Measuring Mastery Across Grades: An Application to Spelling Ability

The distinction between quantitative and qualitative differences in mastery is essential when monitoring student progress and is crucial for instructional interventions to deal with learning difficulties. Mixture item response theory (IRT) models can provide a convenient way to make the distinction between quantitative and qualitative differences in mastery. The use of latent groups, rather than focusing on manifest groupings like gender or grade, in these models is very informative to give a substantive interpretation to the qualitative differences. In the current study, mixture IRT modeling is applied to the mastery of two crucial rules in vowel duration spelling in Dutch by pupils in the four final grades of primary school. Results indicate that differences in mastery of the spelling rules are not strictly quantitative. Three latent groups of pupils can be distinguished that show qualitative differences in the mastery of one of the crucial spelling rules involved.