Logic is generally understood to express content-general relationships. This is problematic for the sake of teaching undergraduates logic in proof courses because their reasoning is usually content-specific. In a series of teaching experiments, I have been exploring how to guide students to apprehend logical relationships by reflecting on their mathematical reasoning. This is done by having them compare how they interpret different statements with the same logical form (intentionally varying the mathematical context) or mathematical proofs with parallel logical structure. By studying what students see as the same and different across these parallel tasks, I learn more about how their untrained ways of reasoning are and are not compatible with logic as is taught in early proof courses. I will share some key insights about how students reason and how that informs how we teach logic. The primary implication for teaching is that we should begin with quantified logic (predicates) rather than non-quantified logic (propositions) because it is more compatible with how many novices perceive mathematical language operating.