ࡱ> #`?bjbj8s5%"***>84>z)"<<<iii((((((($f*h,)*KG"iKK)<< 4)$$$K8<*<($K($$*$< ,5eG!$(dJ)0z)$-[#-$-*$i|$dTiii))U$diiiz)KKKK>>> >>>>>> An Experience with Computers Data-Base Analysis: Teaching Mathematics in Primary Level Nielce Meneguelo Lobo da Costa Bandeirante University of So Paulo UNIBAN So Paulo Brazil This paper reports on an in-service teachers training for primary level, designed to enhance teachers mathematical knowledge and pedagogical expertise in the usage of computers for the construction of didactical practices. The study involved four university researchers and five representatives of a public school in So Paulo/Brazil, where the in-service training took place. The analyses showed that the research actors played several roles during the program as apprentice, instructor, researcher and teacher and these roles as the usage of computers in all phases, boost professional development. Particularly for the enlargement of their knowledge, the improvement of their computing skills, autonomy and critical position empowerment and development of share reflection about teaching, curriculum and learning process. Our study reports on an in-service teacher education program involving primary level educators in the exploration of Mathematics and Statistics contents using computers. The inquiry intended to answer the following question: Which are the significant factors in a teachers formation process as using computer for the construction of Mathematics pedagogical practices? The study was based on the Freirean vision of Education and on the constructionism of Papert, who is one of the most important researchers on the development of computer based learning. His theory is grounded on the learning by doing opportunity in which the computer enables students to develop concepts easier, Papert (1985). The analytical perspective has its roots in the so-called concept of "practical reflection for social reconstruction" (PREZ GMEZ, 1998), with a particular focus on action-based investigation and comprehension-intended training which embraces the development of teacher's in-service education oriented by democratic methods and principles. So that, in our study the computer appears as an important tool to enlarge the reflection process during the pedagogical formation. The Project A work team, called the Action Group, formed by four university researchers and five teachers of a public school in So Paulo State/Brazil participated in an in-service training held inside the school. The research actors were the principal, the pedagogical coordinator and three ordinary teachers, all engaged in acting as instructors for all schoolteachers members. This investigation aimed to explain which are the characteristics that contribute to the practical pedagogic development when communication is mediated by computers. The Action Group met during twenty months, weekly basis, to run not only some workshops with pupils and other teachers, but also to assemble working materials and reflecting together about the learning and formation process. At this point, is important to emphasize that, during these meetings and throughout the whole project, we deal with Mathematical concepts and Statistics principles while analyzing computers databases, developed specifically to the research actors context. The TABLETOP software was used by teachers and students aged from 7 to 9 years old to handle and analyze the databases (TABLETOP TM, 1994). Finally, by collecting research data (recorded conversations, interviews, produced materials, video tapes, among others) a qualitative research was developed characterized as a co-generative action-based investigation among collaborative groups (GREENWOOD & LEVIN, 2000; BOAVIDA & PONTE, 2002; HARGREAVES, 1998). Analysis and outcome The in-service training was strategically divided into four "phases" in order to facilitate the analyzes, as described: Phase 1 Held in the university as a training proposal to introduce the TABLETOP software and to plan the in-service training that would be applied to the schoolteachers members. Phase 2 Undergone over the first semester in the school as the initial practical period, when the in-service training in fact got started. At this moment, lead by the sense of team developed in the participants, two distinct groups started to exist: the Action Group and the Full-life Group, integrated by the schoolteachers members. In this phase, the Action Group: 1) started to training the Full-life Group developing a computing class taken outside the IT room and two activities involving the TABLETOP software, 2) developed workshops with their students, 3) developed preparatory works for presentation in an educational congress and 4) understood the investigatory studies over pedagogic practices as part of the project. Phase 3 Undergone