Abstract
Previous studies showed that 6-year-old children can make proportional judgements when the first-order relations are accessible to them and that children use the half boundary in order to make such judgements. In these studies “half” proved to be an important boundary in children's initial understanding of proportion. These studies involved non-numerical tasks (continuous quantities) in which proportional judgements were established on the basis of part-part relations (ratio). This raises a question about ratio comparisons that are numerically represented (discontinuous quantities). Would children again use the half boundary in ratio comparisons between continuous and discontinuous quantities? In this experiment 6- to 8-year olds were given two tasks: In the sliced task, the standard and the choices were discontinuous quantities; in the non-sliced task, the standard was a continuous quantity and the choices were discontinuous quantities. Children's justifications reflected different levels of understanding of proportions and characteristics of the tasks. The results revealed that “dhalf” plays a crucial role in children's proportional reasoning even when discontinuous quantities are involved.