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Individual Differences in Arithmetical Development

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Front. Psychol. | doi: 10.3389/fpsyg.2018.01811

The Open Algorithm Based on Numbers (ABN) method: An effective instructional approach to domain-specific precursors of arithmetic development.

  • 1Faculty of Education, Universidad de Concepción, Chile
  • 2Department of Psychology, University of Cádiz, Spain
  • 3Undergraduate Office, Universidad de O'Higgins, Chile

This article presents the results of a comparative study regarding the impact and contribution of two instructional approaches to formal and informal mathematical reasoning with two groups of Spanish students, aged four and five. Data indicated that for both age groups, children under the ABN method (Open Algorithm Based on Numbers (ABN) (n = 147) achieved better results than the group under the CBC approach (Closed Algorithms Based on Ciphers) (n = 82), which is the widespread approach in Spanish schools to teach formal and informal mathematical reasoning. Furthermore, the comparative analyses showed that the effect is higher in the group of students who received more instruction on skills considered domain-specific predictors of later arithmetic performance. Statistically significant differences were found in 9 of the 10 dimensions evaluated by TEMA-3 (p < .01), as well as on estimation tasks in the number-line for the 5-year-old-group. However, the 4-year-old group only presented significant results in calculation and concepts tasks about informal mathematical reasoning. We discuss that these differences arise by differential exposure to specific number-sense tasks, since the groups proved to be equivalent in terms of receptive vocabulary, processing speed, and working memory. The educational consequences of these results were also analyzed.

Keywords: Domain-specific precursors, TEMA-3, Early arithmetic, ABN method, Mathematics.

Received: 05 Feb 2018; Accepted: 06 Sep 2018.

Edited by:

Ann Dowker, University of Oxford, United Kingdom

Reviewed by:

Robert Reeve, The University of Melbourne, Australia
Annemie Desoete, Ghent University, Belgium
Natividad Adamuz-Povedano, Universidad de Córdoba, Spain  

Copyright: © 2018 Cerda, Aragón, Pérez, Navarro and Aguilar. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

* Correspondence: PhD. Gamal Cerda, Universidad de Concepción, Faculty of Education, Concepción, Chile,