数字线和离散物体任务训练对儿童整数偏向的影响

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

通过数字线任务和离散物体任务对81名拥有错误整数偏向的儿童进行干预,再施测分数比较任务,以考查不同干预对错误整数偏向的影响以及分数在心理数字线上的表征方式。结果表明:(1)离散物体组儿童在干预任务中表现较好,在分数比较仟务中得分也显著高于数字线组儿童,但反应时要慢于数字线组儿童。(2)正确比较分数时,两组均出现正确整数偏向,但错误的整数偏向依然存在,二者在整数系统扩展到有理数系统这个过渡期同时存在。

When children solve the fractional problems, they usually use previously formed single - unit counting scheme to interpret the fractions. This phenomenon is called ＂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 prevent 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 to 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 paperpencil 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, the children performed a series of fractional comparison tasks via computer. A within - subjects and between - subjects crossed three - factor design was used to investigate the effects of the group （the number line group versus the discrete object group）, the 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 accuracy and react time. Each child was presented with 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, 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 the intervention task, the children in the discrete objects group perform better than those in the number line group. The children using the number line model are more likely to make mistakes. （2） The children in the discrete objects group have better performance in the fraction comparison task but their mean react time is significantly longer than the children in the number line group. （3） Both 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, teachers should use varied models to improve their students＂ understanding of fraction concepts when teaching fraction. （2） During the process of conceptual change from the whole number to the rational number, students often have both correct and wrong whole number bias.