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A Theoretical Analysis of the Validity of the Van Hiele Levels of Reasoning in Graph Theory

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Title: A Theoretical Analysis of the Validity of the Van Hiele Levels of Reasoning in Graph Theory
Language: English
Authors: González, Antonio (ORCID 0000-0002-2137-5835), Gavilán-Izquierdo, José María (ORCID 0000-0002-3369-5377), Gallego-Sánchez, Inés (ORCID 0000-0002-1088-3172), Puertas, María Luz (ORCID 0000-0002-9093-5461)
Source: Journal on Mathematics Education. 2022 13(3):515-530.
Availability: Indonesian Mathematical Society. Jl. Padang Selasa 524, Palembang, South Sumatra 30139, Indonesia. Tel: +618-127-106777; Fax: +627-113-20310; Web site: http://jme.ejournal.unsri.ac.id/index.php/jme
Peer Reviewed: Y
Page Count: 16
Publication Date: 2022
Document Type: Journal Articles
Reports - Evaluative
Descriptors: Graphs, Validity, Mathematics Instruction, Geometry, Geometric Concepts, Thinking Skills, Teaching Methods, Learning Processes, Mathematics Skills, Problem Solving, Classification, Mathematical Logic, Mathematical Models
ISSN: 2087-8885
2407-0610
Abstract: The need to develop consistent theoretical frameworks for the teaching and learning of discrete mathematics, specifically of graph theory, has attracted the attention of the researchers in mathematics education. Responding to this demand, the scope of the Van Hiele model has been extended to the field of graphs through a proposal of four levels of reasoning whose descriptors need to be validated according to the structure of this model. In this paper, the validity of these descriptors has been approached with a theoretical analysis that is organized by means of the so-called processes of reasoning, which are different mathematics abilities that students activate when solving graph theory problems: recognition, use and formulation of definitions, classification, and proof. The analysis gives support to the internal validity of the levels of reasoning in graph theory as the properties of the Van Hiele levels have been verified: fixed sequence, adjacency, distinction, and separation. Moreover, the external validity of the levels has been supported by providing evidence of their coherence with the levels of geometrical reasoning from which they originally emerge. The results thus point to the suitability of applying the Van Hiele model in the teaching and learning of graph theory.
Abstractor: As Provided
Entry Date: 2023
Accession Number: EJ1379741
Database: ERIC
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  Data: <searchLink fieldCode="AR" term="%22González%2C+Antonio%22">González, Antonio</searchLink> (ORCID <externalLink term="https://orcid.org/0000-0002-2137-5835">0000-0002-2137-5835</externalLink>)<br /><searchLink fieldCode="AR" term="%22Gavilán-Izquierdo%2C+José+María%22">Gavilán-Izquierdo, José María</searchLink> (ORCID <externalLink term="https://orcid.org/0000-0002-3369-5377">0000-0002-3369-5377</externalLink>)<br /><searchLink fieldCode="AR" term="%22Gallego-Sánchez%2C+Inés%22">Gallego-Sánchez, Inés</searchLink> (ORCID <externalLink term="https://orcid.org/0000-0002-1088-3172">0000-0002-1088-3172</externalLink>)<br /><searchLink fieldCode="AR" term="%22Puertas%2C+María+Luz%22">Puertas, María Luz</searchLink> (ORCID <externalLink term="https://orcid.org/0000-0002-9093-5461">0000-0002-9093-5461</externalLink>)
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  Data: <searchLink fieldCode="SO" term="%22Journal+on+Mathematics+Education%22"><i>Journal on Mathematics Education</i></searchLink>. 2022 13(3):515-530.
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  Data: Indonesian Mathematical Society. Jl. Padang Selasa 524, Palembang, South Sumatra 30139, Indonesia. Tel: +618-127-106777; Fax: +627-113-20310; Web site: http://jme.ejournal.unsri.ac.id/index.php/jme
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  Data: The need to develop consistent theoretical frameworks for the teaching and learning of discrete mathematics, specifically of graph theory, has attracted the attention of the researchers in mathematics education. Responding to this demand, the scope of the Van Hiele model has been extended to the field of graphs through a proposal of four levels of reasoning whose descriptors need to be validated according to the structure of this model. In this paper, the validity of these descriptors has been approached with a theoretical analysis that is organized by means of the so-called processes of reasoning, which are different mathematics abilities that students activate when solving graph theory problems: recognition, use and formulation of definitions, classification, and proof. The analysis gives support to the internal validity of the levels of reasoning in graph theory as the properties of the Van Hiele levels have been verified: fixed sequence, adjacency, distinction, and separation. Moreover, the external validity of the levels has been supported by providing evidence of their coherence with the levels of geometrical reasoning from which they originally emerge. The results thus point to the suitability of applying the Van Hiele model in the teaching and learning of graph theory.
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  Data: EJ1379741
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RecordInfo BibRecord:
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    Languages:
      – Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 16
        StartPage: 515
    Subjects:
      – SubjectFull: Graphs
        Type: general
      – SubjectFull: Validity
        Type: general
      – SubjectFull: Mathematics Instruction
        Type: general
      – SubjectFull: Geometry
        Type: general
      – SubjectFull: Geometric Concepts
        Type: general
      – SubjectFull: Thinking Skills
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      – SubjectFull: Teaching Methods
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      – SubjectFull: Learning Processes
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      – SubjectFull: Mathematics Skills
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      – SubjectFull: Problem Solving
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      – SubjectFull: Classification
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      – SubjectFull: Mathematical Logic
        Type: general
      – SubjectFull: Mathematical Models
        Type: general
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      – TitleFull: A Theoretical Analysis of the Validity of the Van Hiele Levels of Reasoning in Graph Theory
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