Illusion of linearity: Effect in multiple-choice problems - Rajter, Miroslav (Array, 2007)
The aim of this study was to examine if there is a difference in successfulness of non-linear problems solving between younger and older, male and female students and between a group of students who had an offered linear solution for non-linear problems and a group that was not offered a linear solution. For the requirements of this study three lists of mathematical problems were constructed. Form A contained five non-linear problems, and for every problem five answers were offered. Among these five answers, one was a correct solution ; one was incorrect linear solution, while the remaining solutions served to reduce the probability of guessing. Form B was identical to Form A, but a linear solution was not offered in it. Problems in the Form C were classical proportionality problems with five offered solutions. One half of participants were asked to solve forms A and C, and the other half to solve forms B and C. A convenience sample of high school students was examined. The sample consisted of 112 first grade (N=52) and fourth grade students (N=60), 53 girls and 59 boys. There were no differences between participants in the solving of linear problems. The older students were more successful in the solving of non-linear problems than the younger ones. The students in the group without the linear solution were more successful than those who had an offered linear solution. The interaction effect of age and solving situation showed that older students were somewhat better than younger students when a linear solution was offered, but that difference was even larger when a linear solution was not offered. The results suggest that methods of education should be re-examined if we want the students to learn different models that can be applied successfully in the school and real-life situations.