Psychological Development and Education ›› 2014, Vol. 30 ›› Issue (1): 1-8.

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Relationship between the Magnitude Representation of Whole Numbers and Fractions for 3 to 6 Graders

ZHANG Li1, LU Cai-fang1, YANG Xin-rong2   

  1. 1. Faculty of Psychology, Southwest University, Chongqing 400715;
    2. Department of Mathematics and Statistics, Southwest University, Chongqing 400715
  • Online:2014-01-15 Published:2014-01-15

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Abstract: In order to explore the relationship between whole number magnitude representation and fraction magnitude representation as well as the influence of grade on the relationship, this study examined the performance of 155 third to sixth graders in the 0-1000 whole number line and 0-1 fraction line estimation tasks. The results showed (1) For whole number estimate, the estimates of most children fitted a linear function; (2) But for symbolic fractions only fifth and sixth graders produced estimates consistent with a linear function; (3) As a whole, whole number magnitude representation (WMR) was positively related to symbolic fraction magnitude representation (SFMR). However, the grade had significant influence on the relationship between WMR and SFMR: only fifth and sixth grader's WMR could significantly predict SFMR but third and fourth grader's WMR could not.

Key words: number line estimation, magnitude representation, logarithmic function, linear function

CLC Number: 

  • B844.1

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