El origen del error de inversión y las bases neuronales subyacentes

• Autores: Noelia Ventura Campos , David Arnau Vera , José Antonio González-Calero Somoza
• Localización: Revista de educación de la Universidad de Granada, ISSN 0214-0489, Nº 25, 2018, págs. 281-297
• Idioma: español
• DOI: 10.30827/reugra.v25i0.128
• Títulos paralelos:
  • The Origin of the Reversal Error and the Underlying Neural Bases
• Enlaces
  • Texto completo
• Resumen
  • español

    Una línea de investigación importante en la enseñanza-aprendizaje de las matemáticas, más concretamente en la resolución algebraica de problemas verbales, es la centrada en identificar los procesos cognitivos que se ponen en juego desde que un sujeto identifica una relación matemática en un problema hasta que la expresan mediante una expresión algebraica. Un caso en el que un número importante de estudiantes reconocen el esquema conceptual, pero no son capaces de plasmar una expresión matemática correcta sería el conocido como error de inversión. Este error aparece en los problemas en los que se plantean proposiciones verbales de comparación aditiva y multiplicativa. El nombre del error proviene de que ante la tarea “Escribe una ecuación para representar el enunciado siguiente: ‘Hay seis veces tantos estudiantes como profesores en esta universidad’. Usa E para el número de estudiantes y P para el número de profesores” (Clement, Lochhead y Monk, 1981, p. 288) la mayoría de las respuestas incorrectas fueron P = 6·E, lo que implicaría invertir el orden de las letras frente a la respuesta correcta E = 6·P. Diversos estudios han tratado de identificar el origen del error. Sin embargo, únicamente se han conseguido establecer relaciones entre variables y establecer hipótesis plausibles de posibles procesos cognitivos erróneos. En estos estudios no se ha tomado en consideración la importancia que tiene el desarrollo cerebral del alumnado en el aprendizaje ni su potencial explicativo para justificar las relaciones causales observadas entre características de los problemas y su dificultad.El objetivo principal de esta investigación es identificar las bases neurales subyacentes ligadas a las diferencias individuales entre los participantes durante la resolución de problemas verbales aritmético-algebraicos, más concretamente en el error de inversión.

  • English

    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.

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