Problem posing is identified as an important activity in mathematics education. In problem posing, it is important but difficult for learners to generate diverse problems. In this study, we examine a method and implement a system for facilitating learners' diverse thinking in the task of posing mathematical word problems. Since we focus on an aspect of problem posing as a creative generation task, we utilize the presentation of problems as cases in supporting problem posing. We experimentally investigate the diversifying effect of presenting cases while controlling similarities and then implement a support system for problem posing that can present various cases. We also conduct experimental evaluations to verify the effectiveness of our system.