
05764024
j
2010d.00392
Gagatsis, Athanasios
Modestou, Modestina
Elia, Iliada
Spanoudes, Giorgos
Structural modelling of developmental shifts in grasping proportional relations underlying problem solving in area and volume.
Acta Didact. Univ. Comen., Math., No. 9, 923 (2009).
2009
Comenius University Press, Bratislava
EN
G33
C33
D23
illusion of linearity
linear model
geometrical problem solving
structural modelling
tests
pseudoproportionality
lower secondary
empirical investigations
Summary: This study explores students' abilities in three different dimensions of geometrical problem solving. Students were given a test involving three types of problems on area and volume: usual computation problems, pseudoproportional problems that beget the application of the linear model, and unusual ones. The structural organization of the reasoning processes behind the solutions was found to vary across grades. This organization indicated a weaker impact of the linear model on older students' reasoning.