Gamification is the use of game design and elements in non-game contexts, which has beenused successfully in many businesses and educational settings. In educational settings, it canincrease student engagement and motivation with the game design and elements that areappropriate. In this paper, we consider the gamification in teaching mathematical modeling tosocial science students in Japan. In recent years, the importance of mathematical education tosocial science students increases by development of information and big data technology. Despitethe importance it is difficult to conduct the education effectively in Japanese university, becausemost of the students are allergic to math and their mathematical skills vary with the educationalbackground. In this paper, we provide a model of gamification in the education. By an experimentof the model in a university course, we derived insights on how the game design and elementsin our model affect the behavior of students from qualitative aspects. In our model, we show thatthe leaderboard, avatar, social action, and combat work well as game elements, but the gamedesign of them should be appropriately considered to affect the behavior of students correctly.