This study examined the error patterns in fraction subtraction performed by school children for the erroneous calculation strategies. Raw data were first analyzed qualitatively to reveal the categories of errors. The 30 most frequently occurring error categories were used in designing the Selective Diagnostic Test of Fraction Subtraction and were equally represented in the multiple choices for the test answers. The results were obtained by summing up the number of choices under each error category. The erroneous operation strategies of a particular student could thus be derived quantitatively according to the answers he/she had selected. Subjects of this study, including the 222 hearing-impaired (HI) students and the 485 non-handicapped (NH) students, were analyzed based on the psychometrics of "Selective Fraction Subtraction Diagnostic Test (SFSDT)". Psychometric analyses included the item parameters analysis, the elementary components parameters analysis, ability value estimation, calculation of infit and outfit values by using the Rasch model (RM) and linear logistic model (LLTM). Major findings of the study are as followed. 1.The four steps to develop the cognitive diagnostic model are (1)Substantive Theory Construction, (2)Design Selection, (3)Item Parameter Analysis and (4)Response Scoring. 2.The task analysis and LLTM successfully decomposed the elementary components of fraction subtraction and explained the relationship between the components. HI students, compared with NH students, were found to use similar strategies and make similar errors in computation but performed significantly different from NH students on frequencies of computation rules in the fraction subtraction items. The values of elementary component parameters and frequencies of the computation rules reflected differences between groups.