Large Language Models (LLMs) such as ChatGPT have quickly become part of student programmers' toolkits, whether allowed by instructors or not. This paper examines how introductory programming (CS1) students integrate LLMs into their problem-solving processes. We conducted a mixed-methods study with 14 undergraduates completing three programming tasks while thinking aloud and permitted to access any resources they choose. The tasks varied in open-endedness and familiarity to the participants and were followed by surveys and interviews. We find that students frequently adopt a pattern we call pseudo-apprenticeship, where students engage attentively with expert-level solutions provided by LLMs but fail to participate in the stages of cognitive apprenticeship that promote independent problem-solving. This pattern was augmented by disconnects between students' intentions, actions, and self-perceived behavior when using LLMs. We offer design and instructional interventions for promoting learning and addressing the patterns of dependent AI use observed.
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