over the second semester in the school as the consolidation period of the project. The Full-life Group started to create didactic sequences and exercises to children. From that time on, for the Action Groups teachers the acting sphere got more amplified, once more than conceiving and developing tasks for the training, they start to following and giving support to the Full-life teachers at their work with pupils. At that moment, it was already possible for each member of the Action Group to think over his own action as instructors as well as over his colleagues' practices. Phase 4 It took the last months of the project at the next academic year, when the Action Group could no longer count on the school's pedagogical coordinator neither on the principal as members of the team. With the school under new direction, the in-service education process re-started under new political and practical conditions. Meetings of the Full-life Group were reestablished with the undertaking of a new activity regarding TABLETOP software tools. As for Action Group's teachers, that was not only a period of concepts revision and improvements, but also of returning to IT laboratory classes with their students taking full responsibility for classes without any kind of pedagogical support from the university members. They also wrote a report with the group's conclusions and came up with the second series of didactic exercises to children. As a last activity, the Action Group took part in a scientific meeting where its members gave a presentation on the project's experience. The research data analysis was interpretative, made by triangulation of data (MATHISON, 1988) using the four educative dimensions experienced by the research actors as follow described: acting as apprentices, teachers, instructors as well as researchers. Apprentice Its importance may be attached to the need of a "re-signification" of what is to teach Mathematics, as well as to the need of a change in the vision regarding children Mathematics learning. Not to say the need of, besides "re-significating" the Mathematics contents to teach, acquiring new knowledge, developing data's handling strategies, setting up students IT abilities and, finally, instructing in the use of TABLETOP software. Instructor This role involved, among other aspects, the analysis of the interaction between both group of teachers as well as the analysis of conflict handling. As well as, mainly important the process of learning how to be a teacher to the other schoolteachers. Researcher As a matter of fact, in order to be capable of acting both within school and scientific meetings, each member had to perform as an apprentice, as an instructor and as a teacher. The importance of taking on the role of researcher regarding their professional development could be assessed by occurrences such as of 1) collaborative work groups consolidation, 2) reflection on work practices, 3) reflection on educators and educations roles, 4) development of pedagogic and mathematical knowledge, 5) development of computing skills, and 6) development of self-esteem and confidence. Teacher It got connected to the instructor's and researcher's ones. The Action Groups teacher had the opportunity to report their didactical experiences and teaching strategies, to discuss the difficulties and seek the validation from the group about their attitudes to teaching. Each member of the group act during the in-service training as an assistant teacher and take the opportunity to discuss what had happened in previous classes so as to reflect about it in a reciprocal way. Moreover, they had to compare the outcome of teachers' and pupils' workshops and think about practices' similarities and differences. It was possible, in addition to develop pedagogic strategies in order to closer the individual and the conceptual Statistics dimensions (GODINO & BATANERO, 1998), besides innovate the ways of contents presentation. Among other aspects perceived, one can mention references to practices' restructuring, goals' achievement, actions' planning, activities' assessment, children' approach towards information handling and Statistics language, as well as software's influence on didactic practices. Besides instigating the whole group to create learning situations with the software, the teacher role contributed with actions such as: intervene as mediator in pupil's learning, observe students solution's strategies, prepare pedagogic material for a range of activities, discuss it classes methodology and management, reflect on theory and practice, "re-significate" Mathematics' role in the curriculum, "re-significate" Statistics contents and action-based curriculum, develop new professional skills and, finally, dominate software resources so as to use it as a pedagogic instrument. In the