Examination of Intensity of Illusion of Linearity among High School Pupils

Rajter, Miroslav. (2006). Examination of Intensity of Illusion of Linearity among High School Pupils. Diploma Thesis. Filozofski fakultet u Zagrebu, Department of Psychology. [mentor Vlahović-Štetić, Vesna].

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Abstract

This investigation discusses the strength of the illusion of linearity on high school pupils. Illusion of linearity (or proportionality) is an error in solving mathematical problems when people (wrongly) believe that when a certain length is enlarged by factor k, area and volume should also be enlarged by factor k. Correct solution would be that when a certain length is enlarged by factor k, other lengths are also enlarged by factor k, areas by factor k2, and volumes by factor k3. For the purpose of this investigation three lists of mathematical problems with multiple choice answers were constructed. In Form A there were five problems that were likely to induce the illusion of linearity (also called non-linear problems) and every problem had five answers offered. Among these five answers, one answer represents solution with an illusion of linearity (also called linear solution), one answer represents the correct solution (also called non-linear solution) and other three answers are distracters designed to lower the probability of guessing. Form B had mathematical problems that were identical to problems in Form A, but the linear solution was excluded from the offered answers. Form C had mathematical problems which required the linear solution (also called linear problems). Participants in this investigation were pupils of general-program high school, first grade (aged 14-15) and fourth grade (aged 17-18). The results showed that almost all pupils solved linear problems correctly. They were worse in solving non-linear problems than in solving linear ones. Pupils who didn't have linear solution offered to a non-linear problem were better in solving non-linear problems than pupils who had linear solution among offered answers. When a linear solution was excluded from the list of answers to non-linear problems, boys were better in solving non-linear problems than girls. Difference between the age groups was also found; older pupils were significantly better in solving non-linear problems.

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