Abstract
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.
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14 September 2019
The original version of this article unfortunately contained two instances where the task names are mislabeled by switching the abbreviations “EA” and “AE.” Under “Rates of Normative Construal” in the “Results” section, second paragraph, fourth sentence, the sentence should be written.
Notes
We use the term “normative construal” to describe the way mathematicians interpret statements of a given form. We use the term “normative” to convey that the understandings we intend for students to develop are those generally agreed upon within the mathematical community.
We acknowledge that the example of inverses (and our diagram thereof) could be overgeneralized in the sense that “each to some” relationships need not include every element in the second in a pair and multiple elements of the first set may be paired to the same element. Also, the pairing may be fixed for each member of the first set (functional) or more flexible (Durand-Guerrier and Arsac 2005).
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Dawkins, P.C., Roh, K.H. Assessing the Influence of Syntax, Semantics, and Pragmatics in Student Interpretation of Multiply Quantified Statements in Mathematics. Int. J. Res. Undergrad. Math. Ed. 6, 1–22 (2020). https://doi.org/10.1007/s40753-019-00097-2
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DOI: https://doi.org/10.1007/s40753-019-00097-2