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Cognitive diagnostic computerized adaptive testing (CD-CAT) combines the strength of both computerized adaptive testing (CAT) and cognitive diagnosis (CD), which can not only provide more precise information about student achievement levels, but also diagnose student mastery of the skills tested by an assessment, thereby allowing for effective and tailored instruction and targeted individualized intervention. The study proposes a dual-objective CD-CAT algorithm for college gate-way STEM courses, which will use more information from the estimation of examinees’ overall ability at the beginning of the test and gradually switch the assessment focus to the estimation of examinees’ skill mastery as the test proceed.