in a better position to make defensible claims about student knowledge, skills, and processes that account for test performance. Second, a cognitive model provides a link between cognitive and learning psychology with instruction. Based on an examinee’s observed response pattern, detailed feedback about an examinee’s cognitive strengths and weaknesses can be provided through a score report. This diagnostic information can then be used to inform instruction tailored to the examinee, with the goals of improving or remediating specific cognitive skills. An example of a cognitive model The following hierarchy is an example of a cognitive model task performance for the knowledge and skills in the areas of ratio, factoring, function, and substitution (called the Ratios and Algebra hierarchy). This hierarchy is divergent and composed of nine attributes which are described below. If the cognitive model is assumed to be true, then an examinee who has mastered attribute A3 is assumed to have mastered the attributes below it, namely attributes A1 and A2. Conversely, if an examinee has mastered attribute A2, then it is expected that the examinee has mastered attribute A1 but not A3. The hierarchy contains two independent branches which share a common prerequisite – attribute A1. Aside from attribute A1, the first branch includes two additional attributes, A2 and A3, and the second branch includes a self-contained sub-hierarchy which includes attributes A4 through A9. Three independent branches compose the sub-hierarchy: attributes A4, A5, A6; attributes A4, A7, A8; and attributes A4, A9. As a prerequisite attribute, attribute A1 includes the most basic arithmetic operation skills, such as addition, subtraction, multiplication, and division of numbers. Attributes A2 and A3 both deal with factors. In attribute A2, the examinee needs to have knowledge about the property of factors. In attribute A3, the examinee not only requires knowledge of factoring (i.e., attribute A2), but also the skills of applying the rules of factoring. Therefore, attribute A3 is considered a more advanced attribute than A2. The self-contained sub-hierarchy contains six attributes. Among these attributes, attribute A4 is the prerequisite for all other attributes in the sub-hierarchy. Attribute A4 has attribute A1 as a prerequisite because A4 not only represents basic skills in arithmetic operations (i.e., attribute A1), but it also involves the substitution of values into algebraic expressions which is more abstract and, therefore, more difficult than attribute A1. The first branch in the sub-hierarchy deals, mainly, with functional graph reading. For