The Effect of Number Line Task and Discrete Object Task Training on Children’s Whole Number Bias

XIN Zi-Jiang; LIU Chun-Hui

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Journal of Psychological Science ›› 2013, Vol. 36 ›› Issue (1) : 78-85.

The Effect of Number Line Task and Discrete Object Task Training on Children’s Whole Number Bias

¹,Chun-Hui Liu²

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Abstract

When children solve the fractional problems, they usually use previously formed single-unit counting scheme to interpret the fractions. This phenomenon is named as “whole number bias”, which is ubiquitous in fractional cognition. Previous literature showed that adults represented fractions in a manner with the correct whole number bias, instead of directly representing the magnitude of fractions. However, there is also a wrong whole number bias which may hinder the children from correctly solving the fractional problems. Therefore the purpose of this study is to explore whether the number line task and discrete object task can weaken children’s wrong whole number bias and investigate how children represent fractions when they successfully solve the fraction comparison task. This study consists of two tasks: the intervention task and the fraction comparison task via computer. Eighty-one forth-grade children who had the wrong whole number bias in a paper-pencil fraction comparison task were chosen for the current intervention task. They were divided into two groups: one was asked to accomplish the number line task, the other was asked to accomplish the discrete objects task. Each task had two sub-tasks: representing and comparing fractions with number line/ discrete object model and identifying and comparing fractions through number line/ discrete object model. After completing 20 items of intervention task, children performed a series of fractional comparison tasks via computer. Within-subject and between-subject crossed three factors design was conducted to investigate the effects of group (number line group versus discrete object group), numerical magnitude of a target fraction (either larger than the reference or smaller than the reference) and the response hand (left or right) on children’s accuracy and react time. Each child was presented eight target fractions which had the same numerator “1” but denominators varied from 1 to 9, and except for the fraction 1/5, which was the reference. Children were asked to compare the target fraction and reference. Each target fraction randomly appeared six times, so there were 48 trials in one block. Each child had two blocks in a random order. Stimulus presentation and the recording of behavioral data (reaction time and accuracy) were controlled by E-prime 1.1. The main results are as follows: (1) in intervention task, children in discrete objects group perform better than children in number line group. Children using the number line model are more likely to make mistakes. (2) Children in discrete objects group have better performance in fraction comparison task but their mean react time is significant longer than children in number line group. (3) Both two groups use the mental number line to represent fraction, and they show both correct and wrong whole number bias. From the results, two conclusions are drawn: (1) Using the number line or discrete object model can weaken wrong whole number bias, therefore teacher should use varied models to improve children’s understanding of fraction concept during fraction teaching. (2) During the process of conceptual change from the whole number to the rational number, children often have both correct and wrong whole number bias.

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whole number bias / fraction representation / mental number line

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Chun-Hui Liu. The Effect of Number Line Task and Discrete Object Task Training on Children’s Whole Number Bias[J]. Journal of Psychological Science. 2013, 36(1): 78-85

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