The probability concept occupies an increasingly 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 "frequency intuition" conception of probability, where probability is understood as the long-run relative frequency of events observed through repeated experiments, to a "random variable" conception, where probability is formalized through sample spaces, events as sets, and random variables as numerical functions defined on outcomes. 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 probability as an empirical property of experiments to probability as a formal measure on abstract mathematical structures), semiotic (the shift from verbal and numerical descriptions of experiments to the formal language of set theory and random variables), and cognitive (the demand for a structural conception of probability built on inadequate empirical 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 can inform more coherent instructional design at the critical juncture between school levels.
