CHANGE IN RETIO'S CONCEPTS FOR CHILDREN AND INSTRUCTIONAL INTERVENTION

本项目的目的是调查儿童在日常生活中正式学习之前获得的关于比例的非正式知识，并根据儿童的非正式知识指导比例。在非正式知识的研究中，我们发现学生在正式学习之前就已经获得了非常丰富的非正式比例知识。例如，他们理解比率概念的基本含义，以及比率作为部分整体关系的各个方面。令人惊讶的是，他们可以解决比率的第二种用法，即使他们都没有学过公式来解决比率问题。其中一个问题是“80个人的75%是多少”。从常识的角度来看，学生是不可能解决这类问题的。而在不知道解题公式的高年级学生中，有40%的学生能够解题。通过对比率概念的正式学习，学生在解决比率问题方面积累了丰富的非正式知识。在教学干预方面，我们建立了新的分数课程。其中一所小学开设了这样的新课程。当我们在完成分数单元后比较普通课堂的成绩时，新课程的课堂表现出对分数的深刻理解。

The aim of this project was to investigate informal knowledge on ratio which children acquired before learning formally through everyday life and to instruct ratios based on children's informal knowledge. In research on informal knowledge, we found that students acquired very rich informal knowledge on ratio before learning it formally. For example, they understood basic meaning of ratio concepts and aspects of ratio as part-whole relationship. Very surprisingly, they could solve the second usage of ratio even though none of them learned formula to solve ratio problems. One of such problems was "what is 75% of 80 person". In viewpoint of common sense, it would be impossible for students to solve this kind of problems. But forty percentage of ate fin graders who did not know the formula to solve ratio problem could solve the problem. And by learning ratio concepts formally, it was demonstrated that students impressed rich informal knowledge in solving ratio problems.In instructional intervention, we established new curricula on fractions. Such new curricula was taught in one of elementary school. When we compared results obtained in orodinal class after finishing fraction unit, classes based on the new curricula indicated very deep understanding on fraction.