The purpose of this case study, informed by a Lakatosian perspective, is to identify how an alternative conception that originates in present learning but is related directly to subsequent learning contexts can be constructed. Before the study, one of the authors found by accident that a student who had learned about Avogadro's principle and chemical reaction in South Korea constructed an alternative conception related to the volume of gas. Later, we identified seven Korean high school students with the alternative conception through a test and analyzed their underlying understandings qualitatively through interviews. The results show that they had a scientific conception--core conception--and intuitive assumptions about implicit information of external representations--implicit assumptions--in common. The students' implicit assumptions could be divided into three types again: core assumption, auxiliary assumption, and context-inducing assumption. The core assumption, like the core conception, played a significant role in constructing the alternative conception (hard core), while the auxiliary assumptions were incomplete implicit assumptions to protect the alternative conception (protective belt). The context-inducing assumption was an implicit assumption bringing the context of the subsequent curriculum, and the core conception and the core assumption could be interpreted in this induced context. At the end of the study, the implications related to learning progressions were discussed.