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

摘要: We present an empirical study that investigated seventh-, ninth-, and eleventh-grade students’ understanding of the infinity numbers in interval. The participants (n = 549) were asked how many (i.e., a finite or infinite number numbers) what type decimals, fractions, any type) lie between two rational numbers. results showed idea discreteness fractions decimals had “successors” like natural was robust all age groups; students tended to believe intermediate must be same as interval endpoints only fractions); (natural numbers, fractions) influenced judgments those intervals. interpret these findings within framework theory approach conceptual change.