Student Quantifications as Meanings for Quantified Variables in Complex Mathematical Statements

•The terms quantifying and quantification are defined from the constructivist perspective.•Five meanings for quantifiers held by undergraduate students are reported.•Students may quantify variables differently in different mathematical contexts.•Student meanings for quantified variables may not align with any mathematical quantifier.•Some students may not quantify a variable at all (i.e. have no meaning for a quantified variable). This study investigates undergraduate students’ meanings for quantified variables in mathematical statements involving multiple quantifiers. Clinical interviews with nine undergraduate students were conducted to explore students’ meanings for quantified variables. More specifically, students were asked to interpret and evaluate the Intermediate Value Theorem (IVT) and three other statements with similar logical structure to the IVT. In this paper, we provide our definitions for a quantified variable and student quantification as theoretical constructs from a constructivist viewpoint. Using these theoretical constructs, we interpret our main results, five categories of students’ meanings for quantified variables, which emerged from our qualitative analysis. We also discuss how our findings of students’ various meanings for quantified variables contribute to literature on theories of meaning and address issues in curriculum and instruction.