The Microevolution of Mathematical Representations in Children's Activity
The Microevolution of Mathematical Representations in Children's Activity
复制标题
儿童活动中数学表示的微观演化
DOI：
10.1207/s1532690xci1302_5
复制
发表时间：
1995
影响因子：
3.3
通讯作者：
Luciano Meira
中科院分区：
文献类型：
--
作者：
Luciano Meira
在这篇文章中，我讨论了儿童在纸上的数学表示的设计，并询问如何在活动中构建和转换材料显示。我展示了(a)在解决问题的过程中，展示的设计以至关重要的方式塑造了一个人的数学活动和意义构建，以及(b)数学表示的知识不仅被简单地回忆起来并应用于解决问题，而且还从一个人与活动的社会和物质环境的互动中浮现出来（无论是否重新构建）。还详细描述了学生设计的求解线性函数问题的值表。符号系统在数学活动中的作用通常被认为是双重的：(a)支持认知加工，(b)调解交流（Kaput, 1987）。Fey（1990）补充说，从辅助角色，表征可以成为数学本身的对象，并产生“在具体情况下意想不到的模式”的研究（第73页）。根据Skemp（1979）的工作，Pimm（1987）详细描述了符号系统在数学活动中的作用，列出了符号的以下用途：“交流”、“记录和检索知识”、“帮助显示（思想之间的）结构”、“允许常规操作自动化”和“使反射成为可能”（第138页）。在古典数学教育中，对符号使用的分析倾向于将认知处理（被标记为内部）与对铭文的实际操作（被标记为外部）对立起来，从而产生了所提出的那种映射模型
In this article, I discuss children's design of mathematical representations on paper, asking how material displays are constructed and transformed in activity. I show that (a) the design of displays during problem solving shapes one's mathematical activity and sense making in crucial ways, and (b) knowledge of mathematical representations is not simply recalled and applied to problem solving but also emerges (whether constructed anew or not) out of one's interactions with the social and material settings of activity. A detailed characterization of student-designed tables of values to solve problems about linear functions is also presented. The role of notational systems in mathematical activity is often assumed to be two-fold: (a) supporting cognitive processing, and (b) mediating communication (Kaput, 1987). Fey (1990) added that, from an auxiliary role, representations can become the object of mathematics itself and yield the study of "unanticipated patterns in concrete situations" (p. 73). Drawing on Skemp's (1979) work, Pimm (1987) detailed the role of notational systems in mathematical activity by listing the following uses that symbols can be put to: "communicating," "recording and retrieving knowledge," "helping to show structure [among ideas]," "allowing routine manipulation to be made automatic," and "making reflection possible" (p. 138). In classical mathematics education, the analysis of symbol use tends to oppose cognitive processing (labeled as internal) to the actual manipulation of inscriptions (labeled as external), giving rise to mapping models of the kind proposed