The development of a cognitive model to provide psychometrically sound and useful diagnostic information for a quantitative measure
The cognitive model in this dissertation was developed from a number of sources: subject matter experts, particularly teachers who teach AP Calculus AB and college professors who teach calculus classes which cover the material specified in the College Board's course description for AP Calculus AB; textbooks used in calculus classes: Advanced Placement as well as college; and the AP Calculus course description (CEEB, 2001. These sources provided the foundation with which to build the cognitive model. This cognitive model was then used to build the Q-matrix, which is an explicitly stated representation of the cognitive model. With the cognitive model (Q matrix) in place, this research study applied proficiency scaling, as developed by ETS for use in interpreting NAEP achievement scales, to the 2003 AP Calculus AB Exam data. The main objective for this second part of the dissertation was to use a psychometric model to provide interpretations of what students at different points along the AP Calculus AB scale know and are able to do. These interpretations are intended to enhance the public's understanding of the reported scores in the context of the domain being assessed, elementary calculus. In the process of using the psychometric model, a comparison was made between two methods for identification of items-an empirical method and a model-based method---similar to what was described by Beaton and Allen (1992). Similar score interpretations were found using the two methods.
Mathematics education|Educational evaluation|Psychological tests|Cognitive therapy
Michel, Rochelle S, "The development of a cognitive model to provide psychometrically sound and useful diagnostic information for a quantitative measure" (2006). ETD Collection for Fordham University. AAI3240063.