Conceptual Mis(understandings) of Fractions: From Area Models to Multiple Embodiments

Autor/inn/en	Zhang, Xiaofen; Clements, M. A.; Ellerton, Nerida F.
Titel	Conceptual Mis(understandings) of Fractions: From Area Models to Multiple Embodiments
Quelle	In: Mathematics Education Research Journal, 27 (2015) 2, S.233-261 (29 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	1033-2170
DOI	10.1007/s13394-014-0133-8
Schlagwörter	Mathematics Instruction; Elementary School Mathematics; Grade 5; Mathematical Concepts; Teaching Methods; Interviews; Mathematics Skills; Pretests Posttests; Intervention; Mathematics Achievement; Achievement Gains; Concept Formation; Problem Solving; Instructional Effectiveness + Suchen Sie Ihr Suchwort? Mathematics lessons; Mathematikunterricht; Elementare Mathematik; Schulmathematik; School year 05; 5. Schuljahr; Schuljahr 05; Teaching method; Lehrmethode; Unterrichtsmethode; Interviewing; Interviewtechnik; Mathmatics achievement; Mathematics ability; Mathematische Kompetenz; Mathmatics sikills; Mathematical ability; Achievement gain; Leistungssteigerung; Concept learning; Begriffsbildung; Problemlösen; Unterrichtserfolg
Abstract	Area-model representations seem to have been dominant in the teaching and learning of fractions, especially in primary school mathematics curricula. In this study, we investigated 40 fifth grade children's understandings of the unit fractions, 1/2, 1/3, and 1/4, represented through a variety of different models. Analyses of pre-teaching test and interview data revealed that although the participants were adept at partitioning regional models, they did not cope well with questions for which unit fractions were embodied in non-area-model scenarios. Analyses of post-teaching test and interview data indicated that after their participation in an instructional intervention designed according to Dienes' (1960) dynamic principle, the students' performances on tests improved significantly, and their conceptual understandings of unit fractions developed to the point where they could provide reasonable explanations of how they arrived at solutions. Analysis of retention data, gathered more than 3 months after the teaching intervention, showed that the students' newly found understandings had, in most cases, been retained. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2020/1/01