| Children have difficulties learning and understanding rational number concepts, such as fractions, ratios and proportions in elementary school. Recently, efforts have been made to design appropriate teaching strategies which could foster children's learning. In order to help develop appropriate teaching strategies, it is important to understand what knowledge children bring with them before they receive any formal instruction, so that instruction could build on what they have already known. This study is designed to add to this growing literature by studying 4-, 5- and 6-year-old children's understanding of rational numbers, especially in the understanding of sharing and proportional reasoning. When children engage in partitioning activities, do children know that no matter how one object is divided, the amount remains the same? Do children know the concept that the more people one object is shared with, the less amount each person has? Do young children make proportional reasoning quantitatively? How and when does this proportional reasoning develop? These are the questions addressed in this study.;Children at the age of 4, 5 and 6 were interviewed individually. One set of tasks was used to assess children's understanding of sharing, which included 17 items. The other set of questions was used to assess children's proportional reasoning, which included 11 items. The accuracy and children's explanations for their answers were analyzed. For the understanding of sharing tasks, older children (6-year-olds) did better than their younger peers, and they were able to give more advanced explanations. In addition, if the problems were closer to children's daily life experience, children were more able to perform better. For the proportional reasoning tasks, older children also performed better than 4- and 5-year-olds, and they were also more able to provide advanced and quantifiable explanations. The results also showed that children were more comfortable working with discrete quantities than continuous quantities. The above results revealed that children's early understanding of sharing and proportional reasoning develop progressively from age 4 to age 6. Finally, educational implications were discussed. With the knowledge and processes of how children work with sharing activities and proportional reasoning problems, more developmentally appropriate instruction might be designed. |
