Mediation in the Construction of Mathematical Knowledge: A Case Study Using Dynamic Geometry
ABSTRACT
According to the social-historical theory, interaction between individuals plays a major role in building the human being. It is through such interpersonal relationships that the individual’s psychological development takes place. Therefore, in school education, interaction with teacher and with classmates is essential; in addition, their mediation along the educational process is an extremely relevant factor to achieve goals. Mediation also includes use of tools and signs in the social context, enabling the development of superior psychological processes. This research was carried out using the social-historical theory as theoretical background and considering that digital technologies enable adequate spaces to perform investigation activities. It was performed with a group of students Mathematics teachers and aimed at analyzing a learning situation about Triangle Similarity Cases using a Dynamic Geometry software program. The importance of mediation (tools, teacher, classmates) in knowledge building was evaluated by performing investigative activities aided by the software. Qualitative research, through case study, was chosen and three data collection techniques were used: participant observation, questionnaire and semi-structured interview. Research-related tasks were divided into three stages: preparation; de velopment and analysis of collected data, relating them with the adopted theoretical background. Considering all that was observed and collected through questionnaires and interview, it is possible to state that mediation played an important role during software activities.
According to the social-historical theory, interaction between individuals plays a major role in building the human being. It is through such interpersonal relationships that the individual’s psychological development takes place. Therefore, in school education, interaction with teacher and with classmates is essential; in addition, their mediation along the educational process is an extremely relevant factor to achieve goals. Mediation also includes use of tools and signs in the social context, enabling the development of superior psychological processes. This research was carried out using the social-historical theory as theoretical background and considering that digital technologies enable adequate spaces to perform investigation activities. It was performed with a group of students Mathematics teachers and aimed at analyzing a learning situation about Triangle Similarity Cases using a Dynamic Geometry software program. The importance of mediation (tools, teacher, classmates) in knowledge building was evaluated by performing investigative activities aided by the software. Qualitative research, through case study, was chosen and three data collection techniques were used: participant observation, questionnaire and semi-structured interview. Research-related tasks were divided into three stages: preparation; de velopment and analysis of collected data, relating them with the adopted theoretical background. Considering all that was observed and collected through questionnaires and interview, it is possible to state that mediation played an important role during software activities.
Cite this paper
nullBarcelos, G. , Batista, S. and Passerino, L. (2011) Mediation in the Construction of Mathematical Knowledge: A Case Study Using Dynamic Geometry. Creative Education, 2, 252-263. doi: 10.4236/ce.2011.23034.
nullBarcelos, G. , Batista, S. and Passerino, L. (2011) Mediation in the Construction of Mathematical Knowledge: A Case Study Using Dynamic Geometry. Creative Education, 2, 252-263. doi: 10.4236/ce.2011.23034.
References
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[1] Artigue, M. (2002). Learning Mathematics in a CAS Environment: The Genesis of a Reflection about Instrumentation and the Dialectics between Technical and Conceptual Work. International Journal of Computers for Mathematical Learning, 7, 245-274. doi:10.1023/A:1022103903080 [2] Baldin, Y. Y. (2002). Utiliza??es Diferenciadas de Recursos Computacionais no Ensino de Matemática (Differentiated uses of computer resources in the Teaching of Mathematics). In L. M. Carvalho and L. C. Guimar?es, (Org). História e Tecnologia no Ensino da Matemática (pp. 29-37). Rio de Janeiro: IME-UERJ. [3] Baquero, R. (1996). Vigotsky y el aprendizaje escolar. Buenos Aires: Aique Grupo Editor. [4] Bogdan, R., & Biklen, S. K. (1998). Qualitative Research for Education: An introduction to theories and methods. Boston: Allyn and Bacon, Inc. [5] Borba, M. de C., & Penteado, M. G. (2005). Informática e Educa??o Matemática (Informatics and Mathematics Education) (3rd ed.) Belo Horizonte: Autêntica. [6] Bueno-Ravel, L., & Gueudet, G. (2009). Online Resources in Mathematics, Teachers’ Geneses and Didactical Techniques. International Journal of Computers for Mathematical Learning, 14, 1-20. doi:10.1007/s10758-009-9143-0 [7] Cole, M. (1986). The zone of proximal development: where culture and cognition create each other. In J. Wertsch, (Org.). Culture, Communication and Cognition: Vygotskian Perspective (pp. 146-161). USA: