Measuring Mathematical Knowledge for Teaching Fractions With Drawn Quantities
Andrew Izsák, Erik Jacobson, Zandra de Araujo, and Chandra Hawley Orrill
July 2012, Volume 43, Issue 4, Page 391
Researchers have recently used traditional item response theory (IRT) models to measure mathematical knowledge for teaching (MKT). Some studies (e.g., Hill, 2007; Izsák, Orrill, Cohen, & Brown, 2010), however, have reported subgroups when measuring middle-grades teachers’ MKT, and such groups violate a key assumption of IRT models. This study investigated the utility of an alternative called the mixture Rasch model that allows for subgroups. The model was applied to middle-grades teachers’ performance on pretests and posttests bracketing a 42-hour professional development course focused on drawn models for fraction arithmetic.