appendices, four figures graphically resume the mentioned professional roles. During every phase of this research, the computer was used and once in the context, it is not a neutral tool and interferes in the learning process. Particularly, in Statistics teaching computers are excellent tools to facilitate data analysis, to perform calculations and different graphic representations. The computer helped us not only on the global data visualization but also on its accessibility, due to the possibility to teachers and pupils to manage, organize and access easily databases built on TABLETOP. The software enabled reflection on hypotheses, predictions, analyses and interpretation of given results through graphic representations, statistic calculations, data storage and information connections. The in-service program was fully planed based on set activities using a specific TABLETOP toll for one variable data analysis by the interpretation of Venn Diagrams and another to develop activities involving relationships between two variables. Teachers interacted with the software and could realize significant differences between manual and computerized graphics. From that moment on, by understanding and performing connections on different graphics representations (one and two axes graphic) we clearly found evidences that the TABLETOP software were effective to help teachers to expand their Statistics concepts evolving from the personal meaning to the institutional meaning, as referred by Batanero et al. (1998). Conclusion The research on teachers formation process shows as evident results: enlargement of their mathematical and statistical knowledge, the improvement of their computing skills, autonomy and critical position empowerment and development of share reflection about teaching, curriculum and learning process. In fact, the research concluded that it was essential for their skill development the action of all roles and the usage of computers in every phase of the in-service education program. References BOAVIDA, A. M.; PONTE, J. P. Investigao colaborativa: Potencialidades e problemas. In GTI (Ed.), Reflectir e investigar sobre a prtica profissional, p. 43-55. Lisboa: APM, 2002. GODINO, J. D., BATANERO, C. Clarifying the meaning of mathematical objects as a priority area of research in mathematics education. In: SIERPINSKA, A.& KILPATRICK, J.(Eds) Mathematics Education as a research domain: a search for identity. Dordrecht: Kluwer A. P., 1998, p. 177 - 195. GREENWOOD, D.; LEVIN, M. Reconstructing the relationships between universities and society through action research.In: DENZIN and LINCOLN Eds Handbook for Qualitative Research. 2nd ed. Thousand Oaks, California: Sage Publications Inc. p. 85 106, 2000. HARGREAVES, A. Os professores em tempo de mudana: O trabalho e a cultura dos professores na idade ps-moderna. Lisboa: Mc Graw-Hill, 1998. LOBO DA COSTA, N. Formao de professores para o ensino da matemtica com a informtica integrada prtica pedaggica: explorao e anlise de dados em bancos computacionais. 2004. 300f. So Paulo: PUC. Tese (Doutorado em Educao: Currculo). MATHISON, S. Why Triangulate? Educational Researcher. 17 (2), p.13-17, 1988. PREZ GMEZ,A. O pensamento prtico do professor: a formao do professor como profissional reflexivo. In: NVOA, Antnio. (coord.) Os professores e sua formao. 3. ed. Lisboa: Publicaes Dom Quixote Instituto de Inovao Educacional. (Nova Enciclopdia Temas de Educao. vol.1), 1997. p. 93 114. _____. A funo e formao do professor/a no ensino para a compreenso: diferentes perspectivas. In: SACRISTN, Jos Gimeno e PREZ GMEZ, Angel. Compreender e transformar o ensino. Traduo por Ernani F. da Fonseca Rosa. 4. ed. Porto Alegre: Artmed Editora, 1998, p.353 379. TABLETOP TM. New computers tools for Logic, Information, Graphing and Data Analysis. Hands on! 17 (2), U.S.A., 1994. available: . Appendices       Lulu Healy, Sandra Magina, Sandra Santos and Nielce M. Lobo da Costa.  Rosa, Margarida, Orqudea, the principal Hortnsia, and the pedagogical coordinator Violeta (these are all fictional names).  TABLETOP was developed by Chris Hancock in the TERC - Technical Education Research Centers, Inc /Harvard.  Both of them, motivated by particular reasons, independently of the project, moved away from the school upon being selected in another governmental aptitude test.  For more information: LOBO DA COSTA, 2004.     PAGE  PAGE 1 UVWv O Q R V \ _ g h ǯxi]TK?K3K?KhM h CJ\]h:Yh)^CJ\]h)^CJ\]h;h)^CJh;hM CJ\]h|{6CJOJQJ^JaJhyk6CJOJQJ^JaJ#hA%Fhyk6CJOJQJ^JaJ+hA%Fhyk6CJOJQJ^JaJmHsH.h|{hyk6>*CJOJQJ^JaJmHsH&h|{hyk5CJ OJQJ]^JaJ h)<+5CJ OJQJ]^JaJ &h)<+h)<+5CJ OJQJ]^JaJ Wv h j }}}$d5$7$8$9DH$a$gd|{ $da$gd|{ $da$gdJ$d5$7$8$9DH$`a$gd|{$ 7d5$7$8$9DH$a$gdKsHd^H`gdb$ 7d5$7$8$9DH$a$gd|{s={???h i l  / 1 2 D E I J  ! 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