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Logo Revista Latinoamericana de Investigación en Matemática Educativa

Artículos

Vol. 15 N.º 1 (2012): Marzo

RELACIONES IMPLICATIVAS ENTRE LAS ESTRATEGIAS EMPLEADAS EN LA RESOLUCIÓN DE SITUACIONES LINEALES Y NO LINEALES

Enviado
julho 14, 2023
Publicado
2012-03-01

Resumo

Este estudo analisa as relações envolvidas entre as estratégias usadas por 136 estudantes do primeiro ano do ensino médio na resolução de problemas lineares e não lineares. Em primeiro lugar, são descritas as estratégias utilizadas pelos estudantes, e depois, empregando o software CHIC, são identificadas as relações envolvidas entre elas. Os resultados mostram a importância da compreensão da ideia da razão para identificar as situações lineares, e é feita uma contribuição de informação sobre os possíveis precursores do desenvolvimento da lógica proporcional.

Referências

  1. Alatorre, S. & Figueras, O. (2005). A developmental model for proportional reasoning in ratio comparison tasks. In Chick, H. L. & Vincent, J. L. (Eds.)., Proceedings of the 29 th Conference of the International Group for the Psychology of Mathematics Education. (Vol. 2, pp. 25-32)
  2. Christou, C. & Philippou, G. (2002). Mapping and development of intuitive proportional thinking. Journal of Mathematical Behavior, 20 (3), 321 - 336.
  3. Cramer, K. & Post, T. (1993). Connecting research to teaching proportional reasoning. Mathematics Teacher, 86(5), 404 – 407.
  4. De Bock, D., Van Dooren, W., Janssens, D. & Verschaffel, L. (2002). Improper use of linear reasoning: An in-deph study of the nature and the irresistibility of secondary school students’ errors. Educational Studies in Mathematics, 50(3), 311- 334.
  5. De Bock, D., Van Dooren, W., Janssens, D.& Verschaffel (2007). The illusion of linearity. From analysis to improvement. New York: Springer.
  6. De Bock, D., Verschaffel, L. & Janssens, D. (1998). The predominance of the linear model in secondary school students’ solutions of word problems involving length and area of similar plane figures. Educational Studies in Mathematics, 35 (1), 65 - 83. doi: 10.1023/A:1003151011999
  7. Ebersbach, M., Van Dooren, W., Goudriaan, M. N. & Verschaffel, L. (2010). Discriminating non-linearity from linearity: Its cognitive foundations in five-year-olds. Mathematical Thinking and 19. doi: 10.1080/10986060903465780
  8. Fernández, A. (2009). Razón y proporción. Un estudio en la escuela primaria. Universitat de València. Departament de Didàctica de la Matemática.
  9. Fernández, C. y Llinares, S. (2011). De la estructura aditiva a la multiplicativa: efecto de dos variables en el desarrollo del razonamiento proporcional. Infancia Aprendizaje, 34(1), 67 - 80.
  10. Fernández, C. y Llinares, S. (en prensa). Características del desarrollo del razonamiento proporcional en la educación primaria y secundaria. Enseñanza de las Ciencias.
  11. Fernández, C., Llinares, S., Modestou, M. & Gagatsis, A. (2010). Proportional Reasoning: How task variables influence the development of students’ strategies from Primary to secondary School. Acta Didactica Universitatis Comenianae Mathematics, 10, 1- 18.
  12. Fernández, C., Llinares, S., Van Dooren, W., De Bock, D. & Verschaffel, L. (2010). How do proportional and additive methods develop along primary and secondary school? In M. F. Pinto & T. F. Kawasaki (Eds.), Proceedings of the 34th Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 353 - 360). Belo Horizonte, Brazil: PME
  13. Fernández, C., Llinares, S., Van Dooren, W., De Bock, D. & Verschaffel, L. (2011). Effect of number structure and nature of quantities on secondary school students’ proportional reasoning. Studia psychologica, 53(1), 69 - 81.
  14. Freudenthal, H. (1983). Didactical phenomenology of mathematical structures. Dordrecht: Kluwer. Gras, R., Suzuki, E., Guillet, F. y Spagnolo, F. (F.) (Eds.) (2008). Statistical Implicative analysis. Theory and Applications. London: Springer.
  15. Gagatsis, A., Modestou, M. Elia, I. y Spanoudes, G. (2009). Structural modelling of development of shifts in grasping proportional relational relations underlying problem solving in area and volume. Acta Didactica Universitatis Comenianae, 9, 9-23.
  16. Hart, K. (1981). Children’s understanding of mathematics: 11-16. London: Murray.
  17. Hart, K. (1984). Ratio: Children’s strategies and errors. Windsor, UK: NFER Nelson.
