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The current study aimed to reveal the changes to the identities of two tenth graders in mathematics learning at a Japanese high school during the COVID-19 pandemic from the perspective of learning from home versus learning in the classroom. The following research questions are raised: How has the pandemic situation affected and changed Japanese students' triadic relationship between knowledge, practice, and identity? What overlooked equity issue in this triadic relationship is caused by the pandemic? Two male students participated in and completed semi-structured interviews that asked how they managed to study at home during the school shutdown. First, we extracted from the transcript the part concerning the interviewees' difficulties in studying mathematics at home, as well as the role of mathematics lessons and their classmates. Secondly, we classified their utterances into three categories (identity, practice, and knowledge sentences), based on their grammatical patterns. The study results delineated the dynamic and complicated relationships among the three elements. Students lost opportunities to (1) obtain positive social feedback on their mathematical behaviors and (2) learn the social aspects of mathematical problem-solving, such as what strategy was socially acceptable and authorized. We also pointed out an overlooked soft equity issue; rich learning resources are substantially unavailable to students owing to the lack of appropriation of necessary knowledge and positive self-identification, despite the assurance of accessibility to such resources. We should continue to tackle helping learners construct their identities during future unexpected events.