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Pupils' over-reliance on linearity: A scholastic effect?


Correspondence should be addressed to Wim Van Dooren, Center for Instructional Psychology and Technology, Vesaliusstraat 2, B-3000 Leuven, Belgium (e-mail:


Background. From upper elementary education on, children develop a tendency to over-use linearity. Particularly, it is found that many pupils assume that if a figure enlarges k times, the area enlarges k times too. However, most research was conducted with traditional, school-like word problems.

Aims. This study examines whether pupils also over-use linearity if non-linear problems are embedded in meaningful, authentic performance tasks instead of traditional, school-like word problems, and whether this experience influences later behaviour.

Sample. Ninety-three sixth graders from two primary schools in Flanders, Belgium.

Method. Pupils received a pre-test with traditional word problems. Those who made a linear error on the non-linear area problem were subjected to individual interviews. They received one new non-linear problem, in the S-condition (again a traditional, scholastic word problem), D-condition (the same word problem with a drawing) or P-condition (a meaningful performance-based task). Shortly afterwards, pupils received a post-test, containing again a non-linear word problem.

Results. Most pupils from the S-condition displayed linear reasoning during the interview. Offering drawings (D-condition) had a positive effect, but presenting the problem as a performance task (P-condition) was more beneficial. Linear reasoning was nearly absent in the P-condition. Remarkably, at the post-test, most pupils from all three groups again applied linear strategies.

Conclusions. Pupils' over-reliance on linearity seems partly elicited by the school-like word problem format of test items. Pupils perform much better if non-linear problems are offered as performance tasks. However, a single experience does not change performances on a comparable word problem test afterwards.