Understanding fraction in children and intervention to them

本研究探讨了下列问题；(1)孩子们是如何获得分数或小数摩擦等概念的？(2)它们代表了什么样的知识？(3)可以进行什么样的干预？为了检验这些问题，我们对公立小学的儿童进行了为期三年的纵向研究。研究框架为(1)学习分数单元前的集体预测，(2)基于预测分析的个人访谈，(3)正式教师对分数单元的干预，(4)单元完成后的后测。我们发现了非常有趣的结果。然而，我们总结了一些结果。(1)在学习分数之前，几乎所有儿童都已经理解了分数的基本含义，尽管他们的知识是建立在已有知识的基础上的。在三年级学习分数单位后，正确理解分数概念的比例下降了63%。这个结果是非常令人惊讶的，因为孩子们的理解是通过学习分数的形式知识而变差的。当孩子们没有正式的分数课时，这种趋势在10个月内加速了。(2)儿童判断分数大小的策略主要分为三种模式之一，即(1)形式策略，即儿童运用分数的形式知识；(2)S规则策略，即儿童将分数的数量（分母或分子）大的分数排序为小的分数；(3)L规则策略，即儿童将分数的数量（分母或分子）大的分数排序为大的分数。(3)通过访谈，有S规则的学生在一定程度上容易转变为分数的形式知识。然而，L规则的人拒绝改变这些知识，他们拥有原始的策略。

The present study pursued the following questions ; (1) How do children acquire concepts like fraction or decimal frictions, (2) What kind of knowledge do they represent? (3) What kind of intervention is it possible to conduct?To examine these questions, we have conducted longitudinal study over the three years using children in public elementary school. Framework of the research was(1)collective pre-test before learning fraction unit, (2)individual interview based on analyses of the pre-test, (3)intervention of fraction unit by formal teacher, and(4)post-test after finishing the unit.We found very interesting results. However, we summed up some of the results.(1)Before learning fraction, almost all children had understood basic meaning of fraction although their knowledge was based on pre-existing knoweledge. After learning the fraction unit in three grade, percentage of those who understood fraction concept correctly dropped 63 %. This result was very surprising because children's understanding got worse by learning formal knowledge on fraction. The tendency was accelerated for ten months when children had no formal lesson on fraction.(2)Children's strategies on judging magnitude of fractions were divided into one of main three patterns, (1)formal strategy, in which children applied formal knowledge of fraction, (2)Rule S strategy, in which children ordered fractions whose number(denominator or numerator)is big as small magnitude, (3)Rule L strategy, in which children ordered fractions whose number(denominator or numerator)is big as big magnitude.(3)By interview, those who had Rule S changed to formal knowledge of fraction easily to some exten. However, those who Rule L resisted to change such knowledge and they possessed the original strategy.