Linguagem (des)contextualizada, matemática e lógica Desempenho dos alunos na lógica formal e relação com a sua língua e classe social
DOI:
https://doi.org/10.22267/relatem.20133.65Palavras-chave:
Lógica, Língua, Estatuto Social, Regras de reconhecimento e de realizaçãoResumo
Moçambique é uma sociedade multilingue e, consequentemente multicultural, com mais de 40 línguas nativas. Excluindo o Português e poucas de poucos imigrantes todas elas são línguas Bantu. Segundo o Censo Geral de 1997, somente 6,5% da população tinha o Português como língua mãe e, como primeira língua e destes 14% tinham idade inferior a 50 anos, e só 2.1% tinha 50 ou mais anos de idade.
Apesar deste panorama a língua de ensino em Moçambique é o Português, mesmo sabido que apenas menos de 5% de crianças ingressam na Escola sabendo comunicar nesta língua. As línguas dominantes no local onde a pesquisa foi desenvolvida são: Ci-Changana, Ci-Ronga e Ci-Tshwa, as quais são, mutuamente, entendíveis entre os falantes.
O objectivo da pesquisa é (i) explorar o entendimento do estudante ao simbolismo algébrico, linguagem abstracta e lógica e (ii) relacionar este entendimento com o sucesso escolar na disciplina de matemática com a sua condição socio-económica e linguística.
Para delimitar a área de estudo foram colocadas as seguintes questões de pesquisa: (1) quais são as estratégias preferidas pelos alunos quando resolvem problemas baseados na lógica em relação ao seu estatuto sócio-económico e linguístico? (2) em particular: Como é que a língua materna e o estatuto sócio-económico estão associados ao raciocínio e procedimentos dos alunos?
Como orientação teórica a pesquisa apoiu-se na abordagem discursiva de aprendizagem de matemática.
O presente artigo pretende, apoiado na etnomatemática, discutir a relação entre o raciocínio e os procedimentos dos alunos e a sua ligação com a sua língua materna e estatuto socio-económico.
Downloads
Referências
Anyon, J. (1981). Social Class and School knowledge. Curriculum Inquiry, 11, 3-42.
Atweh, B., Bleicher, B., & Cooper, T. (1998). The construction of the social context of mathematics classrooms: A sociolinguitic analysis. Journal for Research in Mathematics Education, 29, 63-82.
Barile, M. (2007). Sienceworld. Retrieved 09 05, 2012: scienceword.wolfram.com.
Bastin, Y., Coupez, A., & Mann, M. (1999). Continuity and divergence in the Bantu languages (Annales Sciences humaines, vol 162). Tervuren: Musée Royale du Afrique Centrale.
Bauersfeld, H. (1992). Integrating theories for mathematics education. For the Learning of Mathematics 12(2), 19-28.
Bell, A. (1996). Problem-solving aproaches to algebra: Two aspects. In N. Bednarz, C. Kieran, & L. Lee (Eds.), Approaches to algebra: Perspectives for research and teaching (pp. 167-185). Dordretch, The Netherlands: Kluwer Academic.
Bell, J. (1987). Doing your research project: A guide for first-time researchers in education and social science. Buckingham, UK: Open University Press.
Bernsitein, B. (1977). Codes, modalities, and the process of cultural reproduction: a model. London, UK: Cambrigde University Press.
Bernstein, B. (1990). Pedagogy, Symbolic Control and Identity: Theory, research, critique. Revised edition. London, UK: Rowman & Littlefield.
Bernstein, B. (1995). Code, theory and its positioning: A case study in misrecognition. British Journal of Sociology of Education, 16, 3-19.
Bernstein, B. (1997). Pedagogy, symbolic, control and identity: Theory, research, critique. Oxford, England: Taylor & Francis.
Bernstein, B. (2000). Pedagogy, symbolic control and identity: Theory, research and critique. Revised edition. Oxford: Roman & Littlefield.
Bloedy-Vinner, H. (2001). Beyond unknowns and variables - parameters and dumy variables in high school algebra. In R. Sutherland, T. Rojano, A. Bell, & R. Lins, (Eds). Perspectives on School Algebra (pp. 177-189). Dordrecht, The Netherlands: Kluwer Academic Publishers.
