# Illusion of linearity in multiple choice problems: magnitude of geometric shape's size change / Vlahović-Štetić, Vesna ; Lapaine, Valentin.

##### By: Vlahović-Štetić, Vesna.

##### Contributor(s): Lapaine, Valentin [aut].

Material type: ArticleDescription: .Other title: Illusion of linearity in multiple choice problems: magnitude of geometric shape's size change [Naslov na engleskom:].Subject(s): 5.06 | mathematics education, illusion of linearity hrv | mathematics education, illusion of linearity eng In: 14th Biennial EARLI Conference for Research on Learning and Instruction "Education for a Global Networked Society" (29.08.-03.09.2011. ; Exeter, Velika Britanija)Summary: This study is related to illusion of linearity, the tendency to apply properties of linear or proportional relations even in situations where it is not appropriate. It is investigated whether an offered linear solution affects the success of solving non-linear problems. It is also investigated whether the success of solving non-linear problems is affected by the magnitude of geometric shapes' size change. Finally, the relation between correctness of a solution and participants' degree of certainty is investigated. Pupils of third grades of two high schools participated in the research (N=201). They solved five linear and five non-linear word problems. There were four groups of non-linear problems. The difference between them were in whether a linear solution was among the offered solutions and in the magnitude of geometric shapes' size change (2, 3, 4, or 200, 300, 400) Participants solved linear problems very successfully and non-linear problems much worst. Participants who did not have linear solution offered solved significantly more non-linear problems than other group. Participants whose problems contained lesser magnitudes of geometric shapes' size change solved significantly more non-linear problems than group with greater magnitudes of change. The interaction of mentioned variables was also significant. Participants in all groups were equally certain in their correct solutions of non-linear problems. Participants who did not have linear solution offered were significantly less certain in their incorrect solutions of non-linear problems, and participants whose problems also contained lesser magnitudes of geometric shapes' size change were the least certain.This study is related to illusion of linearity, the tendency to apply properties of linear or proportional relations even in situations where it is not appropriate. It is investigated whether an offered linear solution affects the success of solving non-linear problems. It is also investigated whether the success of solving non-linear problems is affected by the magnitude of geometric shapes' size change. Finally, the relation between correctness of a solution and participants' degree of certainty is investigated. Pupils of third grades of two high schools participated in the research (N=201). They solved five linear and five non-linear word problems. There were four groups of non-linear problems. The difference between them were in whether a linear solution was among the offered solutions and in the magnitude of geometric shapes' size change (2, 3, 4, or 200, 300, 400) Participants solved linear problems very successfully and non-linear problems much worst. Participants who did not have linear solution offered solved significantly more non-linear problems than other group. Participants whose problems contained lesser magnitudes of geometric shapes' size change solved significantly more non-linear problems than group with greater magnitudes of change. The interaction of mentioned variables was also significant. Participants in all groups were equally certain in their correct solutions of non-linear problems. Participants who did not have linear solution offered were significantly less certain in their incorrect solutions of non-linear problems, and participants whose problems also contained lesser magnitudes of geometric shapes' size change were the least certain.

Projekt MZOS 130-1301676-1357

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