Department of Psychology, University of Nevada, Las Vegas, NV 89154, USA.
J Exp Child Psychol. 2012 Feb;111(2):246-67. doi: 10.1016/j.jecp.2011.08.005. Epub 2011 Sep 19.
We tested children in Grades 1 to 5, as well as college students, on a number line estimation task and examined latencies and errors to explore the cognitive processes involved in estimation. The developmental trends in estimation were more consistent with the hypothesized shift from logarithmic to linear representation than with an account based on a proportional judgment application of a power function model; increased linear responding across ages, as predicted by the log-to-lin shift position, yielded reasonable developmental patterns, whereas values derived from the cyclical power model were difficult to reconcile with expected developmental patterns. Neither theoretical position predicted the marked "M-shaped" pattern that was observed, beginning in third graders' errors and fourth graders' latencies. This pattern suggests that estimation comes to rely on a midpoint strategy based on children's growing number knowledge (i.e., knowledge that 50 is half of 100). As found elsewhere, strength of linear responding correlated significantly with children's performance on standardized math tests.
我们在数轴估计任务中对 1 年级到 5 年级的儿童以及大学生进行了测试，并考察了潜伏期和错误，以探究估计所涉及的认知过程。估计的发展趋势更符合从对数表示到线性表示的假设转变，而不是基于比例判断应用幂函数模型的解释；根据对数到线性转变位置预测，年龄增长导致线性反应增加，产生了合理的发展模式，而从周期性幂模型得出的值则难以与预期的发展模式相协调。这两种理论观点都没有预测到从三年级儿童的错误和四年级儿童的潜伏期开始出现的明显的“M 形”模式。这种模式表明，估计开始依赖于基于儿童不断增长的数字知识的中点策略（即，知道 50 是 100 的一半）。正如在其他地方发现的那样，线性反应的强度与儿童在标准化数学测试中的表现显著相关。