Clarkson. (2002). Studying bilingual children, studying Mathematics in Australia. Norwich, England: Paper presented at the multilingual mathematics group meeting
Clarkson, P. (1992). Language and mathematics: A comparison of bilingual and monolingual students of mathematics. Educational Studies in Mathematics, 23 (4), 417-429.
Cooper, B., & Dunne, M. (2000). Assessing children's mathematical knowledge: Social class, sex and problem solving. Buckingham, UK: Open University Press.
Cummins, J. (1984). Bilingualism and special education: Issues in assessment and pedagogy. Clevedon, England: Multilingual Matters.
Dawe, L. (1983). Bilingualism and mathematical reasoning in English as a second language. Educational Studies in Mathematics, 14(4), 325-353.
Furinghetti, F., & Paola, D. (1994). Parameters, unknowns and variables: A little difference? In J. P. Da Ponte, & J. F. Matos (Eds.). Proceedings of the eighteenth international conference for the Psychology of Mathematics Education, Vol 2, (pp. 368-375). Portugal: University of Lisbon.
Guadalii, K. E. (2001). Languages in Mozambique. Africa & Asia, 1, 6-12.
Gellert, U. (2009). Analysing accounts, discourse and mathematics classroom interaction. Reflections on qualitative methodology. In R. Kaasila (Hrsg.) Matematiikan ja luonnontieteiden opetuksen tutkimuspäivät (pp. 9-34.). Rovaniemi: Lapin yliopistopaino.
Gellert, U., & Jablonka, E. (2009). “I am not talking about reality”: Word problems and the intricacies of producing legitimate text. In L. Verschaffel, B. Greer, W. v. Dooren, & S. Mukhopadhyay (Eds.), Words and worlds: Modelling verbal descriptions (pp. 39-53). Rotterdam, The Netherlands: Sense.
Gorgório, N., & Planas, N. (2001). Teaching mathematics in multilingual classrooms. Educational Studies in Mathematics 47, 7-33.
Guthrie, M. (1971). Comparative Bantu: An Introduction to the Comparative Linguistics and Prehistory of the Bantu Languages. Bantu Prehistory, Inventory and Indexes (Vol. 2). Gregg.
Halliday, M. (1978). Language as social semiotic: The social interpretation of language and meaning. London, UK: Edward Arnold.
Halliday, M. (1985). Systemic Perspectives in Discourse. London: Edward Arnold.
Halliday, M., & Hassan, R. (1989). Language, context and text: Aspects of language in a social-semiotic perspective. London, England: Oxford University Press.
Herbert, K., & Brown, R. (1997). Patterns as tools for algebraic reasoning. Teaching Children Mathematics, 3 , 340-345.
Hoadley, U. (2009). The reproduction of social class differences through pedagogy: A model for investigation of pedagogic variation. British Journal of Sociology of Education, 29(1), 63-78.
INDE. (2010). Programas de Matematica do II Ciclo do Ensino Secundario Geral [II Cycle Mathematics Syllabus for the Secondary School]. Maputo, Moçambique: Imprensa Universitária da UEM.
Jablonka, E. (2007). Mathematical literacy: Die verflüchtigung eines ambitionierten testkonstrukts. In I. T. Jahnke, & W. Meyerhöferr, (Eds.), Pisa & Co: Kritik eines programms (pp. 249-282). Hildesheim, Germany: Franzbecker.
Jablonka, E. (2009). Sociological perspectives in research in mathematics education. In R. Kaasila (Ed.), Matematiikan ja luonnontieteiden opetuksen tutkimuspäivät Rovaniemellä 7.-8.11.2008 (pp. 31-65). Rovaniemi, Finland: Lapin yliopisto.
Jablonka, E. (2011). The (hidden) rules in a mathematics classroom. In Brandell, G., & Pettersson (Eds.), A. Matematikundervisning: vetenskapliga perspektiv (pp. 65-91). Stockholm, Sweden: Stockholms universitets förlag.
Jablonka, E., & Gellert, U. (2010). Ideological roots and uncontrolled flowering of alternative curriculum conceptions. In U. Gellert, E. Jablonka, & C. Morgan (Eds.). Proceedings of the sixth International Mathematics Education and Society conference (pp. 31-49). Germany: Freie Universität Berlin.
