Developing models and using mathematics are two key practices in internationally recognized science education standards, such as the Next Generation Science Standards (NGSS). However, students often struggle with these two intersecting practices, particularly when developing mathematical models about scientific phenomena. Formative…

The graded response model for two-stage testing was applied to an attitudes toward science scale using real-data simulation. The 48-item scale was administered to 920 students at a grade-8 equivalent in Singapore. A two-stage 16-item computerized adaptive test was developed. In two-stage testing an initial, or routing, test is followed by a…

A two-level model for factor analysis is defined, and formulas for a scoring algorithm for this model are derived. A simple noniterative method based on decomposition of total sums of the squares and cross-products is discussed and illustrated with simulated data and data from the Second International Mathematics Study. (SLD)