Number Words and Number Concepts

描述（由申请人提供）：人类是唯一使用数字的动物——至少是精确的数字，比如2007甚至7。我们和其他物种一样，具有感知小而精确的数字的能力，比如1、2和3，也有感知大而近似的数字的能力，比如“大约50”，而不是“大约25”或“大约100”。但只有人类才会使用既大又精确的数字——比如5,6,7，…等。人类也是唯一使用语言的动物，因此可以为数字创造外部的语言符号。因为孩子们在学习阅读之前学会说话，他们学习的第一个语言数字符号是数字单词：“一”、“二”、“三”……等。本研究探讨了心理符号（数字概念）与语言符号（数字词）之间的关系。数字词只是人类与生俱来的5、6、7等概念的方便标签吗？或者数字概念本身是一种代代相传的文化发明？这项研究旨在回答两个非常基本的问题。首先，当一个孩子学习一个数字单词的意思，比如“二”或“五”，孩子是否构建了一个她以前没有的“二”或“五”的概念？或者她只是学习了一个已经存在的“二性”或“五性”概念的标签？其次，数字单词的含义是逐渐学习的（如果数字概念本身正在构建中，我们可能会这样认为），还是一次性学习的（如果孩子已经有了这个概念，我们可能会这样认为）？具体来说，这项研究有两个目的。目标1是确定数字单词学习实际上是意味着构建新的数字概念，还是仅仅是为旧概念学习新的标签。例如，研究1将确定孩子们对小数字的注意力和记忆力是否在他们学习了这个数字的单词后有所提高。研究2将确定学习一个特定的数字单词是否可以将该数字作为新的数量术语的候选含义，如“一对”、“几个”和“两个”。研究3将确定孩子们什么时候能理解一对一的对应关系是数字的基础。这意味着任何一组，例如，五个项目都可以与任何其他五个项目进行一对一的匹配，而不会留下任何项目。目标2是确定数字单词学习的早期步骤。如果儿童在学习数字单词含义的过程中正在构建数字概念，那么我们可以合理地预期他们会在其他方面之前掌握数字单词含义的某些方面。研究4将告诉我们，当孩子们学习数字词汇适用于离散量化而不是连续量化时。例如，你可以有“五个按钮”，但不能有“五个沙子”。研究5将告诉我们，当孩子们学习数字词指的是集合的属性，而不是个体的属性。例如，绿色是单个海龟的属性，而5是一组海龟的属性。

DESCRIPTION (provided by applicant): Humans are the only animal to use numbers-- at least exact numbers such as 2007 or even seven. We share with other species the ability to perceive small, exact numbers such as one, two, and three, and also to perceive large, approximate numbers such as 'about 50,' as opposed to 'about 25' or 'about 100.' But only humans use numbers that are both large and exact-- numbers such as 5, 6, 7,. . . etc. Humans are also the only animal to use language, and thus to create external, linguistic symbols for numbers. Because children learn to speak before they learn to read, the first linguistic number symbols they learn are the number words: "One," "two," "three," . . . etc. This research asks how the mental symbols (the number concepts) are related to the linguistic symbols (the number words). Are number words just handy labels for ideas of 5, 6, 7, and so forth that humans are born with? Or are number concepts themselves a cultural invention that gets passed down from generation to generation? This research aims to answer two very basic questions. First, when a child learns the meaning of a number word such as "two" or "five," does the child construct a concept of 'twoness' or 'fiveness' that she didn't have before? Or does she simply learn a label for a concept of 'twoness' or 'fiveness' that was already there? Second, are the meanings of number words learned gradually (as we might expect if the number concept itself is being constructed), or are they learned all at once (as we might expect if the child already has the concept)? Specifically, this research has two aims. Aim 1 is to determine whether number-word learning actually means constructing new number concepts, or simply learning new labels for old concepts. For example, Study 1 will determine whether children's attention and memory for small numbers improves after they learn the word for that number. Study 2 will determine whether learning a particular number word makes that number available as a candidate meaning for new quantity terms like "a couple," "a few," and "both." Study 3 will determine when children understand that one- to-one correspondence is the basis for numbers. This means that any set of, for example, five items can be matched up one-to-one with any other set of five items, without having any items left over. Aim 2 is to identify early steps in number-word learning. If children are constructing number concepts in the process of learning number-word meanings, then it is reasonable to expect that they will grasp some aspects of the meaning before others. Study 4 will tell us when children learn that number-words apply to discrete quantification rather than continuous quantification. For example, you can have "five buttons" but not "five sand." Study 5 will tell us when children learn that number words refer to a property of sets rather than a property of individuals. For example, green is a property of an individual turtle, but five is a property of a set of turtles.