Indikasi Epistemological Obstacle Siswa SMA dalam Memahami Bilangan Berpangkat Berdasarkan Theory of Didactical Situations

Abstract

This study describes high school students' epistemological obstacles in understanding exponentiation using the Theory of Didactical Situations (TDS) as an interpretive framework. A qualitative descriptive approach involved 36 Grade XI students at SMA Negeri 1 Ngabang. Diagnostic tasks explored the meaning of exponents, exponent rules, generalization, and the zero exponent. Twenty-six students (72.2%) made at least one error. Four documented representative patterns were 3⁴=3×4, (3+4)²=3²+4², expanding factors to solve 4⁹/4⁷, and stating 5⁰=1 from memorization. The patterns were chosen to represent different types of knowledge (symbol meaning, rule generalization, representation choice, and justification), not by frequency, so they are not claimed to be the dominant difficulties. Analysis through action, formulation, and validation indicates limitations in exponent meaning, overgeneralization of rules, dependence on repeated-multiplication representations, and weak justification of the zero exponent. The obstacles in the first three patterns are read mainly through action and formulation, and in the fourth through weak validation. The findings support learning situations that require students to test rules, compare strategies, construct counterexamples, and provide mathematical justification.