Unit:
Τομέας Διδακτικής των ΜαθηματικώνLibrary of the School of Science
Author:
Οικονόμου Κυριάκος
Supervisors info:
Ξανθή Βαμβακούση Επίκ. Καθηγήτρια
Original Title:
Απόπειρα αντιμετώπισης των δυσκολιών κατανόησης της πυκνής διάταξης των ρητών με τη βοήθεια της 'ελαστικογραμμής' ως αναλογίας-γέφυρας.
Translated title:
An attempt to deal with the diificulties of understanding the density property of rational numbers with the use of the 'rubber' line as a bridging analogy device.
Summary:
It is amply documented that the density property of rational numbers is
difficult to understand for students from elementary up to university level.
With this intervention we attempted to bridge the gap between students’ initial
ideas for the ordering of rational numbers and the mathematically correct
aspect.
The participants of the study were twenty five 9th graders from one class in a
school in the area of Athens. They were tested on their knowledge of various
aspects of the density property before and after the intervention. In addition,
a retention test was administered three weeks later. The intervention was based
on five tasks elaborated in one school hour.
Our intervention was based on the analogy “numbers are points on the
(geometrical) line”. Moreover, we drew on the bridging analogy approach, used
with promising results in the intervention –study of Vamvakkousi & Vosniadou
( 2012), using as bridging device the idea of the rubber number line, that is,
an imaginary line that does not break no matter how much it is stretched. Using
this bridging analogy we aimed at helping students understand not only the
infinity of points between two different points of the number line (thus,
infinite numbers) but also to grasp the more difficult to conceive idea, that
there is not a next rational number to a given one.
The results showed considerable improvement with respect to all aspects of the
density property of rational numbers, which was retained three weeks after the
intervention.
Keywords:
Density property, Discreteness, Bridging analogy, Rubber line, Intervention
