This study seeks to understand the "what" and the "why" of student engagement by investigating the "aims" that students pursue through engagement (i.e., their achievement goals) and the "reasons" driving such engagement (i.e., their motivation). Self-report instruments measuring students' motivational reasons, achievement goals, and engagement in the context of their mathematics classes were administered to a sample of 491 Singapore elementary students (54% girls; M[subscript age] = 11 years). Mediational path analysis showed that achievement goals, collectively, played a significant mediating role in almost all the links connecting motivational reasons to different engagement outcomes. Specifically, whilst autonomous motivation (AM) was associated with greater effort/persistence, heightened elaboration, and lower anxiety, controlled motivation (CM) was associated with higher anxiety. Although self-based goals strengthened the positive direct effects of AM on effort/persistence and elaboration, and channeled the adaptive effects of CM on these two engagement outcomes, this goal type also heightened the effect of CM on anxiety and cancelled out the benefits of AM in reducing anxiety. Taken together, findings pointed to the more adaptive role of AM relative to CM, and the apparently double-edged-sword effects of self-based goals on student engagement. Key findings and their implications for teaching and school psychology practices are discussed.