Revisiting a Theoretical Model on Fractions: Implications for Teaching and Research

Abstract

Fractions are among the most complex mathematical concepts that children encounter in their years in primary education. One of the main factors contributing to this complexity is that fractions comprise a multifaceted notion encompassing five interrelated subconstructs (part-whole, ratio, operator, quotient and measure). During the early 1980s a theoretical model linking the five interpretations of fractions to the operations of fractions and problem solving was proposed. Since then no systematic attempt has been undertaken to provide empirical validity to this model. The present paper aimed to address this need, by analysing data of 646 fifth and sixth graders’ performance on fractions using structural equation modelling. To a great extent, the analysis provided support to the assumptions of the model. Based on the findings, implications for teaching fractions and further research are drawn.