Title: What fills the gap between discrete and dense? Greek and Flemish students’ understanding of density
Authors: Vamvakoussi, Xenia ×
Konstantinos, P. Christou
Mertens, Lieve
Van Dooren, Wim #
Issue Date: Oct-2011
Publisher: Pergamon Press
Series Title: Learning and Instruction vol:21 issue:5 pages:676-685
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.
ISSN: 0959-4752
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Education and Training
Office for Educational Policy (-)
× corresponding author
# (joint) last author

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