The four basic operations (addition, subtraction, multiplication and division) have always occupied an important position in the Mathematics curriculum. Many teachers, parents, and researchers have dedicated much effort in order to demonstrate what procedures and strategies are most appropriate for teaching.

Four decades ago, Ablewhite (1971) focused us on the problem of training students with traditional methods based on closed figures, emphasizing the complexity of them. With these methods, students learn mathematical procedures without fully understanding the underlying concept. They are able to learn complicated and routine algorithms, but they do not know what practical situations they can resolve with them.

In the latest PISA report (2012), Spain scored 10 points below the OECD average and 5 points below the European Union. That means it is necessary to review Early Mathematics teaching and learning procedures. And implement a more applied approach.

Another fact that confirms this necessity for change is the Basic Mathematical Competence definition which appears in Spanish legislation. Basic Mathematical Competence is the ability to use and relate numbers, basic operations, symbols and forms of mathematical expression and reasoning. Both to produce and understand different types of information expanding knowledge about quantitative and spatial reality, and solving problems related to everyday life and the workplace.

The Open Based on Numbers Algorithm (ABN) methodology represents a significant change in the quantity and quality of children’s mathematical achievement. According to Jaime Martínez Montero (designer of ABN methodology), children can learn faster and in more depht. ABN teaching is based on understanding rather than memorizing concepts. In addition, this new method dramatically improves students ability stimating mental calculation and problem solving. Finally, ABN procedure allows them to perform number facts according to their ability. This new approach develops in students an effective improvement in motivation and positive students attitude to Mathematics.

This research focused on addition, one of the basic Mathematical concepts. ABN approach uses a new format to solve addition, and the number facts always are presented as a problem solving. The addition fact could be represented in three columns (see Table 1): in the left column the student chooses one quantity from any addends (e.g. 300 out of 329); the central column shows the remaining amount it is necessary add from the first addend (e.g. 29). And on the right column the result from such partial addition (876), and the final result (905).
The use of this format is a major change on the ABN calculation method. The students do not work with numerals but use the whole numbers. As specific teaching equipment, ABN uses low cost tools, such us number lines, ten-frames, toothpicks (which represent units, tens and hundreds).

Table 1.

329 + 576 =905

Adding Remaining Result
300 (out of 329) 29 876 (300 + 576)
20 (out of 29) 9 896 (876 + 20)
4 (out of 9) 5 900 (896 + 4)
5 (out of 5) 0 905 (900 + 5)

Note: The brackets indicate the mental processes used by the students.