Relaciones entre el conocimiento conceptual y el procedimental en el aprendizaje de las fracciones
DOI:
https://doi.org/10.18861/cied.2016.7.1.2573Palabras clave:
aprendizaje matemático, fracciones, conocimiento conceptual, conocimiento procedimental, niñosResumen
El objetivo de este trabajo fue analizar las relaciones entre el conocimiento conceptual y el procedimental de las fracciones durante su aprendizaje. Para esto se efectuó una búsqueda bibliográfica en las bases de datos ERIC, PsycInfo, Scielo y Redalyc, con los siguientes términos en español y sus equivalentes en inglés: fracciones (fractions), conocimiento conceptual (conceptual knowledge), conocimiento procedimental (procedural knowledge) y niños (children), combinados de diferente forma con el operador booleano AND (Y). Los resultados de esta búsqueda permitieron hallar quince artículos empíricos que pueden clasificarse en cuatro grupos de investigaciones: las que indican una relación bidireccional, las que sugieren una relación unidireccional, las que muestran cierta independencia o restricciones en su vinculación y, por último, las que señalan que las relaciones varían según los sujetos. Esta falta de acuerdo podría explicarse por ciertas diferencias metodológicas de los estudios, por ejemplo, diferencias en el grado de consolidación del conocimiento de las fracciones de los participantes, el sentido conceptual o la habilidad procedimental estudiada, el tipo de enseñanza matemática recibida, etc. Por ello se sugiere que, para profundizar la comprensión de las relaciones entre el conocimiento conceptual y procedimental de las fracciones, estos aspectos metodológicos deben ser controlados.
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Ancker, J. S. & Kaufman, D. (2007). Rethinking health numeracy: a multidisciplinary literature review. Journal of the American Medical Informatics Association, 14(6), 713–21.
Baron, R. M. & Kenny, D. A. (1986). The moderator–mediator variable distinction in social psychological research: Conceptual, strategic, and statistical considerations. Journal of personality and social psychology, 51(6), 1173.
Baroody, A. J. (2003). The development of adaptive expertise and flexibility: the integration of conceptual and procedural knowledge. Mahwah, Nueva Jersey: Lawrence Erlbaum Associates.
Behr, M.J.; Harel, G.; Post, T. & Lesh, R. (1993). Rational numbers: Toward a semantic analysis-emphasis on the operator construct, en T.P. Carpenter, E. Fennema and T.A. Romberg (eds.), Rational Numbers: An Integration of Research pp. 13–47. Nueva Jersey: Lawrence Erlbaum Associates.
Bisanz, J. & LeFevre, J. A. (1992). Understanding elementary mathematics. Advances in psychology, 91, 113-136.Byrnes, J. P. & Wasik, B. A. (1991). Role of conceptual knowledge in mathematical procedural learning. Developmental Psychology, 27(5), 777.
Charalambous, C. Y. & Pitta-Pantazi, D. (2007). Drawing on a theoretical model to study students’ understandings of fractions. Educational Studies in Mathematics, 64(3), 293-316.
Clark, K. E. (1988). The importance of developing leadership potential of youth with talent in mathematics and science. En J. Dreyden; S. A. Gallagher; G. E. Stanley & R. N. Sawyer (Eds.), Report to the National Science Foundation: Talent Identification Program/National Science Foundation Conference on Academic Talent (pp. 95–104). Durham, North Carolina: National Science Foundation.
Fuchs, L. S.; Schumacher, R. F.; Long, J.; Namkung, J.; Hamlett, C. L.; Cirino, P. T. ... & Changas, P. (2013). Improving at-risk learners’ understanding of fractions. Journal of Educational Psychology, 105(3), 683.
Fuchs, L. S.; Schumacher, R. F.; Sterba, S. K.; Long, J.; Namkung, J.; Malone, A.; ... & Changas, P. (2014). Does working memory moderate the effects of fraction intervention? An aptitude–treatment interaction. Journal of Educational Psychology, 106(2), 499.
Fuson, K. C. (1998). Pedagogical, mathematical, and real-world conceptual-support nets: A model for building children’s multidigit domain knowledge. Mathematical Cognition, 4(2), 147-186.
Geary, D. C. (1994). Children’s mathematical development: Research and practical applications. American Psychological Association.
Gelman, R. & Williams, E. M. (1998). Enabling constraints for cognitive development and learning: Domain specificity and epigenesis.
Greeno, J. G.; Riley, M. S. & Gelman, R. (1984). Conceptual competence and children’s counting. Cognitive Psychology, 16(1), 94-143.
Grinyer, J. (2005). Literacy, numeracy and the labour market. Londres: DfESHalford, G. S. (2014). Children’s understanding: The development of mental models. Psychology Press.
Hallett, D.; Nunes, T. & Bryant, P. (2010). Individual differences in conceptual and procedural knowledge when learning fractions. Journal of Educational Psychology, 102(2), 395.
Hallett, D.; Nunes, T.; Bryant, P. & Thorpe, C. M. (2012). Individual differences in conceptual and procedural fraction understanding: The role of abilities and school experience. Journal of Experimental Child Psychology, 113(4), 469-486.
Hecht, S. A. & Vagi, K. J. (2010). Sources of group and individual differences in emerging fraction skills. Journal of educational psychology, 102(4), 843.
Hecht, S. A. & Vagi, K. J. (2012). Patterns of strengths and weaknesses in children’s knowledge about fractions. Journal of Experimental Child Psychology, 111(2), 212-229.
