Inappropriately applying natural number properties in rational number tasks: characterizing the development of the natural number bias through primary and secondary education

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• 作者：Jo Van Hoof ; Lieven Verschaffel ; Wim Van Dooren
• 关键词：Rational number ; Fraction ; Natural number bias ; Primary education ; Secondary education
• 刊名：Educational Studies in Mathematics
• 出版年：2015
• 出版时间：September 2015
• 年：2015
• 卷：90
• 期：1
• 页码：39-56
• 全文大小：748 KB
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• 作者单位：Jo Van Hoof (1)
  Lieven Verschaffel (1)
  Wim Van Dooren (1)
  
  1. Centre for Instructional Psychology and Technology, University of Leuven, Dekenstraat 2, 3000, Leuven, Belgium
  
• 刊物类别：Humanities, Social Sciences and Law
• 刊物主题：Education
  Mathematics Education
  Education
  
• 出版者：Springer Netherlands
• ISSN：1573-0816

文摘

The natural number bias is known to explain many difficulties learners have with understanding rational numbers. The research field distinguishes three aspects where natural number properties are sometimes inappropriately applied in rational number tasks: density, size, and operations. The overall goal of this study was to characterize the development of the natural number bias across the span between 4th and 12th grade. To achieve this goal, a comprehensive test was constructed to test 4th to 12th graders-natural number bias. This test was administered to 1343 elementary and secondary school students. Results showed that an overall natural number bias could be found. This bias appeared to be equally strong in tasks with decimal numbers and tasks with fractions. Moreover, the natural number bias was weakest in size tasks, somewhat stronger in operations tasks, and by far the strongest in density tasks. An overall decrease of the strength of the natural number bias—but no disappearance except for size tasks—could be found with grade.