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Characterizing Levels of Reasoning in Graph Theory

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Title: Characterizing Levels of Reasoning in Graph Theory
Language: English
Authors: González, Antonio, Gallego-Sánchez, Inés, Gavilán-Izquierdo, José María, Puertas, María Luz
Source: EURASIA Journal of Mathematics, Science and Technology Education. 2021 17(8).
Availability: Modestum. No: 1 Windrush Road, Hilton Derbyshire, DE65 5LB, UK. e-mail: ejmste@ejmste.com; Web site: https://www.ejmste.com/
Peer Reviewed: Y
Page Count: 16
Publication Date: 2021
Document Type: Journal Articles
Reports - Research
Descriptors: Graphs, Logical Thinking, Problem Solving, Cognitive Structures, Recognition (Psychology), Definitions, Classification, Mathematical Logic, Validity, Models
ISSN: 1305-8223
Abstract: This work provides a characterization of the learning of graph theory through the lens of the van Hiele model. For this purpose, we perform a theoretical analysis structured through the processes of reasoning that students activate when solving graph theory problems: recognition, use and formulation of definitions, classification, and proof. We thus obtain four levels of reasoning: an initial level of visual character in which students perceive graphs as a whole; a second level, analytical in nature in which students distinguish parts and properties of graphs; a pre-formal level in which students can interrelate properties; and a formal level in which graphs are handled as abstract mathematical objects. Our results, which are supported by a review of the literature on the teaching and learning of graph theory, might be very helpful to design efficient data collection instruments for empirical studies aiming to analyze students' thinking in this field of mathematics.
Abstractor: As Provided
Entry Date: 2021
Accession Number: EJ1309536
Database: ERIC
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  Availability: 0
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  – Url: https://eric.ed.gov/contentdelivery/servlet/ERICServlet?accno=EJ1309536
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  Data: Characterizing Levels of Reasoning in Graph Theory
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  Data: Modestum. No: 1 Windrush Road, Hilton Derbyshire, DE65 5LB, UK. e-mail: ejmste@ejmste.com; Web site: https://www.ejmste.com/
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  Data: <searchLink fieldCode="DE" term="%22Graphs%22">Graphs</searchLink><br /><searchLink fieldCode="DE" term="%22Logical+Thinking%22">Logical Thinking</searchLink><br /><searchLink fieldCode="DE" term="%22Problem+Solving%22">Problem Solving</searchLink><br /><searchLink fieldCode="DE" term="%22Cognitive+Structures%22">Cognitive Structures</searchLink><br /><searchLink fieldCode="DE" term="%22Recognition+%28Psychology%29%22">Recognition (Psychology)</searchLink><br /><searchLink fieldCode="DE" term="%22Definitions%22">Definitions</searchLink><br /><searchLink fieldCode="DE" term="%22Classification%22">Classification</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+Logic%22">Mathematical Logic</searchLink><br /><searchLink fieldCode="DE" term="%22Validity%22">Validity</searchLink><br /><searchLink fieldCode="DE" term="%22Models%22">Models</searchLink>
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  Data: This work provides a characterization of the learning of graph theory through the lens of the van Hiele model. For this purpose, we perform a theoretical analysis structured through the processes of reasoning that students activate when solving graph theory problems: recognition, use and formulation of definitions, classification, and proof. We thus obtain four levels of reasoning: an initial level of visual character in which students perceive graphs as a whole; a second level, analytical in nature in which students distinguish parts and properties of graphs; a pre-formal level in which students can interrelate properties; and a formal level in which graphs are handled as abstract mathematical objects. Our results, which are supported by a review of the literature on the teaching and learning of graph theory, might be very helpful to design efficient data collection instruments for empirical studies aiming to analyze students' thinking in this field of mathematics.
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    Languages:
      – Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 16
    Subjects:
      – SubjectFull: Graphs
        Type: general
      – SubjectFull: Logical Thinking
        Type: general
      – SubjectFull: Problem Solving
        Type: general
      – SubjectFull: Cognitive Structures
        Type: general
      – SubjectFull: Recognition (Psychology)
        Type: general
      – SubjectFull: Definitions
        Type: general
      – SubjectFull: Classification
        Type: general
      – SubjectFull: Mathematical Logic
        Type: general
      – SubjectFull: Validity
        Type: general
      – SubjectFull: Models
        Type: general
    Titles:
      – TitleFull: Characterizing Levels of Reasoning in Graph Theory
        Type: main
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            NameFull: González, Antonio
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            NameFull: Gallego-Sánchez, Inés
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            NameFull: Gavilán-Izquierdo, José María
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            NameFull: Puertas, María Luz
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              Y: 2021
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