El origen del error de inversión y las bases neuronales subyacentes

  1. Ventura Campos, Noelia
  2. Arnau, David
  3. González-Calero, José Antonio
Revista:
Revista de educación de la Universidad de Granada

ISSN: 0214-0484

Ano de publicación: 2018

Número: 25

Páxinas: 281-297

Tipo: Artigo

DOI: 10.30827/REUGRA.V25I0.128 DIALNET GOOGLE SCHOLAR lock_openAcceso aberto editor

Obxectivos de Desenvolvemento Sustentable

Resumo

An important research line in mathematical teaching and learning and, more specifically, in the solving of word problems in an algebraic way, is focused on establishing the cognitive processes involved from the identification of a mathematical relationship of problem expressed verbally to the subsequent representation of algebraic expressions. A case in which a considerable number of students recognize the conceptual scheme, but are not able to translate this to a correct mathematical expression would be the error known as reversal error. This error takes place in word problems that involve additive and multiplicative comparison. The error is often made on tasks similar to the following: “Write an equation based on the following statement: ‘There are six times as many students as professors at this university.’ Use S for the number of students and P for the number of professors.” A common incorrect answer is P = 6 · S, caused by reversing the order of the letters from the correct answer S = 6 · P. The current literature has only been able to establish relationships between mathematical variables. However, concerning the reversal error these studies have not taken students’ brain development into consideration when analysing students’ learning or have not explored the causal relation between the features of problems and their difficulty.The main objective of this research is to reveal the underlying neural bases linked to individual differences between students when solving arithmetic-algebraic word problems and, in particular, when reversal errors are made.

