TY - JOUR

T1 - How Many Decimals Are There Between Two Fractions? Aspects of Secondary School Students' Understanding of Rational Numbers and Their Notation

AU - Vamvakoussi, Xenia

AU - Vosniadou, Styliani

PY - 2010/4

Y1 - 2010/4

N2 - We present an empirical study that investigated seventh-, ninth-, and eleventh-grade students' under-standing 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.

AB - We present an empirical study that investigated seventh-, ninth-, and eleventh-grade students' under-standing 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.

UR - http://www.scopus.com/inward/record.url?scp=77951261035&partnerID=8YFLogxK

U2 - 10.1080/07370001003676603

DO - 10.1080/07370001003676603

M3 - Article

VL - 28

SP - 181

EP - 209

JO - COGNITION AND INSTRUCTION

JF - COGNITION AND INSTRUCTION

SN - 0737-0008

IS - 2

ER -