Along last decades, it has been questioned the appropriateness of traditional algorithms to develop the number sense. In this work we analyse this development of arithmetic ability numeracy in a group of children in the first grades of Primary Education. These children have been using, as an alternative calculation methodology, the so called ABN algorithms (from the Spanish translation of ‘Open algorithms Based in Numbers’).

Our aim is to analyse the general development of the number sense in children who have been using ABN algorithms. We also want to focus our work in items related to both formal and informal mathematics. We finally compare these children with others who have been using traditional algorithms.

Our working hypothesis is: The methodology used with the ABN algorithms significantly improves the development of the number sense and mathematical competence in second graders.

Children’s early experiences with mathematics are based on numbers. They can use, in a natural way, their thinking skills gained until this moment. That is why a suitable methodology plays a crucial role at the beginning of the construction of their mathematical thinking.

The learning of calculation algorithms and their role in the school is a controversial topic. Researchers state that algorithms have been losing importance due to the advanced of new technologies and their use in class (Castro, Rico & Castro, 1987). Martinez Montero’s research (Martinez, 2001) concluded that traditional algorithms do not promote children’s skills but cancel and deteriorate them.

Most people who are considered skilled in calculating rarely make use of traditional algorithms. They often make previous number manipulations to ease the calculation. In spite of this, most people has learnt traditional calculating.

In the traditional method, the four basic arithmetic operations are very unsuitable for developing the mathematical competence. This is due to it foster fill up the head with signifiers. There is no flexible number handling; sense number is lost in this process. The only skill you need is memory, you do not need think about it, only repeat and repeat.

In this situation, Martínez Montero believes in the necessity of a new method that helps children to develop both their number sense and skills in mental arithmetic. This new methodology is based on the use of the called ‘ABN algorithms’. This is an open method because there is not a unique way to do it and it is based in number not in digits, like traditional algorithms (Martínez, 2010).

Since ABN algorithms are based on numbers, it is easier to connect with the children’s intuitive process, developing a dynamic and flexible sense number. Moreover, it is a transparent algorithm, so it does not hide any intermediate calculations. That is why Martínez (2013) states these algorithms are a real alternative to avoid difficulties and solve them when they appear. 

Castro, E., Rico, L., & Castro, E. (1987). Números y operaciones (Vol. 2). Madrid: Síntesis. Ginsburg, H., & Baroody, A. J. (2007). Tema-3: test de competencia matemática básica (M. C. Núñez del Río & I. Lozano Guerra, Trans.). Madrid: TEA Ediciones. Martínez, J. (2001). Los efectos no deseados (y devastadores) de los métodos tradicionales de aprendizaje de la numeración y de los algoritmos de las cuatro operaciones básicas. Epsilón, 49, 13-26. Martínez, J. (2010, 11 de Junio de 2013). ¿Qué es eso de ABN? [http://algoritmosabn.blogspot.com.es/2010/2004/que-es-eso-de-abn.html]. Martínez, J. (2011). El método de cálculo abierto basado en números (ABN) como alternativa de futuro respecto a los métodos tradicionales cerrados basados en cifras (CBC). Bordón. Revista de pedagogía, 63(4), 95-110. Martínez, J. (2013). La atención a la diversidad en el área de matemáticas. Un enfoque metodológico y curricular. Valladolid: La Calesa.