You are here:

What fills the gap between discrete and dense? Greek and Flemish students’ understanding of density
ARTICLE

, , ,

Learning and Instruction Volume 21, Number 5, ISSN 0959-4752 Publisher: Elsevier Ltd

Abstract

It is widely documented that the density property of rational numbers is challenging for students. The framework theory approach to conceptual change places this observation in the more general frame of problems faced by learners in the transition from natural to rational numbers. As students enrich, but do not restructure, their natural number based prior knowledge, certain intermediate states of understanding emerge. This paper presents a study of Greek and Flemish 9th grade students who solved a test about the infinity of numbers in an interval. The Flemish students outperformed the Greek ones. More importantly, the intermediate levels of understanding—where the type of the interval endpoints (i.e., natural numbers, decimals, or fractions) affects students’ judgments—were very similar in both groups. These results point to specific conceptual difficulties involved in the shift from natural to rational numbers and raise some questions regarding instruction in both countries.

Citation

Vamvakoussi, X., Christou, K.P., Mertens, L. & Van Dooren, W. (2011). What fills the gap between discrete and dense? Greek and Flemish students’ understanding of density. Learning and Instruction, 21(5), 676-685. Elsevier Ltd. Retrieved January 29, 2020 from .

This record was imported from Learning and Instruction on January 29, 2019. Learning and Instruction is a publication of Elsevier.

Full text is availabe on Science Direct: http://dx.doi.org/10.1016/j.learninstruc.2011.03.005

Keywords