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Diagnosing Teachers’ Understandings of Rational Numbers: Building a Multidimensional Test Within the Diagnostic Classification Framework
Author(s) -
Bradshaw Laine,
Izsák Andrew,
Templin Jonathan,
Jacobson Erik
Publication year - 2013
Publication title -
educational measurement: issues and practice
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.158
H-Index - 52
eISSN - 1745-3992
pISSN - 0731-1745
DOI - 10.1111/emip.12020
Subject(s) - test (biology) , mathematics education , multiplication (music) , psychology , cognition , sample (material) , fraction (chemistry) , item response theory , quality (philosophy) , mathematics , psychometrics , developmental psychology , paleontology , philosophy , chemistry , organic chemistry , epistemology , chromatography , combinatorics , neuroscience , biology
We report a multidimensional test that examines middle grades teachers’ understanding of fraction arithmetic, especially multiplication and division. The test is based on four attributes identified through an analysis of the extensive mathematics education research literature on teachers’ and students’ reasoning in this content area. We administered the test to a national sample of 990 in‐service middle grades teachers and analyzed the item responses using the log‐linear cognitive diagnosis model. We report the diagnostic quality of the test at the item level, mastery classifications for teachers, and attribute relationships. Our results demonstrate that, when a test is grounded in research on cognition and is designed to be multidimensional from the onset, it is possible to use diagnostic classification models to detect distinct patterns of attribute mastery.