Using test cases to refute incorrect existentially quantified propositions: An exploratory study
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Date
2025-12-01
Open Access Location
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Elsevier Inc
Rights
(c) 2025 The Author/s
CC BY 4.0
CC BY 4.0
Abstract
Towards the goal of extending the applicability of test cases to the context of existentially quantified propositions, the present study explores how test cases might support learners with refuting their incorrect existentially quantified propositions. We present and analyze data from two separate instances in which two in-service primary school teachers initially made incorrect existentially quantified propositions and then were asked to find a valid example of their respective propositions (i.e., an element of the subject that satisfies the predicate). The participants were given, and sometimes generated their own, test cases which led to an iterative process of ruling out potential examples and classes of potential examples. Our analysis of this iterative process as it emerged within our specific research setting, comprising among aspects, particular researcher-participant interactions, sheds light on how these test cases afford and support the development and refinement of the learners’ respective existentially quantified propositions.
Description
Keywords
Existentially quantified propositions, Test cases, Counterexamples, Domain of validity
Citation
Tupouniua JG, Smith J. (2025). Using test cases to refute incorrect existentially quantified propositions: An exploratory study. Journal of Mathematical Behavior. 80.