Cambridge University Press. [8] Cole, M., & Scribner, S. (1978) Introducion. In L. S. Vygotsky (ed.) Mind in Society: The developmente of higher psychological process (pp. 1-14). United States of America, President and Fellows of Harvard College. [9] Coll, C. (1990). Un marco de referencia psicológico para la educación escolar: la concepción constructivista del aprendizaje y de la ense?anza. In C. Coll, J. Palácios and A. Marchesi, (Org.). Desarrollo psicologico y educacion: psicologia de la educacion escolar, v.2 (pp. 435-453). Madri: Alianza Editorial. [10] D’Ambrósio U. (2001). Etnomatemática: elo entre as tradi??es e a modernidade [Ethnomathematics: link between tradition and modernity]. Belo Horizonte: Autêntica. [11] Doise, W. (1988). El desarrollo social de la inteligencia: compendio histórico. In G. Mugny and J. Pérez, (Eds.). Psicología Social del Desarrollo Cognitivo (pp. 47-64). Espanha: Editorial Anthropos. [12] Fainguelernt, E. (1999). Educa??o Matemática: representa??o e constru??o e geometria (Mathematics Education: representation, construction and geometry). Porto Alegre: Artes Médicas. [13] Gil, A. C. (1999). Métodos e Técnicas de Pesquisa Social (Methods and Techniques of Social Research) (5th ed.). S?o Paulo: Atlas. [14] Gindis, B. (2003). Remediation Through Education: Sociocultural Theory and Children with Special Needs. In A. Kozulin, B. Gindis, V. S. Ageyev and S. M. Miller (Eds.), Vygotsky’s educational theory in cultural context (pp. 200-221). New York: Cambridge University Press. [15] Guven, B. (2008). Using Dynamic Geometry Software to Gain Insight into a proof. International Journal of Computers for Mathematical Learning, 13, 251-262. doi:10.1007/s10758-008-9129-3 [16] Johnston-Wilder S., & Pimm D. (Ed) (2004). Teaching Secondary Mathematics with ICT. London: Open University Press. [17] Karpov, Y. (2003). Development Through the lifespan: a neo-vygotskia approach. In A, Kozulin, B. Gindis, V. S. Ageyev and S. M. Miller (Eds.), Vygotsky’s educational theory in cultural context (pp. 138-155). New York, NY: Cambridge University Press. [18] Kozulin, A (2003). Psychological Tools and Mediated Learning. In A. Kozulin, B. Gindis, V. S. Ageyev and S. M. Miller (Eds.), Vygotsky’s educational theory in cultural context (pp. 15-38). New York: Cambridge University Press. [19] Laplane, A. L. F. (2000). Intera??o e Silêncio na sala de aula (Interaction and Silence in the classroom). Ijuí: Editora UNIJUí. [20] Laville, C., & Dionne, J. A (1997). La construcition dês savoirs: manuel de méthodologie en sciences. Monteral-Canadá: Chenelière/ McGraw-Hill. [21] Maschietto, M. (2008). Graphic Calculators and Micro-Straightness: Analysis of a Didactic Engineering. International Journal of Computers for Mathematical Learning, 13, 207-230. doi:10.1007/s10758-008-9141-7 [22] Moysés, L. (2007). Aplica??es de Vygotsky à Educa??o Matemática (Application of Vygotsky to Mathematics Education) (8th ed.). Campinas-SP: Papirus. [23] Oliveira, M. K. de (1993). Vygotsky Aprendizado e Desenvolvimento um Processo Sócio-Histórico (Vygotsky Learning and Development with a socio-historical process). S?o Paulo: Scipione. [24] Passerino, L. M., Koch, S. K. S., Maciel, M., & Martins, M. del C. (2008). Media??o por Meio de Evidências no Contexto Lingüístico em Ambientes Virtuais de Aprendizagem. In XIX Simpósio Brasileiro de Informática na Educa??o. Fortaleza (CE). Anais ... Fortaleza (CE): Universidade Federal do Ceará, 1, 430-440. [25] Ponte, J. P. da, Brocado, J., & Oliveira, H. (2005). Investiga??es Matemáticas na sala de aula (Investigations mathematics classroom). Belo Horizonte: Autêntica. [26] Ponte, J. P. da, Oliveira, H., & Varandas, J. M. (2003). O Contributo das Tecnologias de Informa??o e Comunica??o para o Desenvolvimento do Conhecimento e da Identidade Profissional (The Contri- bution of Information and Communication Technologies for Develop- ment of Knowledge and Professional Identity). In: D. Fiorentini (Ed.), Forma??o de professores de Matemática: Explorando novos caminhos com outros olhares. Campinas: Mercado de Letras, 159- 192. [27] Preti, d. (Org.) (2002). Intera??o na Fala e na Escrita (Interaction in Speech and Writing). S?o Paulo: Humanitas Publica??es. [28] Valentini, C. B., & Soares, E. M. S. (2005). Fluxos de Intera??o: uma experiência com ambiente de aprendizagem na Web (Interaction Flows: an experience with the learning environment on the Web). In C. B. Valentini and E. M. S. Soares, (Org.), Aprendizagem em ambientes virtuais: compartilhando idéias e construindo cenários v. 1 (pp. 77-86). Caxias do Sul: EDUCS. [29] Vygotsky, L. S. (1993). Pensamiento y Lenguaje. In A. Alvarez and P. Del Rio (Eds), L. S. Vygotsky Obras Escogidas v. II. Problemas de Psicologia general (pp. 9-348). Madrid: Visor Distribuciones. [30] Vygotsky, L. S. (1986). Thought and Language. Cambridge: Harvard University Press. [31] Vygotsky, L. S. (1978). Mind in Society:The Developmente of Higher Psychological Process. United States of America: President and Fellows of Harvard College. [32] Wertsch, J. (1998). Mind as action. New York, NY: Oxford University Press. [33] Yin, R. K. (2003). Case study research: design and methods. Califórnia: Sage Publications.