Analysis of Students' Mathematical Conceptual Understanding on the Topic of Common Tangents of Circles Based on Pirie-Kieren Theory in View of Students' Initial Abilities

This study aims to determine students' abilities in understanding mathematical concepts when solving mathematics problems on the topic of common tangents of circles, as viewed through Pirie and Kieren's Theory. This research is a qualitative descriptive study. The subjects of this research are 36 students of class XI.6 at SMA N 2 Semarang, with three students selected from each category of low, medium, and high abilities. The data collection technique used was a test. Subjects were analyzed based on indicators from Pirie and Kieren, namely Primitive knowing, Image making, Image having, Property noticing, Formalizing, Observing, Structuring, and Inventising. The study results show that students with low conceptual understanding abilities only met the indicators of restating concepts and classifying objects according to their properties, thus, they remain at the Image Having layer. Students with medium conceptual understanding abilities have reached the indicators of using, utilizing, and selecting specific operational procedures, thus, they remain at the Observing layer. Meanwhile, students with high conceptual understanding abilities have met all the indicators of conceptual understanding abilities but are still at the Structuring layer.