Construction and Interaction: Children's Fractional Schemes

本项目的目的是在教师研究员的指导下，研究儿童在计算机环境中结对互动的情况下对分数方案的构建。通过对六对儿童在三年时间里的大约630个教学片段的录像数据，对每对儿童进行回顾性分析。儿童-儿童和成人-儿童的社会互动将与计算机环境中的互动一起进行分析，并与儿童的个人和社会数学活动的分析相关联。每对儿童的个案研究将受到科学的分析，其中儿童的分数方案和这些方案的构建被抽象和组织成一个连贯的结构。皮亚杰（Piaget）的假设，即数学是个体对互动的贡献，以及维果茨基（Vygotsky）的假设，即数学的来源在于社会互动的内化，将通过两种分析（回顾性分析和科学分析）不断得到检验。在这些假设被证伪的程度上，一个取代皮亚杰和维果斯基模型的学习模型也将被不断地测试，在这个模型中，主体环境的相互作用和主体内部的相互作用是相互牵连的。

The goal of this project is to study children's construction of fractional schemes in the context of the children interacting in computer environments in pairs under the guidance of a teacher-researcher. Using a videotaped data of approximately 630 teaching episodes with six pairs of children over a period of three years, a retrospective analysis will be conducted for each pair of children. The child-child and adult-child social interactions will be analyzed along with the interaction in the computer environments and correlated with an analysis of the children's mathematical activity both individual and social. The case study of each pair of children will be subjected to a scientific analysis in which the children's fractional schemes and construction of those schemes are abstracted and organized into a coherent structure. Piaget's hypothesis that mathematics is contributed by the individual to the interactions and Vygotsky's hypothesis that the source of mathematics resides in the internalization of social interaction will be continually tested through both kinds of analysis (retrospective and scientific). To the extent that these hypotheses are falsified, a model of learning that supersedes both Piaget's and Vygotsky's models also will be continually tested in which subject environment interactions and within subject interactions are co-implicated.