Epistemological Rupture in the Transition from Junior to Senior High School: An Analysis of Function Concept in Chinese Mathematics Curriculum

Abstract

The function concept occupies a central position in school mathematics, yet its development across educational levels involves discontinuities that resist smooth cognitive progression. In the Chinese mathematics curriculum, the transition from junior to senior high school requires students to move from a "variable dependency" conception (biànliàng yīlài guān, 变量依赖观) to a "set correspondence" conception (jǐhé duìyìng guān, 集合对应观). This paper argues that such a transition constitutes what Bachelard (1938) termed an epistemological rupture, a break in which previously adequate ways of knowing become obstacles to new knowledge. Through a theoretical analysis grounded in Bachelard's epistemological obstacle, Duval's theory of semiotic representation registers, and Sfard's reification framework, this study identifies three interrelated dimensions of the rupture: ontological (the shift from process to object), semiotic (the shift from natural-language descriptions to set-theoretic formalism), and cognitive (the demand for structural conception built on inadequate operational foundations). By examining textbook definitions, curriculum standards, and the mathematical structure of the concept itself, this paper traces the specific mechanisms through which prior knowledge becomes an impediment and proposes that recognizing this rupture as structurally necessary, rather than contingently problematic, can inform more coherent instructional design at the critical juncture between school levels.