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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Veröffentlicht in:ZDM Jg. 54; H. 4; S. 881 - 893
Hauptverfasser: Dawkins, Paul Christian, Roh, Kyeong Hah
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2022
Springer
Springer Nature B.V
Schlagworte:
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
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Abstract 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.
AbstractList 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.
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.
Audience Higher Education
Postsecondary Education
Author Dawkins, Paul Christian
Roh, Kyeong Hah
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CitedBy_id crossref_primary_10_1080_10511970_2025_2518524
crossref_primary_10_1007_s11858_022_01399_7
crossref_primary_10_1016_j_jmathb_2025_101253
crossref_primary_10_1016_j_jmathb_2025_101269
crossref_primary_10_1016_j_jmathb_2022_100954
Cites_doi 10.1007/s10649-005-9011-3
10.5951/jresematheduc-2020-0151
10.1007/978-3-030-15789-0_51
10.5948/UPO9780883859759.018
10.1090/text/024
10.1016/j.jmathb.2013.02.008
10.1207/S1532690XCI2001_4
10.2307/748576
10.1080/07370008.2021.2000989
10.1007/s40753-019-00108-2
10.1007/s10649-010-9272-3
10.1017/CBO9781139171472
10.1007/s40753-017-0055-4
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Keywords Aspects of predication
Proof
Discrete mathematics
Logic
Multiple relations
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Snippet This theoretical paper sets forth two aspects of predication , which describe how students perceive the relationship between a property and an object. We argue...
This theoretical paper sets forth two "aspects of predication," which describe how students perceive the relationship between a property and an object. We...
This theoretical paper sets forth two aspects of predication, which describe how students perceive the relationship between a property and an object. We argue...
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SubjectTerms 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
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Title Aspects of predication and their influence on reasoning about logic in discrete mathematics
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