Abstract:

Mental calculation is a key skill for mathematics and for everyday life, so this study focused on the topic of Numbers with regard to mental calculation and was carried out with 19 children aged from 9 – 10 years old and enrolled in the 4th grade of primary education.

The study was based on the research question “what is the contribution of Papy’s arrow language to the development of the mental calculation strategies of the 4th-grade students?” and followed a mixed methodological approach. Several methods and tools were used to collect the data during the study: pre-and post-intervention test; naturalistic and participant observation and documentation; interview with the class teacher, before and after the intervention; six learning sessions, which were developed to analyze how Papy’s arrow language brings into focus the most basic number relationship for the building of the mental calculation strategies, and how effective Papy’s arrow language can be in providing a sense of how relationships between numbers and operations are understood; and how the students perceive the use of Papy’s arrow language to solve mathematical problems and operations.

The results of the study showed a positive influence of Papy’s arrow language in the development of the mental calculation skills, since there was an increase of the average percentage of correct answers in the post-test (76%), when compared to the pre-test (38%). The observation and the documentation provided evidence of the progressive appropriation of this language by the students, visible in their written productions, photographs, videos, and evaluation grids, and the self-assessment tables completed by the students at the end of each session, where the students recognized Papy’s arrow language as a facilitating strategy, even in the most difficult tasks. Moreover, the interviews with the class teacher, before and after the intervention, helped to identify the difficulties experienced by the students in the beginning of the study, and to confirm the improvements observed, and highlighted that “the students have a tendency to use this language very naturally, because it is simple, practical and easy to understand, and therefore they use it in many mathematical tasks and in the solving of problem situations.”

Therefore, the study demonstrates the potential of Papy’s arrow language as a didactic tool to facilitate the development of mental calculation strategies and to deepen the students' understanding of the relationships between the numbers and the operations.

Keywords:

Papy's arrow language, mental calculation, numerical relationships, 4th Grade-primary education.