An Integer Linear Programming Model for Diagnosing Unmastered Mathematical Topics Based on Bloom's Cognitive Domains

Irvan Irvan, Krishna Prafidya Romantica, Zainal Azis, Tua Halomoan Harahap

Abstract


This study aims to develop a mathematical model based on Integer Linear Programming (ILP) to map unmastered mathematical topics among senior high school students according to the cognitive domains of Bloom's Taxonomy, namely Knowledge (C1), Comprehension (C2), and Application (C3). The research method employed a quantitative approach, utilizing test result data from a 48-item instrument covering 16 mathematical subtopics, administered to 147 twelfth-grade students in the Natural Science program. The data were analyzed using LINDO 6.1 software to generate a profile of student mastery for each subtopic and cognitive domain. The results indicate that student mastery was generally higher in the Knowledge (C1) domain, with eight subtopics achieved, compared to the Comprehension (C2) domain with six subtopics and the Application (C3) domain with five subtopics. Out of the total 48 test items, only 19 items (39.6%) were mastered by the students, while 29 items (60.4%) were not. The Equations and Inequalities (X2) subtopic was the only material not mastered across all three domains. These findings suggest the need for learning strategies that place greater emphasis on strengthening conceptual understanding and contextual application. The application of the ILP model in this study proves effective as a diagnostic tool for identifying student weaknesses in a detailed and objective manner, thereby serving as a reference for teachers in designing targeted remedial programs. Furthermore, this model has the potential to be replicated in other schools to continuously monitor the development of student proficiency.

Keywords


Mathematical Model, Integer Linear Programming, Proficiency Mapping, Cognitive Domains, Bloom's Taxonomy, Senior High School Mathematics

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References


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DOI: https://doi.org/10.30596/ijems.v7i2.27150

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