Research on children’s recognition of ratio

Abstract

The purpose of this research is to clarify children's recognition of ratio. We developed problems to compare a chance of drawing a lot in three lotteries and carried out the examination intended for 51 students of 5th grade in elementary school. As a result of scalogram analysis and protocol analysis, we clarified the followings.
(1)Children's recognition of ratio can be classified into 5 categories.
(2)The percentage of children who can recognize multiple relation is only 5.9%.
(3)If the number of a lot is equal to the number of a blank in each three lotteries, children can't use the idea that if the number of a lot is equal to the number of a blank in the both lotteries, a chance of drawing a lot in both lotteries is same.