Dificultades y errores en la aplicación del algoritmo de la sustracción en estudiantes de universidad. Implicaciones para la construcción de un modelo didáctico

Abstract

Successful control of basic mathematical operations must be one of the aims in compulsory stages of education. To this respect, previous research has shown that a high percentage of Primary Education school children (6-12 years old) make errors when having to solve subtraction (Brown and Burton, 1978; Sánchez, 2005; López and Sánchez, 2007; VanLehn, 1982; Young and O’Shea, 1981). But not much is known about subtraction error among adults. For this reason, this dissertation was centered on university students, in order to analyze the errors and types of errors university students make when solving subtraction. To achieve this aim, 535 university undergraduate students from the Preschool and Primary school Teacher, B.A. in Small and Medium Business Management and Statistics Degrees from the University of Salamanca completed the questionnaire VanLehn (1990), containing twenty different types of subtractions. Wrong answers were categorized following error categorization established by VanLehn (1990) taking as reference the adaptation thereof by Sánchez (2005), to which other types of errors that came up from the analysis were also added. Results have shown that only one in four among university students were able to complete the whole subtraction questionnaire correctly; and that, from a total of 10700 subtraction operations solved, 1.258 (11.76%) had been done wrong. Analyzing the type of error made, the most frequent ones were the same systematic errors made by the school children. This can indicate that the types of error made at early stages of education when learning this algorithm are kept in the time, which may mean that the teaching and learning process to master this algorithm might not have been the appropriate one. In another sense, this dissertation offers new perspectives for the future, as it could have educational implications in order to improve the teaching and learning process of subtraction in early stages of school education.