Several studies highlight the effects of gamification on behavioral changes in education. Furthermore, the students' personality traits were shown to be an important factor on the different levels of perception of educational gamification systems. However, despite the importance of considering personality in educational gamification, little is known about how students with various personality traits may perceive game elements, resulting in different engaged behaviors. Therefore, to cover this research gap, this study presents and validates a model to elucidate how personality can affect students' perceptions of game elements leading to different engaged behaviors in a gamified course. To test the research hypotheses, an experiment was conducted in a public university with fifty-six students who took an online gamified course. The students' personality traits and perception towards the used game elements were collected using self-report methods along with their interaction log data within the gamified course, and then analyzed. The results showed that different effects of personality traits were found on students' perception of game elements, which led to different engaged behaviors. Specifically, despite the effect of agreeableness, conscientiousness and neuroticism personality traits on students' perception of points, no effect was found on students' behaviors in the gamified course. Additionally, no effect of personality was found on students' perceptions of badges and the leaderboard. However, these two game elements affected students' engaged behaviors in the gamified course. Specifically, badges affected problem-solving and online study related behaviors, and the leaderboard affected students' problem-solving related behaviors. These findings could offer implications to different stakeholders (e.g., researchers, teachers and gamification designers) on how to motivate and engage students with different personality traits in a gamified course.