Development of cognitive diagnostic assessment questions items for integers

Integers are fundamental to mathematics. However, students still struggle with learning integers. Students' abilities and weaknesses can be detected through a series of tests. Cognitive Diagnostic Assessment (CDA) is a form of assessment that can provide detailed information about students' abilities and weaknesses, which teachers can use to improve their teaching. However, limited studies have developed CDA-based diagnostic instruments specifically for integer operations. Therefore, this study aims to develop valid and reliable CDA-based diagnostic test items using a development research approach on integer operations for seventh-grade students. The Generalized Deterministic Inputs, Noisy “And” Gate (G-DINA) model was employed due to its flexibility in accommodating various attribute interaction patterns. This study used the Tessmer model. The diagnostic test questions developed were 40, with three attributes: A1 (comparing integers), A2 (addition and subtraction of integers), and A3 (multiplication and division of integers). The research subjects were 113 seventh-grade students from three junior high schools in the city of Banda Aceh, Indonesia, selected from three schools categorized as low, medium, and high. Content validity was established through expert judgment based on the alignment between test items, cognitive attributes, and learning continuum indicators. Data from the trial were analyzed using the GDINA program in R. The findings showed that all items met validity and reliability criteria, with high classification reliability values for A1 (0.9961), A2 (0.9954), and A3 (0.9976). The diagnostic findings indicated variations in mastery patterns across attributes, with students experiencing difficulties in more complex integer operations that required prerequisite understanding. In addition, the items demonstrated appropriate diagnostic quality and difficulty in identifying students’ mastery of integer attributes. The developed instrument can be used to diagnose students’ cognitive strengths and weaknesses in integer operations and has the potential to support future adaptive and technology-assisted mathematics learning.