Hiebert, J., & Wearne, D. (1986). Procedures over concepts: The acquisition of decimal number knowledge.
Hiebert, J. (2013). Conceptual and procedural knowledge: The case of mathematics. Routledge.
Hoffer, T. B.; Venkataraman, L.; Hedberg, E. C. & Shagle, S. (2007). Final report on the national survey of algebra teachers for the National Math Panel. Retrieved March, 25, 2011.
Karmiloff-Smith, A. (1992). Beyond Modularity: A Developmental Perspective on Cognitive Science. Cambridge, MA: MIT Press.
Kerslake, D. (1986). Fractions: Children’s Strategies and Errors. A Report of the Strategies and Errors in Secondary Mathematics Project. Berkshire: NFER-NELSON Publishing Company, Ltd.
Kieren, T. E. (1976). On the mathematical, cognitive, and instructional foundations of rational numbers, en R. Lesh (ed.), Number and Measurement: Papers from a Research Workshop ERIC/SMEAC, pp. 101–144. Columbus.
Kieren, T. E. (1993). Rational and fractional numbers: From quotient fields to recursive understanding. Rational numbers: An integration of research, 49-84.
Mack, N. K. (1990). Learning fractions with understanding: Building on informal knowledge. Journal for research in mathematics education, 16-32.
National Mathematics Advisory Panel (2008). Foundations for success: The final report of the national mathematics advisory panel. Washington, DC: U.S. Department of Education. Recuperado de http://www2.ed.gov/about/bdscomm/list/mathpanel/report/final-report.pdf
Osana, H. P. & Pitsolantis, N. (2013). Addressing the struggle to link form and understanding in fractions instruction. British Journal of Educational Psychology, 83(1), 29-56.
Paglin, M. & Rufolo, A. M. (1990). Heterogeneous human capital, occupational choice, and male–female earnings differences. Journal of Labor Economics, 8, 123–144.
Parsons, S. & Bynner, J. (2005). Does numeracy matter more? National Research and Development Centre for Adult Literacy and Numeracy. Research Report London: Institute of Education. Recuperado de: http://eprints.ioe.ac.uk/4758/1/parsons2006does.pdf
Peck, D. M. & Jencks, S. M. (1981). Conceptual issues in the teaching and learning of fractions. Journal for Research in Mathematics Education, 339-348.
Peled, I. & Segalis, B. (2005). It’s not too late to conceptualize: Constructing a generalized subtraction schema by abstracting and connecting procedures. Mathematical Thinking and Learning, 7(3), 207-230.
Rittle-Johnson, B. & Schneider, M. (2014). Developing conceptual and procedural knowledge of mathematics. En R. Kadosh & A. Dowker (Eds), Oxford Handbook of Numerical Cognition. Oxford University Press.
Rittle-Johnson, B.; Schneider, M. & Star, J. R. (2015). Not a One-Way Street: Bidirectional Relations between Procedural and Conceptual Knowledge of Mathematics. Educational Psychology Review, 1-11.
Rittle-Johnson, B. & Siegler, R. S. (1998). The relation between conceptual and procedural knowledge in learning mathematics: a review. En C. Donlan (Ed.), The Development of Mathematical Skills (pp. 75–110). Londres: Psychology Press.
Rittle-Johnson, B.; Siegler, R. S. & Alibali, M. W. (2001). Developing conceptual understanding and procedural skill in mathematics: an iterative process. Journal of Educational Psychology, 93, 346–362. doi: 10.1037//0022–0663.93.2.346
Rivera-Batiz, F.L. (1992). Quantitative literacy and the likelihood of employment among young adults in the United States. Journal of Human Resources, 27 (2), 313–328.
Rose, H. & Betts, J.R. (2004). The effect of high school courses on earnings. Review of Economics and Statistics, 86 (2), 497–513.
Sadler, P. M., & Tai, R. H. (2001). Success in introductory college physics: The role of high school preparation. Science Education, 85(2), 111-136.
Schneider, M. & Stern, E. (2010). The developmental relations between conceptual and procedural knowledge: A multimethod approach. Developmental Psychology, 46(1), 178.
Siegler, R. S.; Duncan, G. J.; Davis-Kean, P. E.; Duckworth, K.; Claessens, A.; Engel, M.; ... & Chen, M. (2012). Early predictors of high school mathematics achievement. Psychological science, 23(7), 691-697.
Siegler, R. S. & Stern, E. (1998). Conscious and unconscious strategy discoveries: a microgenetic analysis. Journal of Experimental Psychology: General, 127, 377–397. doi: 10.1037/0096–3445.127.4.377.
Siegler, R. S.; Thompson, C. A. & Schneider, M. (2011). An integrated theory of whole number and fractions development. Cognitive psychology, 62(4), 273-296.
Vamvakossi, X. & Vosniadou, S. (2004). Understanding the structure of the set of rational numbers: A conceptual change approach. Learning and Instruction, 14(5), 453-467.
Vamvakossi, X. & Vosniadou, S. (2010). How many decimals are there between two fractions? Aspects of secondary school students’ understanding of rational numbers and their notation. Cognition and instruction, 28(2), 181-209.
Vizcarra, R. E. & Sallán, J. M. G. (2005). Modelos de medida para la enseñanza del número racional en Educación Primaria. Unión: Revista Iberoamericana de Educación Matemática, (1), 17-35.
Yoshida, H. & Sawano, K. (2002). Overcoming cognitive obstacles in learning fractions: Equal "partitioning and equal"whole. Japanese Psychological Research, 44(4), 183-195.