Generative artificial intelligence (GenAI) often produces responses that are uncertain or factually incorrect. This raises the educational challenge of how learners can critically evaluate GenAI-generated responses rather than accept or reject them unreflectively. This study addressed this challenge through two cycles of action research in which science teachers used a GenAI-based Jigsaw (GJ) activity to explore the history of atomic theory (Dalton, Gay-Lussac, and Avogadro) for nature of science (NOS) education. In Cycle 1, five teachers completed the GJ activity. Their classroom discourse and reports revealed elaborated understanding of NOS. However, several design problems also emerged, including limited individual exploration time and uncritical acceptance of unfamiliar experts’ explanations. These findings informed concrete refinements for Cycle 2, such as expanded individual exploration time, overlapping expert-area assignments, and explicit prompting guidance. The RFN framework was also adopted because it better captures the educational-application and domain-specific dimensions of GenAI-supported instruction. In Cycle 2, 25 chemistry teachers completed the refined GJ activity. Activity records showed teachers verifying GenAI responses through re-questioning, peer comparison, and researcher support, and pre-post RFN questionnaire results showed exploratory increases in three of six categories (Aims and Values, Scientific Knowledge, and Educational Applications). Based on the findings from both cycles and the Cycle 2 interaction analysis, we propose a five-step GJ learning model—Structuring, Individual Inquiry, Expert-Group Learning, Collaborative Verification, and Synthesis. In this model, GenAI functions as a tool for individual distributed cognition, and Jigsaw structures peer and instructor interaction to support socially distributed cognition.