  18. Karplus, R., Pulos, S. & Stage, E. K. (1983). Early adolescents’ proportional reasoning on ‘rate’ problems. Educational Studies in Mathematics 14(3), 219-233.
  19. Lamon, S. (1993). Ratio and proportion: Children’s cognitive and metacognitive processes. In Th. Carpenter, E. Fennema & Th. Romberg (Eds), Rational Numbers. An Integration of Research (pp. 131 - 156). Hillsdale, NJ: Lawrence Erlbaum Associates, Pub.
  20. Lamon, S. (1999). Teaching fractions and ratios for understanding. Essential content knowledge and instructional strategies for teacher. Mahwah, NJ: Lawrence Erlbaum Associates, Pub.
  21. Lamon, S. (2007). Rational numbers and proportional reasoning: Toward a theoretical framework for research. In F. K. Lester, Jr. (ed.), Second Handbook of Research on Mathematics Teaching and Learning pp. 629- 667). NC: Information Age Publishing.
  22. Lesh, R., Post, T. & Behr, M. (1988). Proportional reasoning. In J. Hiebert & M. Behr (Eds.),Number Concepts an Operations in the Middle Grades (pp. 93- 118). Reston, VA: Lawrence Erlebaum y National Council of Teachers of Mathematics.
  23. Misailidou, C. & Williams, J. (2003). Diagnostic assessment of children’s proportional reasoning. Journal of Mathematical Behavior 22 (3), 335 - 368.
  24. Miyakawa, T. & Winslow, C. (2009). Didactical designs for students’ proportional reasoning: an “open approach” and a “fundamental situation”. Educational Studies in Mathematics 72(2), 199-218.
  25. Modestou, M. & Gagatsis, A. (2007). Students’ improper proportional reasoning: A result of the epistemological obstacle of “linearity”. Educational Psychology, 27(1), 75 – 92.
  26. Modestou, M. & Gagatsis, A. (2009-a). Proportional reasoning reformed. In A. Gagatsis, A. Kuzniak, E. Deliyianni y L. Vivier (eds.), First French-Cypriot Conference of Mathematics Education (pp. 19 - 33). Nicosia-Paris: University of Cyprus- University Paris Diderot 7.
  27. Modestou, M. & Gagatsis, A. (2009-b). Proportional Reasoning: The strategies behind the percentages. Acta Academica Universitatis Comenianae Mathematics 9, 25- 40.
  28. Modestou, M. & Gagatsis, A. (2010). Cognitive and meta-cognitive aspects of proportional reasoning. Mathematical Teaching and Learning 12(1), 36 - 53.
  29. Resnick, L. & Singer, J. (1993). Protoquantitative origins of ratio reasoning. In T. Carpenter, E. Fennema, y T. Romberg (eds.), Rational Numbers. An Integration of Research (pp. 107 - 130). Hillsdale, NJ: Lawrence Erlbaum Associates, Inc, Publishers.
  30. Strauss, A. & Corbin, J. (1994). Grounded theory methodology: An overview. In N.K. Denzin y Y. Lincoln (Eds), Handbook of Qualitative Research (pp. 273 - 285). Thousand Oaks: Sage.
  31. Tourniaire, F. & Pulos, S. (1985). Proportional reasoning. A review of literature. Educational Studies in Mathematics 16(2), 181 - 204. doi: 10.1007/BF02400937
  32. Trigueros, M. y Escandón, M.C. (2008). Los conceptos relevantes en el aprendizaje de la graficación. Un análisis a través de la estadística implicativa. Revista Mexicana de Investigación Educativa 13(36), 59 - 85.
  33. Van Dooren, W., De Bock, D., Evers, M. & Verschaffel, L. (2009). Students’ overuse of proportionality on missing-value problems: How numbers may change solutions. Journal for Research in Mathematics Education 40(2), 187 - 211.
  34. Van Dooren, W., De Bock, D., Hessels, A., Janssens, D. & Verschaffel, L. (2005). Not everything is proportional: Effects of age and problem type on propensities of overgeneralization. Cognition and Instruction 23(1), 57 – 86.
  35. Van Dooren, W., De Bock, D., Janssens, D. & Verschaffel, L. (2008). The linear imperative: An inventory and conceptual analysis of students’ overuse of linearity. Journal for Research in Mathematics Education 39(3), 311- 342.
  36. Van Dooren, W., De Bock, D. & Verschaffel, L. (2010). From addition to multiplication… and back: The development of students’ additive and multiplicative reasoning skills. Cognition and Instruction 28(3), 360 - 381.
  37. Van Dooren, W., De Bock, D., Weyers, D. & Verschaffel, L. (2004). Challenging the predictive power of intuitive rules: A replication and extension study on the impact of ‘more A – more B’ and ‘same A- same B’. Educational Studies in Mathematics, 56, 179- 207.
  38. Vergnaud, G. (1983). Multiplicative structures. In R. Lesh & M. Landau (Eds.), Acquisition of Mathematics Concepts and Processes (pp. 128- 175). London: Academic Press, Inc.

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