Analysis of problem posing using different fractions meanings

Abstract

The aim of this work is to study the knowledge that 11 to 12-year-old pupils have about the different meanings of fractions. For this purpose, an investigation about the ability that 11 to 12-year-old pupils have with fraction problems through problem posing is performed. In particular, we analyze if they pose different types of problems depending on the provided help and if they are able to solve the problems they pose. To do so, after making a classification about types of fractions problems, an instrument is designed to see if students are able to invent and solve problems with different conditions (no reference at all, reference to an image, reference to a graphic representation, and reference to an operation). The analysis of results shows that most of the students properly solve what they invent, and points out that they tend to pose part-whole and part-set problems, even when the given reference suggests another type of problem.