
06151322
j
2013b.00461
Izsak, Andrew
Jacobson, Erik
de Araujo, Zandra
Hawley Orrill, Chandra
Measuring mathematical knowledge for teaching fractions with drawn quantities.
J. Res. Math. Educ. 43, No. 4, 391427 (2012).
2012
National Council of Teachers of Mathematics (NCTM), Reston, VA
EN
D69
C49
F40
F70
psychometrics
professional development
item response theory
knowledge base for teaching
pedagogical content knowledge
middle school teachers
arithmetic
mathematical knowledge for teaching
fractions
quantities
doi:10.5951/jresematheduc.43.4.0391
http://www.nctm.org/publications/article.aspx?id=33415
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 middlegrades 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 middlegrades teachers' performance on pretests and posttests bracketing a 42hour professional development course focused on drawn models for fraction arithmetic. Results from psychometric modeling and evidence from videorecorded interviews and professional development sessions suggested that there were 2 subgroups of middlegrades teachers, 1 better able to reason with 3level unit structures and 1 constrained to 2level unit structures. Some teachers, however, were easier to classify than others. (ERIC)