Identifying and measuring cognitive aspects of a mathematics achievement test

Abstract

Cognitive Diagnostic Models (CDMs) are a useful way to identify potential areas of intervention for students who may not have mastered various skills and abilities at the same time as their peers. Traditionally, CDMs have been used on narrowly defined classroom tests, such as those for determining whether students are able to use different algebraic principles correctly. In the current study, the Deterministic Input, Noisy "And" Gate model (DINA; Haertel, 1989; Junker&Sijtsma, 2001) and the Compensatory Reparameterized Unified Model (CRUM; Hartz, 2002), as parameterized by the log-linear cognitive diagnosis model (LCDM; Henson, Templin,&Willse, 2009), were used to analyze the utility of pre-defined cognitive components in estimating students' abilities in a broadly defined, standardized mathematics achievement test. The attribute mastery profile distributions were compared; the majority of students was classified into the extremes of no mastery or complete mastery for both the CRUM and DINA models, though greater variability among attribute mastery classifications was obtained by the CRUM.