Ontology of Algebra Knowledge of Test Questions: A Construction of Instructional Design

Abstract

This study aimed to construct an ontology design for the systematic representation of knowledge associated with a mathematics course based on hierarchical prerequisite relation. In addition, the extraction and inference methods were used by observing the clustering of knowledge with schema representing prerequisite concept dependency. The sample population comprised postgraduate (magister) students of mathematics education, and performance analysis was based on answer grading by 6 graders for a total of 24 questions. The questions were then categorized into high and low-average score groups, and the concept mapping led to clustering in ontology. A total of 90 concepts from 16 topics in 92 statements were collected in this study. The relationships in course ontology were kept to a minimum to enhance expressiveness and computability. The results showed the presence of small clusters of concepts between concepts 20-40. The design obtained was a composite and the characteristics of the elements (concept, principle, and basic theorem) were found to interplay in a very complex way. Furthermore, it accommodated various considerations, such as weight, size, semantic, and optimization objectives, including power, ratio, and rigorous. Based on the results, the design comprised a meta-knowledge of the elements, transcending the individual components.