This study examines the illusion of linearity in high-school students’ solving of geometrical problems related to the perimeter and the area of similarly reduced or enlarged figures. Previous studies have shown that students strongly believe that when one dimension of a geometrical figure is increased or decreased by factor k, the perimeter and area of that figure increase or decrease by the same factor. Such reasoning is correct when it comes to perimeters, but the area is actually modified by a factor k2. Participants in our study were third grade high-school students. They have taken an exam consisting of 6 linear and 6 non-linear items on two occasions. The results on the first exam have shown that students were very successful in solving linear problems, but were markedly unsuccessful in solving non-linear problems. Before applying the second exam, half of the students were given feedback regarding their performance on the first exam and had an opportunity to solve some of the items again. On the second exam these students solved more non-linear problems correctly than the students of the control group, but in parallel, they achieved weaker results on the linear problems when compared to the students who were not involved in our intervention. |