, Reims. ASSUDE T. & GELIS. J.-M. (2001), La dialectique ancien-nouveau dans l intégration de Cabri- Géomètre à l école primaire, Educational Studies in Mathematics, 50,

6 CALISKAN-DEDEOGLU N & ERDOGAN E. (20-22 juin 2003), La place des TICE dans les mémoires professionnels d'iufm, in ITEM : Intégration des Technologies dans l'enseignement des Mathématiques, IUFM, Reims. LABORDE C. & CAPPONI P. (1994), Cabri-géomètre constituant d un milieu pour l apprentissage de la notion de figure géométrique, Recherches en Didactique des Mathématiques, 14(1.2), LAGRANGE J-B. (2003), Analysing the impact of ICT on mathematics teaching practices, in CERME3: Third Conference of the European Society for Research in Mathematics Education, Bellaria, Italy. LAGRANGE J.-B. (2001), L intégration d instruments informatiques dans l enseignement : Une approche par les techniques, Educational Studies in Mathematics, 43, LAGRANGE J.-B. & GRUGEON B. (2003), Vers une prise en compte de la complexité de l'usage des TIC dans l'enseignement. Une méta-analyse des publications d'innovation et de recherche en mathématiques, Revue Française de Pédagogie, n 143, MONAGHAN J. (20-22 juin 2003), Teachers using technology: the complexities of practice, in ITEM : Intégration des Technologies dans l'enseignement des Mathématiques, IUFM, Reims. MONAGHAN J. (2001), Teachers classroom interactions in Ict-based mathematics lessons, in M. van den Heuvel (ed), Proceedings of the 25 th International Conference for the Psychology of Mathematics Education, Vol. I, , Utrecht, Netherlands: OW&OC. MONAGHAN J. (1998), Les enseignants et la technologie, Actes du Colloque "Calculatrices symboliques et géométriques dans l'enseignement des mathématiques", IREM de Montpellier. PRATT D. & AINLEY J. (1997), The Construction of Meanings for Geometric Construction : Two Contrasting Cases, International Journal of Computers for Mathematical Learning, 1, ROBERT A. & ROGALSKI J. (2002), Le système complexe et cohérent des pratiques des enseignants de mathématiques : une double approche, Revue canadienne de l enseignement des sciences, des mathématiques et de la technologie. RUTHVEN K. & HENNESSY S. (2002), A practitioner model of the use of computer-based tools and resources to support mathematics teaching and learning, Educational Studies in Mathematics, 49, SCHNEIDER E. (1998), La TI-92 dans l enseignement des mathématiques Des enseignant(e)s découvrent la didactique des mathématiques, Actes du Colloque "Calculatrices symboliques et géométriques dans l'enseignement des mathématiques", IREM de Montpellier. STACEY K. (2001), Teaching with CAS in a time of transition, in CAME 2001 Symposium: Communicating Mathematics through Computer Algebra Systems, Utrecht, Netherlands, 6