小学儿童数字线估计的心理表征模式

Primary School Children’s Representation Models of Number Line Estimation

采用调查研究法探讨小学儿童数字线估计的表征模式与发展趋势．包括两个实验，实验一以85名一、二、三年级儿童为被试，考察其在0～100范围内的数字估计．结果发现，一年级儿童在数字估计中经常采用对数和线性两种表征，二年级和三年级儿童更多采用线性表征．实验二以96名二、四、六年级儿童为被试，考察其在0～1000范围内的数字估计．结果显示，二年级儿童有一半采用对数表征，另一半采用线性表征，而四年级和六年级儿童大多采用线性表征．中国儿童存在数字估计的多种表征模式，表现出由不精确的对数表征逐步向精确的线性表征发展的趋势．在O～100的数字线上，这种转变出现在二年级；在0～1000的数字线上，这种转变出现在四年级．

Learning from abroad scholars＇ research procedure, two experiments examined the development of children＇s numerical estimation and representations that gave rise to their estimates. In experiment 1, 85 first-graders, second-graders and third-graders were asked to estimate the locations of numbers on number lines with 0 at one end and 100 at the other and no markings in between. The result of experiment 1 indicated that first graders＇ median estimates were fit equally well by the logarithmic and linear models; most second and third graders produced estimates consistent with a linear function. In experiment 2, 96 children from grade two, grade four and grade six were asked to estimate the locations of numbers on number lines with 0 at one end and 1000 at the other and no markings in between. The result of experiment 2 indicated that about half of second graders produced estimates that were best fit by linear function and half by logarithmic function, the large majority of fourth and sixth graders produced estimates consistent with a linear function. Both the results were against the view that people rely on any single representation of numbers, but for the Siegler＇s multiple representations perspective. Compared with the children in the United States, the Chinese children showed the same development trend as that of the children in the United States, that is, with increasing age and numerical experience, they increasingly rely on appropriate linear representation rather than logarithmic representation. On the 0-100 number lines, this transition was found in the second graders; On the 0-1000 number lines, this change was found in the fourth graders.