This study compares the relative influence of syntax, semantics, and pragmatics in university students' interpretation of multiply quantified statements in mathematics, both before and after instruction. Like previous studies, results show that semantics plays a heavy role in student interpretation, especially before instruction. Unlike previous studies, our data suggests that the patterns of student interpretation rely more upon the mathematical context than upon the order of the quantifiers. We operationalize two of Grice's (1975) pragmatic Maxims to evaluate whether they help explain which interpretations are harder for students to adopt for various statements. Our data support the claim that students find it easier to construct relevant interpretations, but do not support the claim that students find it easier to construct interpretations that render the statement true. Finally, based on our sample from six Transition to Proof classes across the US, we observe that after their experiences in such courses students became more sensitive to syntax in their interpretation of the statements.