Unitizing Predicates and Reasoning About the Logic of Proofs

Author:
Paul Christian Dawkins Texas State University

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Kyeong Hah Roh Arizona State University

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Volume/Issue:
Volume 55: Issue 2
Page(s):
76–95
DOI:
https://doi.org/10.5951/jresematheduc-2020-0155
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Keywords:
Reasoning about logic; Unitizing predicates; Conditional statements; Proof; Contrapositive

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.

Footnotes

This research was funded by NSF DUE Grant No. 1954768 and 1954613. All opinions are those of the authors and do not necessarily represent the views of the National Science Foundation.

Contributor Notes

Paul Christian Dawkins, Department of Mathematics, Texas State University, San Marcos, TX 78666; pcd27@txstate.edu

Kyeong Hah Roh, School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287; khroh@asu.edu

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Copyright:
The National Council of Teachers of Mathematics, Inc. All rights reserved. 2024
Page Count:
20
Article Category:
Research Article
Received:
17 Oct 2022
Accepted:
09 Mar 2023
Print Publication Date:
01 Mar 2024
Online Publication Date:
Mar 2024
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