Endah Budi Rahaju, Siti Khabibah, Abdul Haris Rosyidi, Nina Rinda Prihartiwi, Lestariningsih Lestariningsih
This study explores investigates undergraduate students’ critical reasoning in the context of categorizing statements regarding the relationships between geometric shapes, particularly triangles and quadrilaterals. The categorization process requires students to analyze and evaluate the truth value of various statements by referring to the formal definitions and inherent properties of the shapes involved. The primary objective of this research is to classify and interpret students' arguments when assessing these geometric relationships, thereby uncovering their conceptual understanding and possible misconceptions. Data were collected from 104 first-year university students at a university in Surabaya, Indonesia. The findings reveal three key observations that illustrate how students reason about shape classifications: (1) In response to the statement "An equilateral triangle is an isosceles triangle," most students based their arguments on the number of equal sides and angle congruency, with 32.69% incorrectly asserting that it is "never true," and 12.50% claiming it is "sometimes true." These responses suggest confusion about the inclusive nature of geometric definitions. (2) For the statement "A parallelogram is a rectangle," 44.23% of students argued it is "never true," whereas 16.35% believed it is "true," often relying on differing interpretations of angle properties, particularly the right angles required for rectangles. (3) When evaluating the statement "A square is not a rhombus," 16.35% answered "true, " and another 16.35% selected "sometimes true," typically justifying their responses by asserting that a square is a rectangle, while a rhombus is seen as a kite. Students who responded with "sometimes true" generally reasoned that the validity of the statement depends on whether all interior angles of a rhombus are right angles. Overall, these findings highlight the prevalence of misconceptions and demonstrate varied levels of geometric understanding, indicating the need for instructional strategies that emphasize precise definitions and hierarchical relationships among geometric shapes. © 2026, Malque Publishing. All rights reserved.
Faculty of Mathematics and Natural Sciences, Universitas Negeri Surabaya, Indonesia