Referencias bibliográficas

  • Anderson, J. R., Betts, S., Ferris, J. L., y Fincham, J. M. (2012). Tracking children’s mental states while solving algebra equations. Hum. Brain Mapp. 33, 2650–2665. doi: 10.1002/hbm.21391
  • Anderson, J. R., Fincham, J. M., Qin, Y., y Stocco, A. (2008). A central circuit of the mind. Trends Cogn. Sci. 12, 136–143.
  • Blakemore, S. J. (2012). Imaging brain development: the adolescent brain. Neuroimage 61, 397–406. doi: 10.1016/j.neuroimage.2011.11.080
  • Castro, E., Castro, E., Rico, L., Gutiérrez, J., Tortosa, A., Segovia, A., … Fernández, F. (1998). Problemas aritméticos compuestos de dos relaciones. En L. Rico y M. Sierra (Eds.), Actas del Primer Simposio de la Sociedad Española de Investigación en Educación Matemática (pp. 63-76). Zamora: SEIEM.
  • Charles, R., y Lester, F. (1982) Teaching problem solving. What, Why, How. Palo alto, CA: Dale seymour Pu.
  • Clement, J. J. (1982). Algebra word problem solutions: Thought processes underlying a common misconception. Journal for Research in Mathematics Education, 13(1), 16–30.
  • Clement, J., Lochhead, J., y Monk, G. (1981). Translation difficulties in learning mathematics. The American Mathematical Monthly, 88(4), 286–290. doi:10.1080/17470211003787619
  • De Smedt, B., Holloway, I. D., y Ansari, D. (2011). Effects of problem size and arithmetic operation on brain activation during calculation in children with varying levels of arithmetical fluency. NeuroImage, 57(3), 771–781.
  • Dehaene, S. (1997). The Number Sense. NewYork, NY: Oxford University Press.
  • Giedd, J. N., Blumenthal, J., Jeffries, N. O., Castellanos, F. X., Liu, H., Zijdenbos, A.,...Rapoport, J.L. (1999). Brain development during childhood and adolescence: a longitudinal MRI study. Nat.Neurosci. 2, 861–863. doi: 10.1038/13158
  • Giedd, J. N., y Rapoport, J. L. (2010). Structural MRI of Pediatric Brain Development: What Have We Learned and Where Are We Going? Neuron, 67(5), 728–734.
  • Gogtay, N., Giedd, J.N., Lusk, L., Hayashi, K.M., Greenstein, D., Vaituzis, A.C.,... Thompson P.M. (2004) Dynamic mapping of human cortical development during childhood through early adulthood. Proc. Natl. Acad. Sci. U. S. A. 101, 8174–8179
  • González-Calero, J. A., Arnau, D., y Laserna-Belenguer, B. (2015). Influence of additive and multiplicative structure and direction of comparison on the reversal error. Educational Studies in Mathematics, 89(1), 133-147.
  • Halmos, P. R. (1980). The Heart of Mathematics. The American Mathematical Monthly, 87 (7), 519-524.
  • Izard, V., Dehaene-Lambertz, G., y Dehaene, S. (2008) Distinct cerebral pathways for object identity and number in human infants. PLoS Biol 6,e11.
  • Kintsch, W., y Greeno, J. G. (1985). Understanding and Solving Word Arithmetic Problems. Psychological Review, 92(1), 109–129.
  • Kroger, J. K., Nystrom, L. E., Cohen, J. D., y Johnson-Laird, P. N. (2008). Distinct neural substrates for deductive and mathematical processing. Brain Res., 1243, 86–103. doi:10.1016/j.brainres.2008.07.128
  • Lee, K., Lim, Z. Y., Yeong, S. H., Ng, S. F., Venkatraman, V., y Chee, M. W. (2007). Strategic differences in algebraic problem solving: neuroanatomical correlates. Brain Res., 1155, 163–171.
  • Lopez-Real, F. (1995). How important is the reversal error in algebra? En S. Flavel et al. (Eds.), GALTHA (Proceedings of the 18th Annual Conference of the Mathematics Education Research Group of Australasia) (pp. 390–396). Darwin, Australia: MERGA.
  • MacGregor, M., y Stacey, K. (1993). Cognitive models underlying students’ formulation of simple linear equations. Journal for Research in Mathematics Education, 24(3), 217-232.
  • Marshall, S. P. (1995). Schemas in problem solving. New York: Cambridge University Press.
  • Nathan, M. J., Kintsch, W., y Young, E. (1992). A Theory of Algebra-Word-Problem Comprehension and Its Implications for the Design of Learning Environments. Cognition and Instruction, 9(4), 329–389.
  • National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Autor.
  • Nieder, A. y Miller, E.K. (2004) A parieto-frontal network for visual numerical information in the monkey. Proc Natl Acad Sci U S A, 101(19),7457-7462.
  • OECD (2014a), PISA 2012 Results: Creative Problem Solving: Students’ Skills in Tackling Real-Life Problems (Volume V). PISA, OECD Publishing.
  • OECD (2014b). PISA 2012 Results: What Students Know and Can Do – Student Performance in Mathematics, Reading and Science (Volume I). PISA, OECD Publishing. http://dx.doi.org/10.1787/9789264201118-en
  • Pawley, D., Ayres, P., Cooper, M., y Sweller, J. (2005). Translating words into equations: a cognitive load theory approach. Educational Psychology, 25(1), 75-97.
  • Piazza, M., Izard, V., Pinel, P., Le Bihan, D., y Dehaene, S. (2004) Tuning curves for approximate numerosity in the human intraparietal sulcus. Neuron, 44, 547-555.
  • Psychology Software Tools, Inc. [E-Prime 3.0]. (2016). Retrieved from https://www.pstnet.com.
  • Puig, L. (1996). Elementos de resolución de problemas. Granada: Comares.
  • Puig, L. (1998). La didáctica de las matemáticas como tarea investigadora. En Investigar y enseñar. Variedades de la Educación Matemática (pp. 63–75). Bogotá: una empresa docente.
  • Puig, L. y Cerdán, F. (1988). Problemas aritméticos escolares. Madrid: Síntesis.
  • Qin, Y., Carter, C. S., Silk, E. M., Stenger, V. A., Fissell, K., Goode, A.,...Anderson, J.R (2004) The change of the brain activation patterns as children learn algebra equation solving. Proc. Natl. Acad. Sci. U. S. A. 101, 5686–5691
  • Riley, M. S., Greeno, J. G., y Heller, J. L. (1983). Development of Children’s Problem-Solving Ability in Arithmetic. En H. P. Ginsburg (Ed.), The development of mathematical thinking (pp. 153-196). New York: Academic Press.
  • Rivera, S. M., Reiss, A. L., Eckert, M. A., y Menon, V. (2005). Developmental changes inmental arithmetic: evidence for increased functional specialization in the left inferior parietal cortex. Cereb. Cortex, 15, 1779–1790. doi: 10.1093/cercor/bhi055
  • Rosnick, P. (1981). Some Misconceptions concerning the Concept of Variable. Mathematics Teacher, 74(6), 418-420.
  • Sowell, E. R., y Jernigan, T.L. (1998) Further MRI evidence of late brain maturation: limbic volume increases and changing asymmetries during childhood and adolescence. Dev. Neuropsychol. 14, 599–617
  • Starr, A., Libertus, M. E., y Brannon, E. M. (2013). Number sense in infancy predicts mathematical abilities in childhood. Proc. Natl. Acad. Sci. U.S.A., 110, 18116–18120. doi: 0.1073/pnas.1302751110
  • Sweller, J. (1988). Cognitive load during problem solving: Effects on learning. Cognitive Science, 12(2), 257-285.
  • Vergnaud, G. (1983). Multiplicative structures. En R. Lesh y M. Landau (Eds.), Acquisition of mathematics concepts and processes (pp. 127-174). New York: Academic Press.
  • Weber, K., y Leikin, R. (2016). Recent advances in research on problem solving and problem posing. En A. Gutiérrez, G. C. Leder, y P. Boero (Eds.), The Second Handbook of Research on the Psychology of Mathematics Education (pp. 353–382). Rotterdam: Sense Publishers.
  • Wierenga L, Langen M, Ambrosino S, van Dijk S, Oranje B y Durston S. (2014). Typical development of basal ganglia, hippocampus, amygdala and cerebellum from age 7 to 24. Neuroimage, 96, 67-72.
  • Wollman, W. (1983). Determining the Sources of Error in a Translation from Sentence to Equation. Journal for Research in Mathematics Education, 14(3), 169-181.
  • Zamarian, L., Ischebeck, A., y Delazer, M. (2009). Neuroscience of learning arithmetic—Evidence from brain imaging studies. Neuroscience & Biobehavioral Reviews, 33(6), 909–925.
Fonte de datos: Dialnet