Representational Flexibility and Problem-Solving Ability in Fraction and Decimal Number Addition: A Structural Model

Autor/inn/en	Deliyianni, Eleni; Gagatsis, Athanasios; Elia, Iliada; Panaoura, Areti
Titel	Representational Flexibility and Problem-Solving Ability in Fraction and Decimal Number Addition: A Structural Model
Quelle	In: International Journal of Science and Mathematics Education, 14 (2016), S.397-417 (21 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	1571-0068
DOI	10.1007/s10763-015-9625-6
Schlagwörter	Fractions; Problem Solving; Arithmetic; Numbers; Addition; Mathematics; Mathematics Instruction; Elementary School Students; Secondary School Students; Elementary School Mathematics; Secondary School Mathematics; Mathematical Concepts; Mathematical Models; Mathematical Logic; Thinking Skills; Mathematics Skills; Mathematics Education; Structural Equation Models + Suchen Sie Ihr Suchwort? Bruchrechnung; Problemlösen; Addition; Arithmetik; Arithmetikunterricht; Rechnen; Zahlenraum; Mathematik; Mathematics lessons; Mathematikunterricht; Sekundarschüler; Elementare Mathematik; Schulmathematik; Mathematical model; Mathematisches Modell; Mathematical logics; Mathematische Logik; Denkfähigkeit; Mathmatics achievement; Mathematics ability; Mathematische Kompetenz; Mathematische Bildung
Abstract	The aim of this study was to propose and validate a structural model in fraction and decimal number addition, which is founded primarily on a synthesis of major theoretical approaches in the field of representations in Mathematics and also on previous research on the learning of fractions and decimals. The study was conducted among 1,701 primary and secondary school students. Eight components, which all involve representational transformations, were encompassed under the construct of representational flexibility in fraction and decimal number addition. This structure reveals that, for both concepts, the representational transformation competences of recognition and conversion, and therefore representational flexibility as well, were affected by the complexity of the concepts involved and the direction of the conversion, respectively. Results also showed that two first-order factors were needed to explain the problem-solving ability in fraction and decimal number addition, indicating the differential effect of the modes of representation that is diagrammatic and verbal form on problem-solving ability irrespective of the concepts involved, as in the case of the conversions. Representational flexibility and problem-solving ability were found to be major components of students' representational thinking of fraction and decimal number addition. The proposed framework was invariant across the primary and secondary school students. Theoretical and practical implications are discussed. (As Provided).
Anmerkungen	Springer. 233 Spring Street, New York, NY 10013. Tel: 800-777-4643; Tel: 212-460-1500; Fax: 212-348-4505; e-mail: service-ny@springer.com; Web site: http://www.springerlink.com
Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2020/1/01