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Measuring mathematical knowledge for teaching fractions with drawn quantities. (English)
J. Res. Math. Educ. 43, No. 4, 391-427 (2012).
Summary: Researchers have recently used traditional item response theory (IRT) models to measure mathematical knowledge for teaching (MKT). Some studies, 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. Results from psychometric modeling and evidence from video-recorded interviews and professional development sessions suggested that there were 2 subgroups of middle-grades teachers, 1 better able to reason with 3-level unit structures and 1 constrained to 2-level unit structures. Some teachers, however, were easier to classify than others. (ERIC)
Classification: D69 C49 F40 F70
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