Khatupa, M. (1986). Linguistic view in Mozambique and linguistic contribution to the definition of an appropriate linguistic policy. Portugal: Universidade Nova de Lisboa.
Kieran, C. (2007). Learning and teaching algebra at the middle school through college levels: Building meaning for symbols and their manipulation. Second handbook of research on mathematics teaching and learning, 2, 707-762.
Küchemann, D. (1981). Algebra. In K. M. Hart, (Ed.), Children's understanding of mathematics: 11-16 (pp. 102-119). London, UK: John Murray.
Lerman, S. (2006). Learning mathematics as developing identity in the classroom. In P. Liljedhal (Ed). Proceedings of the canadian mathematics education study group (pp. 3-13). Canada: University of Ottawa.
Lerman, S., & Zevenbergen, R. (2004). The socio-political context of the mathematics classroom: Using Bernstein’s theoretical framework to understand classroom communications. Researching the Socio-Political Dimensions of Mathematics Education, 35, 27-42.
MacGregor, M., & Price, E. (1999). An exploration of aspects of language and algebraic learning. Journal for Research in Mathematics Education, 30, 449-467.
MacGregor, M., & Stacey, k. (1994). Progress in learning algebra: Temporary and persistent difficulties. In G. Bell, B. Wright, N. Leeson, & J. Geake (Eds.). Proceedings of the Seventeenth Annual Conference of the Mathematics Education Research Group of Australasia, Vol.2, (pp. pp.403-410). Lismore, NSW: MERGA.
MacGregor, M. & Stacey, K. (1997). Students' understanding of algebra notation: 11-15. Educational Studies in Mathematics, 33, 1-19.
Meaney, T. (2002). Symbiosis or cultural clash? Indigenous students learning mathematics. Journal of Intercultural Studies, 23, 167-187.
Martin, D. B. (2010, March). Not-so-strange bedfellows: Racial projects and the mathematics education enterprise. In Proceedings of the Mathematics Education and Society 6th International Conference (pp. 57-79).
Mason, J. (1988). Learning and doing mathematics. Macmillan International Higher Education.
Mason, J., & Waywood, A. (1996). The role of theory in mathematics education and research. In International handbook of mathematics education (pp. 1055-1089). Springer, Dordrecht.
MINED/DNESG. (2004). Programas da disciplina de Matemática do 1 Ciclo do Ensino Secundário Geral [Mathematics subject syllabus for the I Cycle of the Secondary School] . Maputo, Moçambique: Ministério da Educação.
MINED. (2010). Regulamento de avaliação do Ensino Secundário Geral. Diploma Ministerial no 190/2010. Maputo, Moçambique: Ministério da Educação.
Moschkovich, J. (2002, July). Methodological challenges in studying bilingual mathematics learners. Paper presented at the multilingual mathematics group meeting, Norwich, England.
Moschkovich, J. (2010a). Language(s) and learning mathematics: Resources, challenges and issues for research. In J. Moschkovich (Ed.), Language and mathematics education: Multiple perspectives and directions for research (pp. 1-28). Charlotte, NC: Information Age .
Moschkovich, J. (2010b). Recommendations for research on language and mathematics education. In J. Moschkovich (Ed.), Language and mathematics education: Multiple perspectives and directions for research (pp. 151-170). Charlotte, NC: Information Age.
Maho, J. (2001). The Bantu area:(towards clearing up) a mess. Africa & Asia, 1, 40-49.
Mutemba, B. (2010). Innovation or not? Consitency in the curriculum prescription in the new curriculum in Mozambique. In U. Gellert, E. Jablonka & C. Morgan (Eds). Proceedings of the sixth International Mathematics Education and Society conference (pp. 349-357). Germany: Freie Universität Berlin.
Mutemba, B. (2012). Pedagogic Practice Between Tradition and Renewal A Study of the New Mathematics Curriculum in Mozambique. Doctoral thesis. Luleå, Sweden: Luleå University of Technology.
Mutemba, B., & Jablonka, E. (2008). The Interpretational space in the curriculum: Intentions and interpretations of mathematical reasoning in thenew curriculum for secondary schools in Mozambique. In J.F. Matos, P. Valero & K. Yasukawa (Eds.). Proceedings of the fifth international Mathematics Education and Society conference (pp. 154-157). Portugal: Universidade de Lisboa and Aalborg University.
