High School Mathematics Teachers' Discernment of Invariant Properties in a Dynamic Geometry Environment

Autor/inn/en	Nagar, Gili Gal; Hegedus, Stephen; Orrill, Chandra Hawley
Titel	High School Mathematics Teachers' Discernment of Invariant Properties in a Dynamic Geometry Environment
Quelle	In: Educational Studies in Mathematics, 111 (2022) 1, S.127-145 (19 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Zusatzinformation	ORCID (Nagar, Gili Gal) ORCID (Orrill, Chandra Hawley)
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0013-1954
DOI	10.1007/s10649-022-10144-6
Schlagwörter	High School Teachers; Mathematics Teachers; Teacher Attitudes; Geometry; Mathematics Instruction; Geometric Concepts; Teaching Methods; Teacher Characteristics; Teaching Experience; Teacher Education + Suchen Sie Ihr Suchwort? High school; High schools; Teacher; Teachers; Oberschule; Lehrer; Lehrerin; Lehrende; Mathematics; Mathematik; Lehrerverhalten; Geometrie; Mathematics lessons; Mathematikunterricht; Elementare Geometrie; Teaching method; Lehrmethode; Unterrichtsmethode; Lehrerausbildung; Lehrerbildung
Abstract	Variance and invariance are two powerful mathematical ideas to support geometrical and spatial thinking, yet there is limited research about teachers' knowledge of variance and invariance. In this paper, we examined how high school teachers deal with the task of looking for invariant properties in a dynamic geometry environment (DGE) setting. Specifically, we investigated if they even attend to invariant properties; what invariant properties they discern and discuss; and how DGE can support such discernment. Our analysis found that teachers tend to discern and discuss invariant properties mainly when they were probed to consider invariance. We also found four categories of invariant properties that seem to be important for a robust and rich understanding of geometric objects in the context of invariance and DGE. The use of DGE allowed teachers to see and interact with invariant properties, thus suggesting that accessing geometry dynamically may have structural affordances especially when exploring invariance. Teachers were able to enact different DGE movements to discern and discuss invariant properties, as well as to reason with and about them. We also saw that teachers' backgrounds and past experiences can play an important role in their descriptions of invariant properties. Possible future research directions and implications to teacher education are discussed. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2024/1/01