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Critical thinking is identified as a key educational outcome in higher education curricula; however, it is not trivial to support students in building this multifaceted skill. In this study, we evaluated a brief online learning intervention focusing on informal fallacy identification, a hallmark critical-thinking skill. The intervention used a bite-sized video learning approach, which has been shown to promote student engagement. Video-based learning was implemented within a precision teaching (PT) framework, which modulates the exposure of individual learners to the learning material to enable them to build 'fluency' in the targeted skills. In one of the learning conditions, PT was applied synergistically with domain-general problem-based training to support generalisation. The intervention consisted of two learning episodes and was administered to three groups (learning conditions) of 19 participants each: a PT fluency-based training group; a PT + group, where PT was combined with problem-based training; and a self-directed learning control group. All three groups showed comparable improvements in fallacy identification on taught (post-episode tests) and unseen materials (post-intervention assessment), with lower-scoring participants showing higher gains than high-scoring participants. The results of the knowledge retention tests a week later were also comparable between groups. Importantly, in the domain-general fallacy-identification assessment (post-intervention), the two PT groups showed higher improvements than the control group. These findings suggest that the integration of bite-sized video learning technologies with PT can improve students' critical-thinking skills. Furthermore, PT, on its own or combined with problem-based training, can improve their skill to generalise learning to novel contexts. We discuss the educational implications of our findings.