Research On The Relation Between Fraction And Whole Number Magnitude Representation Of Children From Third To Sixth Grade

Previous studies on "whole number bias" revealed that the knowledge of whole number can interfere fraction learning, that is to say, the relation between whole number magnitude representation and fraction number magnitude representation is negative related. However, recent evidence found this Conclusion was affected by the experimental tasks.This study included two studies. Cross-sectional study of Study1, and examined longitudinal study of Study2. Both explored the relation between whole number magnitude representation and fraction number magnitude representation. Three kinds of materials were used, whole number material is0-1000number line estimation; symbolic fraction materials included0-1fraction line estimation, computation and comparison; non-symbolic fraction materials were turned from symbolic fraction materials, except that computations only include Addition and subtraction.Study1examined198second to sixth-grade children’s performance in the three kinds of tasks. The results showed (1)Both for non-symbolic fraction and whole number estimate, the large majority of all graders produced estimates consistent with a linear function. But for symbolic fraction about half of third and fourth graders produced estimates that were best fit by linear function and half by logarithmic function, the large majority of fifth and sixth graders produced estimates consistent with a linear function.(2) Whole number magnitude representation (WMR) was positively related to symbolic fraction magnitude representation (SFMR), and the grade showed moderating effect, only fifth and sixth graders’ WMR can significantly predict SFMR;(3)WMR was positively related to non-symbolic fraction magnitude representation (NSFMR), and the grade also showed moderating effect, only second,third and sixth graders’ WMR can significantly predict NSFMR;(4)SFMR was also positively related to NSFMR, the grade also showed moderating effect, only fourth graders’SFMR can significantly predict NSFMR;(5) Intermediary effect analysis on the relation among the three kinds of magnitude representation showed that WMR had no direct effect on SFMR. NSFMR completely mediated the relationship between WMR and SFMR. NSFMR had only direct effect on SFMR. Grades had no effect on WMR, only direct effect on NSFMR, and both direct and indirect effect on SFMR.Study2examined the relation between WMR in Study1and NSFMR SFMR in study2. The experiment time was eight months from study1, when the children had just finished learning preliminarily knowledge of fraction. The children are second and third grades from studyl but third and fourth grades in study2.Experiment task only inlude symbolic and non-symbolic fractional material. The results showed (1)For non-symbolic fraction, the large majority of all graders produced estimates consistent with a linear function. This is consistent with that of study1. But for symbolic fraction about half of third graders produced estimates that were best fit by linear function and half by logarithmic function, the large majority of fourth graders produced estimates consistent with a linear function.(2) WMR in study1was positively related to SFMR in. study2, the grade also showed moderating effect, only third graders’ WMR can significantly predict SFMR; however, WMR had on relation to NSFMR.(3)A cross-lagged correlation analyses between SFMR and NSFMR of fourth grade showed that NSFMR is the cause of SFMR. This result was also consistent with studyl.In sum, WMR was positively related to SFMR, and NSFMR acted as a competely mediator. NSFMR.is the cause of SFMR. Grade also showed moderating effect.