A psychometric model called Saltus, which represents the qualitative aspects of hierarchical development in a form applicable to additive measurement, was applied. Both Piaget's theory of cognitive development and Gagne's theory of learning hierarchies were used to establish the common features of hierarchical development: (1) gappiness--the…

The stability of Rasch test item difficulty parameters was investigated under varying conditions. Data were taken from a mathematics achievement test administered to over 2,000 Australian students. The experiments included: (1) relative stability of the Rasch, traditional, and z-item difficulty parameters using different sample sizes and designs;…