Abstract 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.

中文翻译：

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学生量化作为复杂数学陈述中量化变量的含义

摘要 本研究调查了本科生在涉及多个量词的数学语句中对量化变量的意义。对九名本科生进行了临床访谈，以探索学生对量化变量的含义。更具体地说，要求学生解释和评估中值定理 (IVT) 和其他三个与 IVT 具有相似逻辑结构的陈述。在本文中，我们从建构主义的角度提供了量化变量和学生量化作为理论结构的定义。使用这些理论结构，我们解释了我们的主要结果，即从我们的定性分析中得出的五类学生对量化变量的含义。