The development of students’ understanding of the numerical value of fractions

An experiment is reported that investigated the development of students’ understanding of the numerical value of fractions. A total of 200 students ranging in age from 10 to 16 years were tested using a questionnaire that required them to decide on the smallest/biggest fraction, to order a set of given fractions and to justify their responses. Students’ responses were grouped in categories that revealed three main explanatory frameworks within which fractions seem to be interpreted. The first explanatory framework, emerging directly from the initial theory of natural numbers, is that fraction consists of two independent numbers. The second considers fractions as parts of a whole. Only in the third explanatory framework, students were able to understand the relation between numerator and denominator and to consider that fractions can be smaller, equal or even bigger than the unit.