Mathematical Strategies with Flags of The World for Learning the Part-Whole Model of Fractions

Abstract

This article aims to present a contextualised task for learning the part-whole model of fractions based on the use of national flags, and to analyse the resolution strategies and levels of difficulty that arise from its implementation in different educational contexts. The results obtained are analysed from a qualitative phenomenological approach, obtaining evidence of the level of reasoning about fractions put into practice. The task, originally designed for compulsory basic education, is based on the question What fraction of the flag occupies the colour red? in front of a selection of different flags. In order to identify specific fraction calculation strategies, this task was implemented with students in basic education and both pre-service and in-service teachers in Spain and Portugal. Six different resolution strategies were identified: visual, decomposition, recomposition, operational, measurement with a graduated ruler and fractional measurements. Likewise, different levels of difficulty were identified depending on whether the flags require graphic strategies or knowledge of geometric properties to calculate the fraction. The proposal favours the development of skills in the calculation, measurement and estimation of fractions and is adaptable to different grades, from 3rd year of primary or basic education onwards, by modifying the selection of flags. The predominance of visual, decompositional and operational additive strategies was observed among students and trainee teachers. The transformation of geometry by recomposition and the use of a graduated ruler to calculate triangular areas were also observed in pre-service and in-service teachers. Notably absent across all participant groups were fractional measurement strategies, as well as subtractive, multiplicative, and quotient-based approaches.