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.

中文翻译：

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评估语法，语义和语用学对学生解释数学中的量化陈述的影响

这项研究比较了语法，语义和语用学在大学生在教学前后对数学中的多量化陈述的解释中的相对影响。像以前的研究一样，结果表明，语义在学生的解释中起着重要的作用，尤其是在授课之前。与以前的研究不同，我们的数据表明，学生解释的模式更多地依赖于数学上下文而不是量词的顺序。我们对Grice（1975）的两篇实用的格言进行了操作，以评估它们是否有助于解释哪种解释更难于学生用于各种陈述。我们的数据支持这样的说法，即学生发现更容易构造相关的解释，但不支持这样的说法，即学生发现更容易构建使陈述正确的解释。最后，根据我们从全美六个过渡到证明课程的样本，我们观察到，在经历了此类课程的学习后，学生对陈述的语法解释变得更加敏感。