Abstract

Higher-order thinking skills are essential competencies in 21st-century mathematics education, particularly for higher education students. One crucial aspect of this skill is the understanding of interconnected mathematical concepts. However, students often experience misconceptions that hinder their comprehension. This study aims to analyze the types and causes of students' misconceptions in the concepts of combinatorics and number theory. The research adopts a quantitative approach to measure the percentage of each type of misconception and a descriptive qualitative approach to explain how these misconceptions occur. The subjects of this study were 113 preservice mathematics teachers. The shows that a Three-Tier Diagnostic Test, was developed to identify misconceptions in detail. The findings revealed that pure misconceptions are the most dominant type, occurring in both combinatorics (34.80%) and number theory (27.80%). Students often fail to connect new concepts with their prior knowledge, a problem exacerbated by fragmented understanding from early education. These misconceptions have the potential to impact their future mathematics teaching, especially if they become educators

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