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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

Abstract:
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.