Title in English:
A Developmental Scale of Mental Computation with Part-Whole Numbers
Abstract in English:
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.