Unitizing Predicates and Reasoning About the Logic of Proofs

This article offers the construct unitizing predicates to name mental actions important for students’ reasoning about logic. To unitize a predicate is to conceptualize (possibly complex or multipart) conditions as a single property that every example has or does not have, thereby partitioning a univ...

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Bibliographic Details
Published in:Journal for research in mathematics education 2024-03, Vol.55 (2), p.76-95
Main Authors: Dawkins, Paul Christian, Roh, Kyeong Hah
Format: Article
Language:English
Subjects:
Cognition & reasoning
Cognitive ability
College students
Logic
Reasoning
Students
Teaching methods
Undergraduate study
Online Access:Get full text
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Summary:This article offers the construct unitizing predicates to name mental actions important for students’ reasoning about logic. To unitize a predicate is to conceptualize (possibly complex or multipart) conditions as a single property that every example has or does not have, thereby partitioning a universal set into examples and nonexamples. This explains the cognitive work that supports students to unify various statements with the same logical form, which is conventionally represented by replacing parts of statements with logical variables p or P ( x ). Using data from a constructivist teaching experiment with two undergraduate students, we document barriers to unitizing predicates and demonstrate how this activity influences students’ ability to render mathematical statements and proofs as having the same logical structure.
ISSN:0021-8251
1945-2306
DOI:10.5951/jresematheduc-2020-0155