From discreteness to infinity: Stages in students' understanding of the rational number density

This research investigated students’ intermediate stages in understanding the dense structure of rational numbers. A cross-sectional study with 953 students from 5th to 10th grade was performed. After an inductive analysis coding the open answers to a question about how many numbers there are between two given rational numbers, a TwoStep Cluster Analysis was carried out revealingdifferent student reasoning profiles. Results showed that the most naïve natural number bias did not disappear at the end of secondary school. Moreover, different intermediate stages in the understanding of density were found along grades. A characteristic of these stages is that the understanding of infinity was reached in decimal numbers earlier than in fractions.

Jaar van publicatie:2020

Toegankelijkheid:Closed