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

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.