CORRECT PROCEDURE AND UNCERTAIN UNDERSTANDING: A CASE STUDY OF PRODUCT RULE PERFORMANCE IN A MALE ENGINEERING STUDENT WITH MASCULINE LEARNING TENDENCIES

Abstract

This study examines whether procedural correctness in applying the product rule reflects secure conceptual understanding in a male Mechanical Engineering student at the Faculty of Science and Technology, Universitas Sembilanbelas November Kolaka, exhibiting “masculine” learning tendencies characterized in the literature by high self-assurance and a preference for memorized procedures over conceptual reasoning. Rather than conventional error analysis, this study investigates correct procedural performance accompanied by conceptual uncertainty. Using a descriptive qualitative single-case design, S2 was purposively selected from 15 male students who had completed a Calculus course at a university in Southeast Sulawesi. Selection was based on medium mathematical ability, determined from final course grades, and observable masculine learning characteristics, identified through four classroom observations using a checklist and a screening interview. Data were collected through a written test involving F(x) = (3x² − 2x)(x³ + 1), an in-depth interview, and documentation, then analyzed using the Miles and Huberman interactive model of data reduction, data display, and conclusion drawing. The written test showed that S2 correctly identified u = 3x² − 2x and v = x³ + 1, calculated (u'=6x-2) and (v'=3x²), and applied (uv)'=u'v+uv' to obtain the correct derivative, F'(x) = 15x⁴ − 8x³ + 6x − 2. However, the interview revealed uncertainty about the correctness of his differentiation despite accurate calculations. This discrepancy between procedural success and conceptual uncertainty is interpreted through the distinction between procedural and conceptual knowledge, APOS theory, and literature on gendered patterns of mathematical confidence. The study recommends probing students’ reasoning through interviews or think-aloud protocols, even when written answers are correct, because procedural fluency may conceal fragile, memorization-based understanding.