Proof Schemes Combined: Mapping Secondary Students' Multi-Faceted and Evolving First Encounters with Mathematical Proof

Autor/inn/en	Kanellos, Ioannis; Nardi, Elena; Biza, Irene
Titel	Proof Schemes Combined: Mapping Secondary Students' Multi-Faceted and Evolving First Encounters with Mathematical Proof
Quelle	In: Mathematical Thinking and Learning: An International Journal, 20 (2018) 4, S.277-294 (18 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	1098-6065
DOI	10.1080/10986065.2018.1509420
Schlagwörter	Secondary School Students; Secondary School Mathematics; Validity; Mathematical Logic; Mathematical Concepts; Grade 9; Foreign Countries; Algebra; Geometry; Taxonomy; Greece + Suchen Sie Ihr Suchwort? Sekundarschüler; Gültigkeit; Mathematical logics; Mathematische Logik; School year 09; 9. Schuljahr; Schuljahr 09; Ausland; Geometrie; Taxonomie; Griechenland
Abstract	In this paper, we propose an enriched and extended application of Harel and Sowder's proof schemes taxonomy that can be used as a diagnostic tool for characterizing secondary students' emergent learning of proof and proving. We illustrate this application in the analysis of data collected from 85 Year 9 (age 14-15) secondary students. We capture these students' first encounters with proof and proving in an educational context (mixed ability, state schools in Greece) where mathematical proof is explicitly present in algebra and geometry lessons and where proving skills are typically expected, and rewarded, in key national examinations. We analyze student written responses to six questions, soon after the students had been introduced to proof and we identify evidence of six of the seven proof schemes proposed by Harel and Sowder as well as a further eight combinations of the six. We observed these combinations often within the response of the same student and to the same item. Here, we illustrate the eight combinations and we claim that a dynamic use of the proof schemes taxonomy that encompasses sole and combined proof schemes is a potent theoretical and pedagogical tool for mapping students' multi-faceted and evolving competence in, and appreciation for, proof and proving. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2020/1/01