This study examined the structural relationships among elementary students’ beliefs about intelligence, achievement goal orientation, and engagement in cognitive tasks involving fluid and crystallized intelligence. Using data from 274 fifth- and sixth-grade students in South Korea, structural equation modeling (SEM) was conducted to investigate whether goal orientation mediates the relationship between intelligence beliefs and cognitive task engagement. The results showed that students with growth-oriented beliefs were more likely to adopt adaptive achievement goals, which in turn influenced their engagement in both f luid (analogical reasoning) and crystallized (curriculum-based academic performance) tasks. However, goal orientation partially mediated the relationship between intelligence beliefs and cognitive task engagement, exhibiting a suppressor effect that weakens the positive influence of intelligence beliefs. These findings underscore the complex interplay between self-beliefs and motivational constructs and suggest that promoting mastery goals alongside growth beliefs may enhance students’ cognitive task engagement. This study underscores the value of fostering growth beliefs and adaptive goals to enhance cognitive engagement. Targeted interventions can support sustained and meaningful learning behaviors.