Question asking is an important tool for constructing academic knowledge, and a self-reinforcing driver of curiosity. However, research has found that question asking is infrequent in the classroom and children's questions are often superficial, lacking deep reasoning. In this work, we developed a pedagogical agent that encourages children to ask divergent-thinking questions, a more complex form of questions that is associated with curiosity. We conducted a study with 95 fifth grade students, who interacted with an agent that encourages either convergentthinking or divergent-thinking questions. Results showed that both interventions increased the number of divergent-thinking questions and the fluency of question asking, while they did not significantly alter children's perception of curiosity despite their high intrinsic motivation scores. In addition, children's curiosity trait has a mediating effect on question asking under the divergent-thinking agent, suggesting that question-asking interventions must be personalized to each student based on their tendency to be curious.