The efficacy of educational robots in children’s school education and home learning has been established. There has been a growing demand for robots that effectively support parent-child learning at home, but the design of robots that can assist without disrupting their dialogue has remained unclear. This study proposes a novel form of robot for supporting home learning while promoting parent-child dialogue: a semi-autonomous para-operated robot, which is partially controlled by the parent from the side. We hypothesized that this approach, unlike autonomous robots which may reduce parental burden but lead to parental disengagement, would increase parental involvement through active operation. To validate this hypothesis, we conducted an experiment with parent-child pairs comparing three conditions: (1) no robot, (2) autonomous robot, and (3) the proposed semi-autonomous robot. The results revealed that the proposed robot significantly increased parental utterances without increasing parental burden compared to the other conditions, supporting our hypothesis. This study contributes by demonstrating the effectiveness of semi-autonomous para-operated robots in facilitating parent-child home learning.