Izsak, A., Jacobson, E., de Araujo, Z., & Orrill, C. H. (2012). Measuring mathematical knowledge for teaching fractions with drawn quantities. Journal for Research in Mathematics Education, 43(4), 391-427.
Andrew Izsák University of Georgia
Erik Jacobson, University of Georgia
Zandra de Araujo, University of Missouri
Chandra Hawley Orrill, University of Massachusetts Dartmouth
Jouranl for Research in Mathematics Education, Volume 43, Issue 4, 2012, pp. 391-427
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.