| Learning difficulties in mathematics are frequently identified via poor performance on a standardized achievement test, such as the Woodcock Johnson III (WJIII) or the Wechsler Individual Achievement Test (WIAT). Though these instruments enjoy widespread use, they reveal little information as to the nature and quality of performance or the reasons why a child experiences difficulty. This dissertation explores whether systematic observation of specific behaviors---or qualitative features of performance---which accompany and give rise to performance on arithmetic tasks might be used in conjunction with standardized tests of arithmetic achievement to better describe a child's areas of vulnerability in mathematics. Seven qualitative features of performance are identified, specifically Pace, Precision, Graphomotor Output, Perceptual Judgment, Language Demands, Management of Complexity, and Self-Efficacy. In order to establish the relevance of these features for use in clinical assessment, the association between each feature and (1) arithmetic achievement, (2) traditional, norm-referenced neuropsychological measures of cognitive functioning, and (3) teacher report of the child's achievement in mathematics is investigated within a population of school-aged children, grades 2--6, who were referred for learning problems (n = 52). Results reveal that difficulties with Pace, Precision, Management of Complexity, and Self-Efficacy are associated with low scores on the Numerical Operations subtest of the WIAT I. Difficulties with each of the qualitative features are correlated with low scores on neuropsychological measures of cognitive function. Only the qualitative feature of Self-Efficacy is associated with teacher report of child performance. These results suggest that each qualitative feature may be considered a behavioral manifestation of underlying neuro-cognitive processes as they relate to the particular demands of arithmetic. Results also provide initial support for the use of qualitative features of performance in clinical assessment of mathematics. Accordingly, findings are used to create a Guide for Incorporating Qualitative Features of Performance in Arithmetic Achievement. The Guide is designed to help clinicians incorporate a consideration of qualitative features in mathematics assessment using standardized arithmetic tests, for the purpose of delineating and describing the particular constellation of challenges the child may face in terms of learning and performance in mathematics. |
