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

Autor/inn/en	González, Antonio; Gavilán-Izquierdo, José María; Gallego-Sánchez, Inés; Puertas, María Luz
Titel	A Theoretical Analysis of the Validity of the Van Hiele Levels of Reasoning in Graph Theory
Quelle	In: Journal on Mathematics Education, 13 (2022) 3, S.515-530 (16 Seiten)Infoseite zur Zeitschrift PDF als Volltext kostenfreie Datei Verfügbarkeit
Zusatzinformation	ORCID (González, Antonio) ORCID (Gavilán-Izquierdo, José María) ORCID (Gallego-Sánchez, Inés) ORCID (Puertas, María Luz)
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	2087-8885
Schlagwörter	Graphs; Validity; Mathematics Instruction; Geometry; Geometric Concepts; Thinking Skills; Teaching Methods; Learning Processes; Mathematics Skills; Problem Solving; Classification; Mathematical Logic; Mathematical Models + Suchen Sie Ihr Suchwort? Grafische Darstellung; Gültigkeit; Mathematics lessons; Mathematikunterricht; Geometrie; Elementare Geometrie; Denkfähigkeit; Teaching method; Lehrmethode; Unterrichtsmethode; Learning process; Lernprozess; Mathmatics achievement; Mathematics ability; Mathematische Kompetenz; Problemlösen; Classification system; Klassifikation; Klassifikationssystem; Mathematical logics; Mathematische Logik; Mathematical model; Mathematisches Modell
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. (As Provided).
Anmerkungen	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
Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2024/1/01