Lapaine, Valentin.
(2010).
*Illusion of linearity in multiple choice problems*.
Diploma Thesis. Filozofski fakultet u Zagrebu, Department of Psychology.
[mentor Vlahović-Štetić, Vesna ].

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## Abstract

This thesis is related to some aspects of illusion of linearity, the tendency to apply properties of linear or proportonal relations even in situations where it is not appropriate. In geometry, illusion of linearity entails thinking that a geometric shape's area or a geometric solid's volume is going to be reduced or enlarged k times if its length is reduced or enlarged k times (in fact, areas are reduced or enlarged k2 times and volumes k3 times). In the thesis, it is investigated whether an offered solution which corresponds to the illusion of linearity (i.e. linear solution) affects the success of solving problems for which is is not appropriate to apply the linear model (i.e. non-linear problems). It is also investigated whether successfulness of solving non-linear problems is affected by the magnitude of geometric shapes' size change. Finally, the relation is investigated between correctness of a solution and participants' degree of certainty for groups with and without offered linear solutions and for groups with lesser and greater magnitudes of geometric shapes' size change. Pupils of third grades of two high schools participated in the research. Each of them solved five word problems for which it was appropriate to apply the linear model (i.e. linear problems), each of which had five offered solutions. Each participant also solved five non-linear word problems, each of which also contained five offered solutions. The differences between various groups' non-linear problems were whether a linear solution was among the offered solutions and the magnitude of geometric shapes' size change (2, 3, 4 or 200, 300, 400). Participants solved linear problems very successfully and they solved non-linear problems much worse. Participants who did not have linear solution offered solved significantly more nonlinear problems than other participants. In addition, participants whose problems contained lesser magnitudes of geometric shapes' size change solved significantly more nonlinear problems than other participants. The interaction of mentioned variables was also significant. Participants in all experimental 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.

Item Type: | Diploma Thesis |
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Uncontrolled Keywords: | illusion of linearity, proportionality, teaching of mathematics |

Subjects: | Psychology > Školska psihologija |

Departments: | Department of Psychology |

Supervisor: | Vlahović-Štetić, Vesna |

Date Deposited: | 19 Dec 2011 14:03 |

Last Modified: | 03 Nov 2015 14:18 |

URI: | http://darhiv.ffzg.unizg.hr/id/eprint/1563 |

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