title: Number sense in the transition from natural to rational numbers.
abstract: BACKGROUND
  Rational numbers are of critical importance both in mathematics and in other fields of science. However, they form a stumbling block for learners. One widely known source of the difficulty learners have with rational numbers is the natural number bias, that is the tendency to (inappropriately) apply natural number properties in rational number tasks. Still, it has been shown that a good understanding of natural numbers is highly predictive for mathematics achievement in general, and for performance on rational number tasks in particular.
  
  
  OBJECTIVE
  In this study, we further investigated the relation between learners' natural and rational number knowledge, specifically in cases where a natural number bias may lead to errors.
  
  
  METHODS
  Participants were 140 sixth graders from six different primary schools.
  
  
  METHODS
  Participants completed a symbolic and a non-symbolic natural number comparison task, a number line estimation task, and a rational number sense test.
  
  
  RESULTS
  Learners' natural number knowledge was found to be a good predictor of their rational number knowledge. However, after first controlling for learners' general mathematics achievement, their natural number knowledge only predicted the subaspect of operations with rational numbers.
  
  
  CONCLUSIONS
  The results of this study suggest that the relation between learners' natural and rational number knowledge can largely be explained by their relation with learners' general mathematics achievement.
authors: Centre for Instructional Psychology and Technology, University of Leuven, Belgium.
authors: Jo
authors: J
authors: Van Hoof
authors: Centre for Instructional Psychology and Technology, University of Leuven, Belgium.
authors: Lieven
authors: L
authors: Verschaffel
authors: Centre for Instructional Psychology and Technology, University of Leuven, Belgium.
authors: Wim
authors: W
authors: Van Dooren
mesh_terms: D000073978:Academic Performance; D002648:Child; D005260:Female; D006801:Humans; D007858:Learning; D008297:Male; D055641:Mathematical Concepts; D008433:Mathematics / Q000193:education*; D013334:Students
keywords: fraction; natural number bias; number line; number sense; rational number