Children's Construction of the Rational Numbers of Arithmetic

这项工作的目的是创建儿童构造有理数的数学模型，这些模型在科学和教育工作中是有用的。在一项建构主义教学实验中，研究人员在logo微世界中与儿童一起工作，他们的心理目标是创建一个儿童模型：构建产生有理数的运算，以及一种科学的语言，指定儿童在这个内容领域的数学。教育目标是在计算机微世界的基础上为儿童精心设计可能的学习环境的组成部分，并包括(1)可能的学习阶段的说明以及这些阶段的目标和意图，(2)参与学习的学生在学习阶段和构建过程中的数学概念和操作。(3)在学习期间由参与的学生建立和修改学习环境的问题情境，(4)我们在向学生提出问题时做出的关键决定，以及(5)将他们带入新的和更强大的概念的操作示例。为了促进这项工作，主要研究人员将成立一个关于算术有理数的工作组，并将举办一次科学和教育讲习班。

The purpose of the work is to create models of children's construction of the rational numbers of arithmetic that are useful in scientific and educational endeavors. In the context of working with children in logo microworlds in a constructivist teaching experiment, the psychological goal of the investigators is to create a model of children: construction of the operations that generate the rational numbers of arithmetic, along with a scientific language that specifies the mathematics of children in this contentual domain. The educational goal is to elaborate components of possible learning environments for children based on computer microworlds and to include (1) a specification of possible learning periods along with the goals and intentions within these periods, (2) the mathematical concepts and operations of the involved students within the learning period and itineraries of construction, (3) problem situations that served in the establishment and modification of learning environments by the involved students within the learning periods, (4) critical decisions we made in posing the problems to the students, and (5) examples of operating that carried them to new and more powerful concepts. To facilitate this work, the principal investigators will establish a working group on the rational numbers of arithmetic and will conduct a scientific and an educational workshop.