University of Wisconsin-Madison, Madison, WI 53705, USA.
University of Wisconsin-Madison, Madison, WI 53705, USA.
J Exp Child Psychol. 2020 Jul;195:104844. doi: 10.1016/j.jecp.2020.104844. Epub 2020 Mar 31.
A fundamental question about fractions is whether they are grounded in an abstract nonsymbolic magnitude code similar to that postulated for whole numbers. Mounting evidence suggests that symbolic fractions could be grounded in mechanisms for perceiving nonsymbolic ratio magnitudes. However, systematic examination of such mechanisms in children has been lacking. We asked second- and fifth-grade children (prior to and after formal instructions with fractions, respectively) to compare pairs of symbolic fractions, nonsymbolic ratios, and mixed symbolic-nonsymbolic pairs. This paradigm allowed us to test three key questions: (a) whether children show an analog magnitude code for rational numbers, (b) whether that code is compatible with mental representations of symbolic fractions, and (c) how formal education with fractions affects the symbolic-nonsymbolic relation. We examined distance effects as a marker of analog ratio magnitude processing and notation effects as a marker of converting across numerical codes. Second and fifth graders' reaction times and error rates showed classic distance and notation effects. Nonsymbolic ratios were processed most efficiently, with mixed and symbolic notations being relatively slower. Children with more formal instruction in symbolic fractions had a significant advantage in comparing symbolic fractions but had a smaller advantage for nonsymbolic ratio stimuli. Supplemental analyses showed that second graders relied on numerator distance more than holistic distance and that fifth graders relied on holistic fraction magnitude distance more than numerator distance. These results suggest that children have a nonsymbolic ratio magnitude code and that symbolic fractions can be translated into that magnitude code.
分数的一个基本问题是，它们是否基于类似于整数的抽象非符号大小代码。越来越多的证据表明，符号分数可能基于感知非符号比率大小的机制。然而，系统地研究儿童的这些机制一直缺乏。我们要求二年级和五年级的儿童（分别在进行分数的正式指导之前和之后）比较符号分数对、非符号比率对和混合符号-非符号分数对。这个范式使我们能够测试三个关键问题：(a) 儿童是否对有理数表现出模拟大小代码，(b) 该代码是否与符号分数的心理表示兼容，以及 (c) 分数的正规教育如何影响符号-非符号关系。我们检查了距离效应作为模拟比率大小处理的标记和符号效应作为跨越数值代码转换的标记。二年级和五年级学生的反应时间和错误率表现出经典的距离和符号效应。非符号比率的处理效率最高，混合和符号标记相对较慢。在符号分数方面接受过更多正规教育的儿童在比较符号分数时具有明显优势，但在比较非符号比率刺激时优势较小。补充分析表明，二年级学生更依赖于分子距离而不是整体距离，而五年级学生更依赖于整体分数大小距离而不是分子距离。这些结果表明，儿童具有非符号比率大小代码，并且符号分数可以转换为该大小代码。
