关键词: 数字表征, 数字线估计, 对数-线性转换, 时间赋义效应

Abstract: The representation and processing of pure numbers are studied extensively and previous findings indicated that results of number-line estimation of younger children conform to Fechner's law, that is to say the estimation results increase logarithmically with the increase of the actual number for smaller children, while the estimation results increases linearly for older children in the same number range. But the limitation of this study field is that representation of concretized numbers is nearly ignored. SNARC effect revealed that subjects responded to large numbers faster with the right hand than with the left hand, whereas the reverse held true for small numbers. Based on the hypothesis of mental number line, the researchers developed a number line estimation task to explore the law of number representation and development. In this task, the subjects are presented with a line with numbers on both ends (e.g., 0 and 100), and ask the subjects to determine the position of the number (e.g., 70) on the line. At present, there are two different views on the processing mechanism of time, space and quantity. The first point of view proposes that the processing of the three kinds of information share the common processing mechanism. The representative theory of first point of view is ATOM (A Theory Of Magnitude) proposed by Walsh (2003), which considers that the processing of time, space and quantity depends on a single representation mechanism. Another view is the multi representation system, which holds that the processing of time, space and number are domain-specificity, and each kind of information processing has the unique representation and transformation mechanism. Number representation and processing are handled by a non-abstract system, which processes numbers according to specific situations. So, a lot of studies in the past utilizing the number line estimation task almost ignored the concretized meaning of numbers, that is to say ignoring the difference between pure numbers and concretized numbers. In current study, Siegler’s(2003) number line estimation task is used as prototype to explore the change of number representation from grade two to grade six under the condition of concretized time by appending time unit (秒, 小时) to pure numbers. When the number is given meaning, the numerical semantic information is changed into the time quantity information, and we can compare the similarities and differences between pure number representation and time quantity information representation. Three classes of children attended the experiment. Concretized numbers were divided into two levels, i.e. short time (秒，second) concretization and long time (小时，hour) concretization. The results indicate there exists time concretizing effect in number line estimation in number line estimation task. And within the scale of 0-1000, the logarithmic-to-linear representational shift occurred at second grade which was consistent with previous studies, and when the numbers were concretized with time, explanatory power of logarithmic model was increased and that of linear model decreased correspondingly in all of three grades. The regression analysis of estimation median indicated time concretizing effect in each grade. For second graders, the interaction between concretizing and models was significant, and simple effect test indicated at the level of linear model, time concretizing effect was significant, F（1，26）=4.72，P<.05，while at the level of logarithmic model, time concretizing effect was not significant, F（1，26）=3.50，P=.073。For second graders, time concretizing effect was significant, F（1, 29）=5.710，P<.05，η2=.165，Muncon=.842（Std =.008），Mcon=.853（Std =.007）。For sixth graders, the interaction between concretizing and models was significant, and simple effect test indicated at the level of linear model, time concretizing effect was very significant, F（1，30）=9.78，P<.005，and at the level of logarithmic model, time concretizing effect was significant, F（1，30）=6.19，P<.05. Generally speaking, for all three graders, the data indicated obvious time concretizing effect--under time concretizing condition explanatory power of logarithmic model was increased, meanwhile the explanatory power of linear model decreased. Therefore, it seems that the results support the hypothesis of multi representation system.

Key words: Number representation, number line estimation, logarithmic-to-linear representational shift, time concretizing effect