Guided by self-determination theory to design an authentic learning environment, we attempted repeated engagement in critical evaluation of evidence to foster accuracy-oriented reasoning and critical thinking in an applied science course for non-STEM undergraduates taught completely online during a 6-week summer term and a 16-week fall term. Student outcomes were measured as indicators of the effectiveness of our pedagogical strategies. Results suggest that student engagement in integration and resolution modes of cognitive presence are associated with students' feelings of autonomy, competence, and relatedness. A positive trend of students moving toward accuracy goals during evidence evaluation was also observed, as students visited both sides of evidence at the same frequency or spent about the same amount of time evaluating both sides of evidence regardless of their voting decision at the end of the course. These findings suggest that scientific literacy among nonscientists may be fostered through repeated, supportive engagement in evidence evaluation.