Measuring Mathematical Knowledge for Teaching Fractions With Drawn Quantities

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  • 1 The University of Georgia
  • 2 University of Massachusetts Dartmouth

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. 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.

Contributor Notes

Andrew Izsák, Department of Mathematics and Science Education, University of Georgia, 105 Aderhold Hall, Athens, GA 30602; izsak@uga.edu

Erik Jacobson, Department of Mathematics and Science Education, University of Georgia, 105 Aderhold Hall, Athens, GA 30602; ejacobsn@uga.edu

Zandra de Araujo, Department of Mathematics and Science Education, University of Georgia, 105 Aderhold Hall, Athens, GA 30602; zdearaujo@hotmail.com

Chandra Hawley Orrill, STEM Education Department, University of Massachusetts Dartmouth, 200 Mill Road, Suite 150B, Fairhaven, MA 02719; corrill@umassd.edu

(Corresponding author is Izsák izsak@uga.edu)(Corresponding author is Jacobson ejacobsn@uga.edu)(Corresponding author is de Araujo zdearaujo@hotmail.com)(Corresponding author is Orrill corrill@umassd.edu)
Journal for Research in Mathematics Education

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