We examined children's task engagement during a challenging puzzle task in the presence of their primary caregivers by using a representative sample of rural children from six high-poverty counties across two states. Weighted longitudinal confirmatory factor analysis and structural equation modeling were used to identify a task engagement factor indicated by child positive mood, persistence, enthusiasm, and compliance at both 24 and 35 months. Child attention and maternal responsiveness were significantly related to child task engagement at 24 and 35 months controlling for demographic factors. Additionally, a challenging behavior factor in children's task-oriented behaviors was found as indicated by child negative mood, aggression and noncompliance. This factor was predicted by low maternal acceptance of child behaviors. Theoretical and practical implications are discussed. [This paper was written with Family Life Project Key Investigators.]