title: Pupils' over-reliance on linearity: a scholastic effect?
abstract: 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.
  
  
  OBJECTIVE
  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.
  
  
  METHODS
  Ninety-three sixth graders from two primary schools in Flanders, Belgium.
  
  
  METHODS
  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.
authors.affiliation: Center for Instructional Psychology and Technology, University of Leuven, Leuven, Belgium. wim.vandooren@ped.kuleuven.be
authors.forename: Wim
authors.initials: W
authors.lastname: Van Dooren
authors.forename: Dirk
authors.initials: D
authors.lastname: De Bock
authors.forename: Dirk
authors.initials: D
authors.lastname: Janssens
authors.forename: Lieven
authors.initials: L
authors.lastname: Verschaffel
mesh_terms: D002648:Child; D003071:Cognition; D005260:Female; D006801:Humans; D008297:Male; D012574:Schools; D013334:Students; D013850:Thinking