La transferencia de aprendizaje algorítmico y el origen de los errores en la sustracción

Authors

Ana B. SánchezSalto de línea Universidad de Salamanca, Departamento de Didáctica, Organización y Métodos de Investigación. Salamanca, España.Salto de línea Salto de línea Ricardo López Fernández Salto de línea Universidad de Salamanca, Departamento de Didáctica de las Matemáticas. Salamanca, España.

DOI

10.4438/1988-592X-RE-2011-354-006

Abstract

The transfer of algorithmic learning and the origin of errors in subtraction

The results of the study presented in this paper demonstrate that the influence of formal, intuitive and procedural knowledge in the process of algorithmic learning, the pedagogical context of the classroom and the process of transferring mathematical knowledge are decisive in error generation through mechanisms of analogical transfer. The paper reports this fact in the subtraction algorithm. The answers given by nine children of ages between seven and ten years in a test made up of 20 subtraction problems were analysed. Altogether, the processes executed by the nine children were recorded in 180 subtraction operations. The volume of data obtained via talk-aloud protocols was analysed with the help of the Nud*ist 4.0 statistical program. The study falls within the context of a larger study where the authors analysed a database of 7,140 subtraction operations performed by 357 children between the ages of seven and thirteen years, with the aim of determining whether systematic errors occurred and typing any systematic errors found. The article shows how the errors most commonly found cluster around certain factors of the task. These factors are related to the understanding of essential concepts for the meaningful learning of the ability. In the authors’ opinion, it is essential to help teachers plan how to teach the subtraction algorithm and provide teachers with a specific methodological practice to apply in the classroom; these things would help make the nature of algorithmic processes clearer and reduce error generation in subtraction. Lastly, the paper demonstrates the importance of contextual factors, such as the language used in the teaching process. When children begin learning, they build interpretations of the procedure, based on a series of concepts or specific vocabulary organised within the conceptual field of subtraction.

Keywords

Algorithmic learning, transfer of algorithmic knowledge, primary education, subtraction errors, semantic approach to error, mathematical education, subtraction skills.