Facilitating the Transition from Empirical Arguments to Proof

Autor/inn/en	Stylianides, Gabriel J.; Stylianides, Andreas J.
Titel	Facilitating the Transition from Empirical Arguments to Proof
Quelle	In: Journal for Research in Mathematics Education, 40 (2009) 3, S.314-352 (39 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0021-8251
Schlagwörter	Mathematics Instruction; Validity; Mathematical Logic; Preservice Teacher Education; Elementary School Teachers; Elementary School Mathematics; Teaching Methods; Cognitive Processes; Conflict + Suchen Sie Ihr Suchwort? Mathematics lessons; Mathematikunterricht; Gültigkeit; Mathematical logics; Mathematische Logik; Lehramtsstudiengang; Lehrerausbildung; Elementary school; Teacher; Teachers; Grundschule; Volksschule; Lehrer; Lehrerin; Lehrende; Elementare Mathematik; Schulmathematik; Teaching method; Lehrmethode; Unterrichtsmethode; Cognitive process; Kognitiver Prozess; Konflikt
Abstract	Although students of all levels of education face serious difficulties with proof, there is limited research knowledge about how instruction can help students overcome these difficulties. In this article, we discuss the theoretical foundation and implementation of an instructional sequence that aimed to help students begin to realize the limitations of empirical arguments as methods for validating mathematical generalizations and see an intellectual need to learn about secure methods for validation (i.e., proofs). The development of the instructional sequence was part of a 4-year design experiment that we conducted in an undergraduate mathematics course, prerequisite for admission to an elementary (Grades K-6) teaching certification program. We focus on the implementation of the instructional sequence in the last of 5 research cycles of our design experiment to exemplify our theoretical framework (in which cognitive conflict played a major role) and to discuss the promise of the sequence to support the intended learning goals. (Contains 5 tables, 4 figures, and 15 footnotes.) (As Provided).
Anmerkungen	National Council of Teachers of Mathematics. 1906 Association Drive, Reston, VA 20191-1502. Tel: 800-235-7566; Tel: 703-620-3702; Fax: 703-476-2970; e-mail: orders@nctm.org; Web site: http://www.nctm.org/publications/
Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2017/4/10