Aspects of predication and their influence on reasoning about logic in discrete mathematics

This theoretical paper sets forth two aspects of predication , which describe how students perceive the relationship between a property and an object. We argue these are consequential for how students make sense of discrete mathematics proofs related to the properties and how they construct a logica...

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Bibliographic Details
Published in:ZDM Vol. 54; no. 4; pp. 881 - 893
Main Authors: Dawkins, Paul Christian, Roh, Kyeong Hah
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2022
Springer
Springer Nature B.V
Subjects:
Active Learning
Algorithms
Calculus
Circuits
Cognitive Processes
College Mathematics
College Students
Combinatorics
Concept Formation
Construction (Process)
Education
Educational Experiments
Experiments
Generalization
Graphs
Hypotheses
Inquiry
Iterative methods
Literacy Education
Logic
Logical Thinking
Mathematical analysis
Mathematical Concepts
Mathematical Logic
Mathematics
Mathematics Education
Mathematics Instruction
Number Concepts
Number theory
Original Paper
Reading Instruction
Students
Teaching
Theorems
Undergraduate Students
Undergraduate study
Validity
Aspects of predication
Proof
Discrete mathematics
Logic
Multiple relations
ISSN:1863-9690, 1863-9704
Online Access:Get full text
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Summary:This theoretical paper sets forth two aspects of predication , which describe how students perceive the relationship between a property and an object. We argue these are consequential for how students make sense of discrete mathematics proofs related to the properties and how they construct a logical structure. These aspects of predication are (1) populating the way students generate sets of examples of the property, and (2) testing membership how one tests whether or not a given object has a specific property. Using data from two teaching experiments in which undergraduate students read proofs of theorems about the discrete concept of multiple relations, we illustrate the nature of these aspects of predication and demonstrate how they help explain student interpretations of the proofs. We argue that these particular properties from number theory likely have correlates in many other discrete mathematics topics because of the role of computation/algorithms for defining and testing properties as well as the role of iteration and recursion in populating examples. We anticipate that these constructs will be useful to teachers and researchers of discrete mathematics to foster and assess student understanding of various mathematical properties. They provide tools for thinking about what it means to understand properties in a rich and coherent way that supports understanding complex lines of inference and generalizations.
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ISSN:1863-9690
1863-9704
DOI:10.1007/s11858-022-01332-y