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The Degree of Abstraction in Solving Addition and Subtraction Problems

Published online by Cambridge University Press:  10 April 2014

Vicente Bermejo  and
Juan José Díaz
Vicente Bermejo*
Affiliation:
Universidad Complutense de Madrid
Juan José Díaz
Affiliation:
Universidad Autónoma de Zacatecas (Mexico)
*
Correspondence concerning this article should be addressed to Vicente Bermejo, Facultad de Psicología, Campus de Somosaguas, Universidad Complutense, 28223 Madrid, Spain. E-mail: bermejo@psi.ucm.es
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Abstract

In this study, the incidence of the degree of abstraction in solving addition and subtraction problems with the unknown in the first term and in the result is analyzed. Ninety-six students from first grade to fourth grade in Primary Education (24 students per grade) solved arithmetic problems with objects, drawings, algorithms, and verbal problems. The participants were interviewed individually and all sessions were video-taped. The results indicate a different developmental pattern in achievement for each school grade depending on the levels of abstraction. The influence of the level of abstraction was significant, especially in first graders, and even more so in second graders, that is, at the developmental stage in which they start to learn these arithmetic tasks. Direct modeling strategies are observed more frequently at the concrete and pictorial level, counting strategies occur at all levels of abstraction, whereas numerical fact strategies are found at higher levels of abstraction.

En este estudio se analiza la incidencia del grado de abstracción en la resolución de problemas de suma y resta con la incógnita en el primer término y en el resultado. Noventa y seis alumnos de primero a cuarto curso de Educación Primaria (24 escolares por curso) resuelven tareas aritméticas con objetos, dibujos, algoritmos y verbales. Los participantes se entrevistaron de manera individual y se registraron en vídeo todas las sesiones. Los resultados indican un patrón evolutivo diferente en el rendimiento para cada curso escolar según los niveles de abstracción. Resulta significativa la influencia del nivel de abstracción sobre todo en primero y más aún en segundo curso, es decir, en el momento evolutivo en que se inicia el aprendizaje de estas tareas aritméticas. Las estrategias modelado directo se manifiestan más en el nivel concreto y pictórico, las estrategias conteo ocurren en todos los niveles de abstracción, mientras que las estrategias hechos numéricos se encuentran en los niveles de mayor abstracción.

Keywords

abstraction levelarithmetic problemsstrategiesmathematical developmentnivel de abstracciónproblemas aritméticosestrategiasdesarrollo matemático
Type
Articles
Information
The Spanish Journal of Psychology , Volume 10 , Issue 2 , November 2007 , pp. 285 - 293
Copyright
Copyright © Cambridge University Press 2007

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