Rethinking the Discovery Function of Proof within the Context of Proofs and Refutations

Autor/inn/en	Komatsu, Kotaro; Tsujiyama, Yosuke; Sakamaki, Aruta
Titel	Rethinking the Discovery Function of Proof within the Context of Proofs and Refutations
Quelle	In: International Journal of Mathematical Education in Science and Technology, 45 (2014) 7, S.1053-1067 (15 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0020-739X
DOI	10.1080/0020739X.2014.902135
Schlagwörter	Mathematics Instruction; Mathematical Logic; Validity; Grade 8; Grade 9; Discovery Learning; Teaching Methods; Mathematical Concepts; Problem Solving; Foreign Countries; Geometric Concepts; Questionnaires; Japan + Suchen Sie Ihr Suchwort? Mathematics lessons; Mathematikunterricht; Mathematical logics; Mathematische Logik; Gültigkeit; School year 08; 8. Schuljahr; Schuljahr 08; School year 09; 9. Schuljahr; Schuljahr 09; Entdeckendes Lernen; Teaching method; Lehrmethode; Unterrichtsmethode; Problemlösen; Ausland; Elementare Geometrie; Fragebogen
Abstract	Proof and proving are important components of school mathematics and have multiple functions in mathematical practice. Among these functions of proof, this paper focuses on the discovery function that refers to invention of a new statement or conjecture by reflecting on or utilizing a constructed proof. Based on two cases in which eighth and ninth graders engaged in proofs and refutations, we demonstrate that facing a counterexample of a primitive statement can become a starting point of students' activity for discovery, and that a proof of the primitive statement can function as a useful tool for inventing a new conjecture that holds for the counterexample. An implication for developing tasks by which students can experience this discovery function is mentioned. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2017/4/10