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Related Experiment Videos

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

Wim Van Dooren1, Dirk De Bock, Dirk Janssens

  • 1Center for Instructional Psychology and Technology, University of Leuven, Leuven, Belgium. wim.vandooren@ped.kuleuven.be

The British Journal of Educational Psychology
|May 17, 2007
PubMed
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Children often overuse linearity in math problems. Presenting non-linear problems as performance tasks, rather than traditional word problems, significantly improves understanding, though this effect doesn't persist on subsequent tests.

Area of Science:

  • Mathematics Education
  • Cognitive Psychology

Background:

  • Elementary students frequently exhibit linear over-reliance in mathematical reasoning.
  • A common misconception is that area scales linearly with linear enlargement (k times).
  • Previous research primarily used traditional, school-based word problems.

Purpose of the Study:

  • To investigate if students maintain linear over-reliance when non-linear problems are presented in authentic performance tasks.
  • To determine if experiencing non-linear problems in performance tasks influences subsequent problem-solving behavior.

Main Methods:

  • A pre-test assessed linear reasoning in 93 sixth graders using traditional word problems.
  • Interviews were conducted with students exhibiting linear errors on non-linear area problems.

Related Experiment Videos

  • Students were assigned to conditions: traditional word problem (S), word problem with drawing (D), or performance task (P).
  • A post-test evaluated performance on a comparable non-linear word problem.

    • Main Results:

    • Linear reasoning was prevalent in the traditional word problem (S) condition during interviews.
    • Visual aids (D) showed a positive effect, but performance tasks (P) were most effective in reducing linear reasoning.
    • Linear reasoning was minimal in the performance task (P) condition.
    • However, most students reverted to linear strategies on the post-test, regardless of the intervention condition.

    Conclusions:

    • The format of mathematical problems significantly influences students' reliance on linearity.
    • Performance-based tasks are more effective than traditional word problems or those with drawings for addressing non-linear reasoning errors.
    • A single exposure to performance tasks does not lead to lasting changes in performance on subsequent traditional word problems.