Eighth Grade Students' Representations of Linear Equations Based on a Cups and Tiles Model

Autor/inn/en	Caglayan, Gunhan; Olive, John
Titel	Eighth Grade Students' Representations of Linear Equations Based on a Cups and Tiles Model
Quelle	In: Educational Studies in Mathematics, 74 (2010) 2, S.143-162 (20 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0013-1954
DOI	10.1007/s10649-010-9231-z
Schlagwörter	Mathematics Education; Figurative Language; Grade 8; Equations (Mathematics); Algebra; Psychological Patterns; Interviews; Evaluation Methods; Data Analysis; Comparative Analysis; Video Technology + Suchen Sie Ihr Suchwort? Mathematische Bildung; School year 08; 8. Schuljahr; Schuljahr 08; Equations; Mathematics; Gleichungslehre; Interviewing; Interviewtechnik; Auswertung
Abstract	This study examines eighth grade students' use of a representational metaphor (cups and tiles) for writing and solving equations in one unknown. Within this study, we focused on the obstacles and difficulties that students experienced when using this metaphor, with particular emphasis on the operations that can be meaningfully represented through this metaphor. We base our analysis within a framework of referential relationships of meanings (Kaput 1991; Kaput, Blanton, and Moreno, et al. 2008). Our data consist of videotaped classroom lessons, student interviews, and teacher interviews. Ongoing analyses of these data were conducted during the teaching sequence. A retrospective analysis, using constant comparison methodology, was then undertaken in order to generate a thematic analysis. Our results indicate that addition and (implied) multiplication operations only are the most meaningful with these representational models. Students also very naturally came up with a notation of their own in making sense of equations involving multiplication and addition. However, only one student was able to construct a "family of meanings" when negative quantities were involved. We conclude that quantitative unit coordination and conservation are necessary constructs for overcoming the cognitive dissonance (between the two representations--drawn pictures and the algebraic equation) experienced by students and teacher. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2017/4/10