Chinese Journal of Science Education

Abstract

This study investigated students informal knowledge of fractions and explored the teaching and learning of beginning fractions. Questions of what constitutes a good learning enviroment and an appropriate zone of learning beginning fractions for second graders were also examined.

The informal knowledge of fractions were investigated with one-to-one semi-structured interviews. Second graders (N=25) who had not received formal instruction in fractions were given real objects to manipulate in the context of everyday life situations with words such as a half, fair and equal sharing. As a result of this experience, over 90% of them were able to count and to make equal sharing with even number of objects.

Teaching modules for beginning fractions were developed based on the knowledge about students informal knowledge, the principles of diagnostic teaching, and principles of the real-life mathematics education. Some key features of the module included attention to. choosing real-life situations, using small group discussion, grouping into different size of groups, diagnosting the awareness of equal parts, recognizing the invariant of different partitioning, and the three steps of learning cycle : distributing--recording--describing.

The explorative teaching was conducted by two school teachers in the research group at schools other than their own. Each exploration consisted of six forty-minutes lessons. After one month, all forty students were interviewed to betermine their understanding of fractions. Given a continuous quantity, they are able to solve equal sharing for two, three and four. Given discrete objects, they are able to solve equal sharing for two, three, four and five. The fractions language ½ and ¼ are used appropriately on continuous quantity situations, but not always on discrete objects. Many different strategies of sharing were developed by the students.

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