以小学三到六年级学生117人作为被试,采用非符号性分数材料探讨小学生的分数表征方式,以确定他们能否表征分数值。以心理数字线假设为理论基础,分析被试完成分数比较任务的距离效应和反应编码中的“空间一数字关联”效应(SNARC效应)。结果表明:小学三到六年级学生能够对分数进行整体表征,并且表征效率随年级上升而显著提高。至少从三年级开始,小学生已能够根据分数的值,按从小到大的顺序自左至右地将分数表征在心理数字线上。
How do people represent fractions? Do they represent the real value of a fraction by accessing the magnitude of the whole numbers composing the fraction (componential) or directly represent the magnitude of whole fraction itself (holistic) ? Some researchers argued that, in the symbolic fraction comparison tasks, individuals may not directly access the magnitude of the whole fraction, but they process the magnitude of the components and estimate their ratio. However, other studies on symbolic fraction tasks suggested that peo- ple~ fraction representation can be either holistic or componential. We propose, from an evolutionary perspective, that magnitude repre- sentation may be divided into two systems : physical representation system and symbolic representation system. Compared to the symbolic system, the physical representation system appears earlier, by which people can simulate or represent magnitudes more directly, and a- void some possible interferences of symbolic representation system. Therefore, it is necessary to return to this early magnitude represen- tation system to investigate the representation mode of fractions. Considering the importance of fraction knowledge in the elementary mathematical education, the current study aimed to explore the fraction representation mode of students in primary schools by using non-symbolic fraction materials, which is based on the physical magnitude representation system~ This study sampled 117 third through sixth-grade students in an ordinary primary school, whose par- ents are on the medium level of socioeconomic status. We tested their performance in fraction comparison tasks and recorded the reaction time to examine the distance effect and the effect of the spatial numerical association of response codes ( SNARC), which are based on the assumption of mental number line. Results of ANOVA and regression analysis showed that: ( 1 ) with grade difference, subjects'reaction time in the fraction compari- son tasks significantly reduced ( F