This study aimed to address the need for a comprehensive assessment tool to evaluate the mathematical abilities of first-grade students through cognitive diagnostic assessment (CDA). The primary challenge involved in this endeavor was to delineate the specific cognitive skills and sub-skills pertinent to first-grade mathematics (FG-M) and to determine the most suitable model for assessment. Employing a mixed-methods approach, the research identified nine cognitive attributes essential for FG-M and developed a Q-matrix delineating the relationship between these attributes. A preliminary version of the FG-M checklist comprising 74 items was formulated. Subsequently, the assessment tool was administered to 1018 first-grade students, with their teachers utilizing the FG-M checklist for evaluation. Results indicated a commendable accuracy in classifying the nine cognitive attributes, ranging from 0.68 to 0.92, with an average accuracy of 0.76. Furthermore, the validity of the scores was corroborated by a substantial correlation (r = 0.78) between scores from the FG-M checklist and the arithmetic subtest of the Wechsler Intelligence Scale for Children, Fourth Edition (WISC-IV). Overall, the study concluded that the scores from the FG-M checklist are reliable for assessing the mathematical skills of first-grade students. The findings underscored the students' proficiency in fundamental mathematical concepts such as cardinality, addition, subtraction, weight, and statistics. However, areas of weakness were identified in concepts related to multiplication, time, symmetry, and geometry. This research contributes significantly to the advancement of CDA in educational contexts, providing educators with a valuable tool for identifying students' strengths and weaknesses in mathematical cognition.