Illusion of linearity in area and volume problems: Do metacognitive and visual scaffolds help university students?

TLDR: In this article, the authors examine how different types of help provided to university students influence their achievement in mathematical problems involving the enlargement or reduction of geometrical figures, and find that metacognitive and visual scaffolds enhanced students' performance in volume and area problems.

Abstract: When solving geometry problems, students are prone to the illusion of linearity – a tendency to believe that when one side of a geometrical figure is increased or decreased by a factor k, its area and volume are also changed by that same factor. The aim of this study was to examine how different types of help provided to university students influence their achievement in mathematical problems involving the enlargement or reduction of geometrical figures. The participants, 122 undergraduate psychology students, were divided into four groups. One group solved an introductory task with visual scaffolds (help in the form of illustrations), second group received metacognitive scaffolds (help intended to provoke a cognitive conflict), third group received a combination of these, while the fourth group was the control group. All of the groups then solved a list of area, volume, and linear problems. The results show that metacognitive and visual scaffolds enhanced students’ performance in volume and area problems. There were no differences in the achievement between the experimental groups. The students in all experimental groups were better in solving area problems than volume problems, while there were no differences in the control group between the achievement in these two types of problems.