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Abstract：
The number-line estimation task has become one of the most important methods in numerical cognition research. Originally applied as a direct measure of spatial number representation, it became also informative regarding various other aspects of number processing and associated strategies. However, most of this work and associated conclusions concerns processing numbers in a symbolic format, by school children and older subjects. Symbolic number system is formally taught and trained at school, and its basic mathematical properties (e.g., equidistance, ordinality) can easily be transferred into a spatial format of an oriented number line. This triggers the question on basic characteristics of number line estimation before children get fully familiar with the symbolic number system, i.e., when they mostly rely on approximate system for non-symbolic quantities. In our three studies, we examine therefore how preschool children (3-5-years old) estimate position of non-symbolic quantities on a line, and how this estimation is related to the developing symbolic number knowledge and cultural (left-to-right) directionality. The children were tested with the Give-a-number task, then they performed a computerized number-line task. In Experiment 1, lines bounded with sets of 1 and 20 elements going left-to-right or right-to-left were used. Even in the least numerically competent group, the linear model better fit the estimates than the logarithmic or cyclic power models. The line direction was irrelevant. In Experiment 2, a 1-9 left-to-right oriented line was used. Advantage of linear model was found at group level, and variance of estimates correlated with tested numerosities. In Experiment 3, a position-to-number procedure again revealed the advantage of the linear model, although the strategy of selecting an option more similar to the closer end of the line was prevalent. The precision of estimation increased with the mastery of counting principles in all three experiments. These results contradict the hypothesis of the log-to-linear shift in development of basic numerical representation, rather supporting the linear model with scalar variance. However, the important question remains whether the number-line task captures the nature of the basic numerical representation, or rather the strategies of mapping that representation to an external space.
摘要：
数字线估计任务已成为数字认知研究中最重要的方法之一。最初用作空间数表示的直接度量，它还提供了有关数字处理和相关策略的其他各个方面的信息。然而,这项工作和相关结论的大部分涉及以符号格式处理数字，由学童和年龄较大的科目。符号数字系统在学校正式教学和培训，及其基本数学属性(例如，等距,序）可以轻松地转换为定向数字线的空间格式。在孩子们完全熟悉符号数字系统之前，这就引发了关于数字线估计的基本特征的问题，即，当他们主要依靠非符号量的近似系统时。在我们的三项研究中，因此，我们研究学龄前儿童（3-5岁）如何估计非符号量在一条线上的位置，以及这种估计与发展中的符号数知识和文化（从左到右）方向性有关。孩子们接受了给数字任务的测试，然后他们执行了一个计算机化的数字线任务。在实验1中，使用了由1和20个元素组成的集合从左到右或从右到左的线。即使在数字能力最差的群体中，线性模型比对数或循环功率模型更好地拟合估计值。线方向无关紧要。在实验2中,使用1-9个从左到右取向的线。在群体水平上发现了线性模型的优势，估计的方差与测试的数量相关。在实验3中，位置到数字的过程再次揭示了线性模型的优势，尽管选择更接近行尾的选项的策略很普遍。在所有三个实验中，估计的精度随着对计数原理的掌握而增加。这些结果与基本数值表示的发展中对数到线性移位的假设相矛盾，而是支持具有标量方差的线性模型。然而,重要的问题仍然是数字线任务是否捕获了基本数字表示的性质，或者更确切地说，将该表示映射到外部空间的策略。
