Desde estrategias aditivas hasta estrategias proporcionales: Características identificadas con estudiantes de Educación Básica Media y Superior de Ecuador

  1. Ceneida Fernández 1
  2. Pedro Ivars 1
  3. Francisco Rojas 2
  4. Salvador Castillo 1
  1. 1 Universitat d'Alacant
    info

    Universitat d'Alacant

    Alicante, España

    ROR https://ror.org/05t8bcz72

  2. 2 Universidad Central del Ecuador
    info

    Universidad Central del Ecuador

    Quito, Ecuador

    ROR https://ror.org/010n0x685

Revista:
Educación matemática

ISSN: 1665-5826 0187-8298

Año de publicación: 2024

Volumen: 36

Número: 2

Páginas: 68-91

Tipo: Artículo

DOI: 10.24844/EM3602.03 DIALNET GOOGLE SCHOLAR lock_openDialnet editor

Otras publicaciones en: Educación matemática

Resumen

Estudios previos han mostrado que, al resolver situaciones proporcionales y aditivas, los estudiantes transitan desde usar indiscriminadamente estrategias aditivas a usar indiscriminadamente estrategias proporcionales. Además, el tipo de razón y la naturaleza de las cantidades parece influir en el uso de estas estrategias. Este estudio explora qué estrategias usan los estudiantes de Educación Básica Media y Superior de Ecuador cuando resuelven problemas aditivos y proporcionales de valor ausente con razones ente ras/no enteras y cantidades discretas/continuas. Los resultados muestran una tendencia diferente: cuando los estudiantes dejan de usar indiscriminada mente estrategias aditivas en situaciones proporcionales y aditivas, no usan indiscriminadamente la proporcionalidad. Estos estudiantes usan otros procedimientos erróneos para resolver los problemas proporcionales. Además, ambas variables influyeron significativamente: (I) se usaron más las estrategias aditivas con relaciones/razones no enteras y las proporcionales con relaciones/razones enteras; y (II) se usaron mayormente las estrategias proporcionales en problemas proporcionales con cantidades discretas y las aditivas en problemas aditivos con cantidades continuas

