When teaching infants new actions, parents tend to modify their movements. Infants prefer these infant-directed actions (IDAs) over adult-directed actions and learn well from them. Yet, it remains unclear "how" parents' action modulations capture infants' attention. Typically, making movements larger than usual is thought to draw attention. Recent findings, however, suggest that parents might exploit movement variability to highlight actions. We hypothesized that variability in movement amplitude rather than higher amplitude is capturing infants' attention during IDAs. Using EEG, we measured 15-month-olds' brain activity while they were observing action demonstrations with normal, high, or variable amplitude movements. Infants' theta power (4-5 Hz) in fronto-central channels was compared between conditions. Frontal theta was significantly higher, indicating stronger attentional engagement, in the variable compared to the other conditions. Computational modelling showed that infants' frontal theta power was predicted best by how surprising each movement was. Thus, surprise induced by variability in movements rather than large movements alone engages infants' attention during IDAs. Infants with higher theta power for variable movements were more likely to perform actions successfully and to explore objects novel in the context of the given goal. This highlights the brain mechanisms by which IDAs enhance infants' attention, learning, and exploration.