Oppenheim, A. N. (1992). Questionnaire design and attitude measurement. London, UK: Heineman.
Posner, G., & Gertzog, W. (1982). The clinical interview and measurement of conceptual change. Science Education, 66, 195-209.
Radford, L. (2003). Onthe Epistemological Limits of language: Mathematical and social Practice during the Renaissance. Educational Studies in Mathematics. 52 (2), 123-150.
Ríordáin, M. N. (2010). Where did it all go right? The socio-political development of Gaeilge as a medium for learning mathematics in Ireland. In Mathematics Education and Society Conference (p. 387).
Sanders, M., & Mokuku, T. (1994). How valid is face validity? Proccedings of the 2nd annual meeting of the Southern African Association for Research and Development in Mathematics and Science Education. South Africa: Univesity of Durban.
Secada, W. G. (1992). Race, ethnicity, social class, language, and achievement in mathematics. In D. Grows, Handbook of research on mathematics teaching and learning: A project of the National Council of Teachers of Mathematics (pp. 623-660). New York, US: Macmillan .
Taylor, N., & Vinjevold, P. (1999). Teaching and learning in South African schools. Getting Learning Right. Johannesburg: Wits, Joint Education Trust. Using African Languages for Teacher Education.
Usiskin, Z. (1988). Conceptions of school algebra and uses of variables. In A. F. Coxford (Ed.), The ideas of algebra, K-12 (1988 Yearbook of the NCTM) (pp. 8-19). Reston, VA: NCTM.
Usiskin, Z. (1997). Doing Algebra in Grade k-4. Teaching Children Mathematics, 3, 346-356.
Veel, R. (1997). Learning how to mean scientifically speaking: Apprenticeship into discourse in the secondary school. In F. Christie, & J. R. Martin, (Eds.). Genre and institutions social process in the workplace and school (pp. 161-195). London, UK: Continuum.
Wheeler, D. (1996). Reflections on different approaches to algebra. In N. Bednarz, & L. Lee (Eds.), Approaches to algebra: Perspectives for research and teaching (pp. 317-325). Dordrecht, The Netherlands: Dordrecht, The Netherlands.
Zevenbergen, R. (1995). The research story collection. In J. Mousley, M. Robson, & D. Calquhoun (Ed.), Discourse analysis of the classroom (pp. 78-87). Geelong, Australia: Deakin University Press.
Zevenbergen, R. (1998). Gender, media and conservative politics. In C. Keitel (Ed.), Social justice and mathematics education: Gender, class ethnicity and politics of schooling (pp. 59-68). Germany: IOWME and Freie Universitat Berlin.
Zevenbergen, R. (2000). Cracking the code of mathematics: school success as a functional of linguistic, social and cultural background. In J. Boaler (Ed.), Multiple perspectives on Mathematics teaching and learning (pp. 201-223). Westport, CT: Ablex
Zevenbergen, R. (2001). Mathematics, social class, and linguistic capital: An analysis of mathematics classroom Interactions. In B. Atweh, H. Forgasz, & B. Nebres (Eds.), Sociocultural research on mathematics education: An international perspective (pp. 201-215). Mahwah, NJ: Lawrence Erlbaum & Association.
Downloads
Publicado
Como Citar
Edição
Seção
Licença
Copyright (c) 2020 Revista Latinoamericana de Etnomatemática
Este trabalho está licenciado sob uma licença Creative Commons Attribution 4.0 International License.
Autoria
Uma vez que o artigo seja aceito pela Revista Latinoamericana de Etnomatemática, os/as autores transferem os direitos de publicar e distribuir o texto eletronicamente, assim como para arquivar e torna-lo acessível online.
Os autores podem distribuir seu próprio material sem a permissão da Revista Latinoamericana de Etnomatemática, mas devem sempre esclarecer que a versão original esta em http://www.revista.etnomatematica.org
Copyright © 2008, Revista Latinoamericana de Etnomatemática. Todo o conteúdo da Revista Latinoamericana de Etnomatemática está disponível sob a Licencia Creative Commons Atribución 4.0 Internacional e pode ser usado livremente dando crédito aos autores e da revista, conforme é estabelecido por esta licença.
