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Title: The effects of different problem presentations and formulations on the illusion of linearity in secondary school students
Authors: De Bock, Dirk ×
Verschaffel, Lieven
Janssens, Dirk #
Issue Date: 2002
Publisher: L. Erlbaum Associates
Series Title: Mathematical Thinking and Learning vol:4 issue:1 pages:65-89
Abstract: This investigation focuses on the overgeneralization of the linear model — the so-called illusion of linearity. Previous studies by De Bock, Verschaffel, and Janssens (1998) generated strong empirical evidence for the strength of this phenomenon in 12- to 13-year-old and 15- to 16-year-old students working on applied geometrical
problems about the relation between the linear measurements and the area of similar plane figures. In this article, we report on two follow-up studies wherein we investigated the effects of problem presentation and formulation on the strength of the illusion of linearity in the same age groups. In the first follow-up study, we altered the
problem presentation by including metacognitive and visual scaffolds aimed at arousing students’ doubts about the appropriateness of the linear model and at helping them to find the appropriate mathematical model. In the second follow-up study, we changed the problem formulation by transforming the problems, which were originally formulated in a missing-value format, into comparison problems. Both experimental manipulations had a positive effect on students’ ability to resist the linearity illusion and to discover the nonproportional character of the problem situations, but these effects remained rather small, indicating that students’ tendency toward linear modeling is indeed very strong, deep-rooted, and resistant to change.
Description: Academisch Vormingsinstituut voor leraren (AVL) AVL - Academische lerarenopleiding. AVL - Nascholing (Vliebergh-Senciecentrum) Departement Pedagogische wetenschappen. Afdeling Didactiek. Centrum voor Instructiepsychologie en -technologie. Leuvens Instituut voor onderwijsonderzoek (LIVO) Afdeling Meetkunde.
ISSN: 1098-6065
VABB publication type: VABB-1
Publication status: published
KU Leuven publication type: IT
Appears in Collections:AVL - Academic Teacher Training
Teacher Training Mathematics (-)
Education and Training
Instructional Psychology and Technology
Research Centre for Educational Research & Development, Campus Brussels (-)
Faculty of Economics and Business (FEB) - miscellaneous
× corresponding author
# (joint) last author

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