수학교육에서 재귀적 사고의 교육적 가능성 고찰
Exploring the Educational Potential of Recursive Thinking in Mathematics Education
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This study investigates the role of recursive thinking in mathematics education. Defined as a cognitive process of repetition and self-reference, recursive thinking underpins areas such as discrete mathematics, algebra, geometry, and probability. However, it is largely absent from the Korean curriculum, which prioritizes explicit formulas and procedural efficiency. A comparative analysis of Korean and U.S. mathematics textbooks reveals that recursive thinking is more systematically integrated in U.S. materials. Building on this, a four-phase instructional model—numerical exploration, recursive formulation, explicit generalization, and semantic interpretation—is proposed. Incorporating recursive reasoning may enhance students’ problem-solving, conceptual understanding, and cognitive flexibility.
Abstract
This study investigates the role of recursive thinking in mathematics education. Defined as a cognitive process of repetition and self-reference, recursive thinking underpins areas such as discrete mathematics, algebra, geometry, and probability. However, it is largely absent from the Korean curriculum, which prioritizes explicit formulas and procedural efficiency. A comparative analysis of Korean and U.S. mathematics textbooks reveals that recursive thinking is more systematically integrated in U.S. materials. Building on this, a four-phase instructional model—numerical exploration, recursive formulation, explicit generalization, and semantic interpretation—is proposed. Incorporating recursive reasoning may enhance students’ problem-solving, conceptual understanding, and cognitive flexibility.