K-Means Clustering Analysis of the Relationship Between Critical and Metaphorical Thinking Abilities

The low level of metaphorical thinking ability affects students' ability to solve complex mathematical problems. This study aims to examine the strength of the relationship between critical thinking ability and metaphorical thinking ability. Data were collected from the mid-semester assessment of the SPLDV (Simultaneous Linear Equations with Two Variables) topic. The population in this study consisted of 170 ninth-grade students from SMP Negeri 2 Pangkalan in the 2024/2025 academic year, with a sample of 63 students selected using a simple random sampling technique. The objectives of this study include categorizing students' abilities using the K-means clustering method and determining the relationship, direction, strength, and coefficient of determination between critical thinking ability and metaphorical thinking ability through Spearman’s rank correlation analysis. The results show that 37 students fall into the high ability category, 20 into the moderate ability category, and 6 into the low ability category. The Spearman’s rank correlation analysis yielded a correlation coefficient of 0.632 for the entire dataset and 0.482 for Cluster 1, indicating a significant positive (direct) relationship between critical thinking ability and metaphorical thinking ability, with a moderately strong correlation. The coefficient of determination shows that critical thinking and metaphorical thinking abilities influence 39.9% of the overall data and 23.2% of Cluster 1, while the remaining variance is influenced by other factors beyond these two cognitive abilities.