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Computational Thinking (CT) is a key component of information literacy and future employment skills, and has gained increasing importance in K-12 education. While pair programming (PP) has been recognized as an effective collaborative approach for CT education, its impact on elementary students' CT abilities, self-efficacy, and engagement remains underexplored. We address this gap by implementing a four-week course and comparing CT skills, self-efficacy, and engagement of students in PP versus individual learning groups. Results demonstrated that PP significantly improved CT skills and self-efficacy compared to individual learning. Additionally, engagement mediated the relationship between self-efficacy and CT skills only in PP groups, highlighting the benefits of PP for younger students and suggesting that engagement plays a key role in CT learning.