A Developmental Scale of Mental Computation with Part-Whole Numbers

In this article, data from a study of the mental computation competence of students in grades 3 to 10 are presented. Students responded to mental computation items, presented orally, that included operations applied to fractions, decimals and percents. The data were analysed using Rasch modelling techniques, and a six-level hierarchy of part-whole computation was identified. This hierarchy is described in terms of the three different representations of part-whole reasoning – fraction, decimal, and percent – and is elaborated by a consideration of the likely cognitive demands of the items. Discussion includes reasons for the relative difficulties of the items, performance across grades and directions for future research.