The goal of this article is to contribute to understanding the interplay between students' disciplinary engagement and their identity construction. The term appropriation, borrowed from scholars in linguistics and education, was chosen to capture this broader sense of productive learning that sits at the nexus of disciplinary engagement and identity. Appropriation implies deep conceptual understanding, but it also involves a reflexive process of transforming scientific discourse in a way that is authentic and personal. The core aim of this article is to turn the term appropriation into a theoretical construct by means of an analytic process of defining, operationalizing, and testing the definition against student interview and classroom data. Five discourse markers for operationalizing appropriation were discovered through this process. Appropriation, in our study, implies students' discourse is (A) an expression of a personal "signature" idea, (B) grounded in the discipline, (C) thick, in that it involves a metacognitive and epistemological dimension, (D) non-incidental, in the sense of being consistently used throughout classroom activities, and (E) a carrier of social relationships, in that it positions the student within classroom. The study is grounded in an extended intervention on thermodynamics in an Italian secondary school class (grade 12).