Problem posing is identified as an important activity in mathematics education as well as problem solving is. While problem solving is a comprehension task, problem posing is regarded as a production task because it requires diverse thinking and generation of novel ideas in some ways. In problem posing, it is important but difficult for learners to generate diverse problems. In this study, we propose a strategy for learning from examples in problem posing in order to promote diverse problem posing by learners. We introduce an activity of imitation that is widely adopted in domains of creative generation tasks. We also implement a system that supports learning by imitation in a task of posing mathematical word problems. Our system presents a learner with cases of problems and their generation processes, and it then has the learner engage in reproducing cases by following the processes.