Promoting the power of mathematics: children learning fractions with understanding

Abstract

This paper focuses on a teaching experiment that helps second grade students to discover the power of mathematics by building on their informal knowledge of fractions with understanding. It describes a study on children’s understanding of fractions when the quotient interpretation of fractions is used to introduce them this concept, after a contact with partitioning and equal sharing activities. The study tries to address two questions: How do children understand ordering of fractions when introduced to this concept using the quotient interpretation? How do children understand the equivalence of fractions in this interpretation? An intervention program comprising 7 sessions was conducted in a 2nd-grade classroom, with 7-years-old children, from a public primary school, in Portugal. The findings of this study suggest that to solve ordering problems of fractions using the quotient interpretation can help children to easily understand the inverse relation between the divisor and the quotient, when the dividend is the same; the equivalence problems presented in quotient interpretation can give the children an opportunity to promote their proportional reasoning. Issues on their learning process are analyzed and discussed here.