The Effect of Feedback on the Intensity of Illusion of Linearity in Geometrical Problems

Paić – Antunović, Jelena. (2011). The Effect of Feedback on the Intensity of Illusion of Linearity in Geometrical Problems. Diploma Thesis. Filozofski fakultet u Zagrebu, Department of Psychology. [mentor Vlahović-Štetić, Vesna].

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Abstract

Illusion of linearity is a tendency to think that certain measures are linearly or proportionally associated even in situations where it is inadequate. This study examines the illusion of linearity in geometry, in tasks related to the perimeter or surface area of reduced or enlarged geometric figures. Previous studies have shown that students believe that when one dimension of a geometrical figure is increased or decreased by factor k, perimeter and surface of the figure increases or decreases by that same factor. Such reasoning is correct when it comes to perimeters of figures, but the surface is actually modified by a factor k2. Participants in the study were third grade high school students. They have taken an exam which consisted of 6 linear and 6 non-linear tasks on two occasions. Within each of these groups, the tasks were related to one of three different types of geometric figures. After the first exam we tested students’ performance on both linear and non-linear tasks with different geometric figures. The results have shown that students were very successful in solving linear tasks, especially with the ones involving irregular figures, while they were less successful with the ones involving squares and circles. On the other hand, students were markedly unsuccessful in solving non-linear tasks. Among them, they solved irregular figures tasks the worst, circles tasks slightly better and squares tasks the best. Before applying the second exam, half of the students were given feedback regarding their performance in the first exam and an opportunity to solve some of the tasks again. In second exam these students solved more non-linear tasks than the students from the control group, but in parallel, they achieved weaker results on linear tasks when compared to the students who were not involved in our intervention.

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