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Autor/inn/en | Vamvakoussi, Xenia; Vosniadou, Stella |
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Titel | How Many "Decimals" Are There between Two "Fractions"? Aspects of Secondary School Students' Understanding of Rational Numbers and Their Notation |
Quelle | In: Cognition and Instruction, 28 (2010) 2, S.181-209 (29 Seiten)Infoseite zur Zeitschrift
PDF als Volltext |
Sprache | englisch |
Dokumenttyp | gedruckt; online; Zeitschriftenaufsatz |
ISSN | 0737-0008 |
Schlagwörter | Secondary School Students; Intervals; Numbers; Mathematics; Arithmetic; Mathematical Concepts; Concept Formation; Theories; Foreign Countries; Greece (Athens) |
Abstract | We present an empirical study that investigated seventh-, ninth-, and eleventh-grade students' understanding of the infinity of numbers in an interval. The participants (n = 549) were asked how many (i.e., a finite or infinite number of numbers) and what type of numbers (i.e., decimals, fractions, or any type) lie between two rational numbers. The results showed that the idea of discreteness (i.e., that fractions and decimals had "successors" like natural numbers) was robust in all age groups; that students tended to believe that the intermediate numbers must be of the same type as the interval endpoints (i.e., only decimals between decimals and fractions between fractions); and that the type of interval endpoints (natural numbers, decimals, or fractions) influenced students' judgments of the number of intermediate numbers in those intervals. We interpret these findings within the framework theory approach to conceptual change. (Contains 8 tables, 5 figures and 3 footnotes.) (As Provided). |
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Erfasst von | ERIC (Education Resources Information Center), Washington, DC |
Update | 2017/4/10 |