Referencias bibliográficas

  • Begolli, K. N., Booth, J. L., Holmes, C. A., y Newcombe, N. S. (2020). How many apples make a quarter? The challenge of discrete proportional formats. Journal of Experimental Child Psychology, 192, 104774. https://doi.org/10.1016/j.jecp.2019.104774
  • Ben-Chaim, D., Fey, J. T., Fitzgerald, W. M., Benedetto, C., y Miller, J. (1998). Proportional reasoning among 7th grade students with different curricular experiences. Educational Studies in Mathematics, 36(3), 247-273. https://doi.org/10.1023/a:1003235712092
  • Boyer, T. W., y Levine, S. C. (2015). Prompting children to reason proportionally: Processing discrete units as continuous amounts. Developmental Psychology, 51(5), 615–620. https://doi.org/10.1037/a0039010
  • Boyer, T. W., Levine, S. C., y Huttenlocher, J. (2008). Development of proportional reasoning: Where young children go wrong. Developmental Psychology, 44(5), 1478–1490. https:// doi.org/10.1037/a0013110
  • Cramer,K. A., Post, T., y Currier, S. (1993). Learning and teaching ratio and proportion: Research implications: Middle grades mathematics. En D. Owens (Ed.), Research ideas for the classroom: Middle grades mathematics (pp. 159-178). Macmillan Publishing Company.
  • De Bock, D., Van Dooren, W., Janssens, D., y Verschaffel, L. (2007). The illusion of linearity: From analysis to improvement. Springer Science & Business Media.
  • Degrande, T., Verschaffel, L., y Van Dooren, W. (2020). To add or to multiply in open problems? Unraveling children’s relational preference using a mixed-method approach. Educational Studies in Mathematics, 104(3), 405-430. https://doi.org/10.1007/s10649-020-09966-z
  • Fernández, C., y Llinares, S. (2011). De la estructura aditiva a la multiplicativa: efecto de dos variables en el desarrollo del razonamiento proporcional. Infancia y Aprendizaje, 34(1), 67-80. https://doi.org/10.1174/021037011794390111
  • Fernández, C., y Llinares, S. (2012). Características del desarrollo del razonamiento proporcional en la Educación Primaria y Secundaria. Enseñanza de las Ciencias, 30(1), 129-142. https://doi.org/10.5565/rev/ec/v30n1.596
  • Fernández, C., Llinares, S., Van Dooren, W., De Bock, D., y Verschaffel, L. (2011). Effect on number structure and nature of quantities on secondary school students’ proportional reasoning”. Studia Psychologica, 53(1), 69-81.
  • Fernández, C., Llinares, S., Van Dooren, W., De Bock, D., y Verschaffel, L. (2012). The development of students’ use of additive and proportional methods along primary and secondary school. European Journal of Psychology of Education, 27(3), 421-438. https://doi.org/10.1007/s10212-011-0087-0
  • Freudenthal, H. (1999). Ratio and proportionality. En H. Freudenthal (Ed.), Didactical phenomenology of mathematical structures (pp. 178–209).Kluwer Academics Publishers.
  • Harel, G., y Behr, M. (1989). Structure and hierarchy of missing-value proportion problems and their representations. Journal of Mathematical Behavior, 8(1), 77-119.
  • Harel, G., y Confrey, J. (1994). The development of multiplicative reasoning in the learning of mathematics. State University of New York Press.
  • Hart, K. (1988). Ratio and proportion. En J. Hiebert y M. Behr (Eds.), Number concepts and operations in the middle grades, (pp. 198-219).National Council of Teachers of Mathematics and Lawrence Erlbaum Associates.
  • Hurst, M. A., y Cordes, S. (2018). Attending to relations: Proportional reasoning in 3- to 6-yearold children. Developmental Psychology, 54(3), 428–439. https://doi.org/10.1037/dev0000440
  • Jeong, Y., Levine, S. C., y Huttenlocher, J. (2007). The development of proportional reasoning: Effect of continuous versus discrete quantities. Journal of Cognition and Development, 8(2), 237-256. https://doi.org/10.1080/15248370701202471
  • Jiang, R., Li, X., Fernández, C., Fu, X. (2017). Students’ performance on missing-value word problems: a cross-national developmental study. European Journal of Psychology of Education 32, 551–570. https://doi.org/10.1007/s10212-016-0322-9
  • Kaput, J. y West, M. M. (1994). Missing-value proportional reasoning problems: Factors affecting informal reasoning patterns. En G. Harel y J. Confrey (Eds.), The development of multiplicative reasoning in the learning of mathematics, (pp. 235-287). State University of New York Press. Karplus, R., Pulos, S., & Stage, E. K. (1983). Early adolescents’ proportional reasoning on ‘rate’ problems. Educational Studies in Mathematics, 14(3), 219-233. https://doi. org/10.1007/BF00410539
  • Lamon, S. (1994). Ratio and proportion: Cognitive foundations in unitizing and norming. En G. Harel y J. Confrey (Eds.), The development of multiplicative reasoning in the learning of Mathematics, (pp. 89–120). State University of New York Press.
  • Lamon, S. (1999). Teaching fractions and ratios for understanding. Essential content knowledge and instructional strategies for teacher. Lawrence Erlbaum Associates. Ley Orgánica de Educación Intercultural (LOEI), 17 de febrero de 2016, relativa a los currículos de educación general básica para los subniveles de preparatoria, elemental, media y superior; y, el currículo de nivel de bachillerato general unificado, con sus respectivas cargas horarias. Acuerdo Ministerial Nro. MINEDUC-ME-2016- 00020-A, de 17 de febrero de 2016.
  • Lo, J., y Watanabe, T. (1997). Developing ratio and proportion schemes: A story of a fifth grader. Journal for Research in Mathematics Education, 28(2), 216-236. https://doi. org/10.5951/jresematheduc.28.2.0216
  • Misailidou, C., y Williams, J. (2003). Diagnostic assessment of children’s proportional reasoning. The Journal of Mathematical Behavior, 22(3), 335-368. https://doi. org/10.1016/S0732-3123(03)00025-7
  • Modestou, M., y Gagatsis, A. (2007). Students’ improper proportional reasoning: A result of the epistemological obstacle of “linearity”. Educational Psychology, 27(1), 75-92. https://doi.org/10.1080/01443410601061462
  • Moss, J., y Case, R. (1999). Developing children’s understanding of the rational numbers: A new model and an experimental curriculum. Journal for Research in Mathematics Education, 30(2), 122-147. https://doi.org/10.2307/749607
  • Pi̇şki̇n, M. (2020). Investigation of middle school students’ solution strategies in solving proportional and non-proportional problems. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 11(1), 1–14. https://doi.org/10.16949/turkbilmat.560349
  • Siemon, D., Breed, M., y Virgona, J. (2005). From additive to multiplicative thinking: The big challenge of the middle years. En J. Mousley, L. Bragg y C. Campbell (Eds.), Proceedings of the 42nd Conference of the Mathematical Association of Victoria, (pp. 278– 286). Mathematical Association of Victoria.
  • Singer, J., Kohn, A., y Resnick, L. (1997). Knowing about proportions in different contexts. En T. Nunes y P. Bryant (Eds.), Learning and teaching mathematics. An international perspective, (pp.115-132). Psychology Press Ltd. Publishers.
  • Spinillo, A. G., y Bryant, P. E. (1999). Proportional reasoning in young children: Part-part comparisons about continuous and discontinuous quantity. Mathematical Cognition, 5(2), 181-197. https://doi.org/10.1080/135467999387298
  • Steinthorsdottir, O. (2006). Proportional reasoning: Variable influencing the problems difficulty level and one’s use of problem solving strategies. En J. Novotná, H. Moraová, M. Krátká y N. Stehlíková (Eds.), Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education vol. 5, (pp. 169-176). PME.
  • Tourniaire, F., y Pulos, S. (1985). Proportional reasoning: A review of the literature. Educational Studies in Mathematics, 16, 181-204.
  • Van Dooren, W., De Bock, D., y 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. https://doi.org/10.1080/07370008.2010.488306
  • Van Dooren, W., De Bock, D., Evers, M., y 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. https://www.jstor.org/stable/40539331
  • Van Dooren, W., De Bock, D., Hessels, A., Janssens, D., y Verschaffel, L. (2005). Not everything is proportional: Effects of age and problem type on propensities for overgeneralization. Cognition and instruction, 23(1), 57-86. https://doi.org/10.1207/ s1532690xci2301_3 Van Dooren, W., De Bock, D., Janssens, D., y 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. https://doi.org/10.2307/30034972
  • Vanluydt, E., Degrande, T., Verschaffel, L., y Van Dooren, W. (2020). Early stages of proportional reasoning: a cross-sectional study with 5-to 9-year-olds. European Journal of Psychology of Education, 35(3), 529-547. https://doi.org/10.1007/s10212-019-00434-8
  • Verschaffel, L., Greer, B., y De Corte, E. (2007). Whole number concepts and operations. En F. Lester (Ed.), Second handbook of research on mathematics teaching and learning, (pp. 557–628). Information Age Publishing.