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Artículos

Vol. 15 No. 1 (2012): Marzo

IMPLICATIVE RELATIONS BETWEEN STRATEGIES USED IN SOLVING PROPORTIONAL AND NON–PROPORTIONAL PROBLEMS

Submitted
July 14, 2023
Published
2012-03-01

Abstract

This study analyzes the implicative relations between strategies used by 136 first year high school students in solving linear and non-linear problems. First of all, it describes the strategies used by students and then, using the CHIC software, it identifies implicative relations between them. The results demonstrate the importance of understanding the idea of reason in order to identify linear situations and information is provided in relation to possible precursors to the development of proportional reasoning.

References

  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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