FRACTIONS AND THEIR INTERPRETATIONS

DISCUSSIONS AND REFLECTIONS ABOUT MEASUREMENT

Abstract

This theoretical paper seeks to discuss and present aspects concerning the different interpretations of fractions, especially the interpretation of fractions as measurement. At least five interpretations should be considered when discussing the fractions teaching: measure, part-whole, quotient, ratio, and operator. However, it is not provided to Brazilian students and from many countries the instruction of fractions with the various meanings, being restricted, especially in the introduction of fractions, only to the part-whole meaning, which has not been effective. Although, research has shown favorable results in fractions teaching from the measurement perspective. In this context, we present studies related to the measurement perspective based on the partition notion of a quantity, and fraction notion in the measurement perspective, in which a fraction is a multiplicative comparison between two quantities of the same type measured by the same unit, as presented by Powell (2019b), which coincides with the fractions historical genesis, that emerges from the need to measure continuous quantities. Findings show that introduction of fractions should be performed by the meaning of measure, initially as a relation of multiplicative comparison between quantities and later as a point on the number line.