Can the Proof Image Exist in the Absence of the Formal Proof?: Analyses of an Unsuccessful Proving Attempt

Autor/inn/en	Pala, Ozan; Aksoy, Esra; Narli, Serkan
Titel	Can the Proof Image Exist in the Absence of the Formal Proof?: Analyses of an Unsuccessful Proving Attempt
Quelle	15 (2021) 1, S.1-31 (31 Seiten)Infoseite zur Zeitschrift PDF als Volltext kostenfreie Datei Verfügbarkeit
Zusatzinformation	ORCID (Pala, Ozan) ORCID (Aksoy, Esra) ORCID (Narli, Serkan)
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	1307-6086
Schlagwörter	Mathematics Instruction; Validity; Mathematical Logic; Algebra; Preservice Teachers; Student Attitudes; Teaching Methods; Task Analysis; Problem Solving; Middle School Teachers; Cognitive Processes; Foreign Countries; Turkey + Suchen Sie Ihr Suchwort? Mathematics lessons; Mathematikunterricht; Gültigkeit; Mathematical logics; Mathematische Logik; Schülerverhalten; Teaching method; Lehrmethode; Unterrichtsmethode; Aufgabenanalyse; Problemlösen; Middle school; Middle schools; Teacher; Teachers; Mittelschule; Mittelstufenschule; Lehrer; Lehrerin; Lehrende; Cognitive process; Kognitiver Prozess; Ausland; Türkei
Abstract	As proof and proving are the key elements of mathematics, several frameworks evaluating this process have been presented. Proof image, being one of them, was introduced by Kidron and Dreyfus (2014) through analyses of two mathematicians' activities. Authors clarified it in the context of components, and emphasized its relation with formal proof. However, despite mentioning its possibility, they didn't present any case where proof image exists without the formal proof. This led us investigating dynamics of such cases. Multi-stage sampling was preferred, and 120 pre-service teachers were asked to prove two theorems about algebra firstly. Then, task-based interviews were conducted with 3 participants, who proved both theorems. Moment-by-moment analyses were conducted and sub-dimensions were discussed in detail. Additionally, role of "enlightenment" was reinterpreted and feeling dimension was elaborated. Consequently, it was identified that one participant had an image although she couldn't reach the formal proof, and her story was presented. (As Provided).
Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2024/1/01