# 수학의 1차적 개념이 초등학교 3학년 영재아의 수학적 개념구성과정에 미치는 영향에 대한 사례연구 - 분수의 덧셈과 곱셈을 중심으로 -

• Accepted : 2014.02.21
• Published : 2014.02.28

#### Abstract

On the subjects of elementary 3rd grade three child prodigies who had learned the four fundamental arithmetic operations and primary concepts of fraction, this study conducted a qualitative case research to examine how they composed schema of addition and multiplication of fractions and transformed schema through recognition of precise concepts and linking of concepts with addition and multiplication of fractions as the contents. That is to say, this study investigates what schema and transformed schema child prodigies form through composition of primary mathematic concepts to succeed in relational understanding of addition and multiplication of fractions, how they use their own formed schema and transformed schema for themselves to approach solutions to problems with addition and multiplication of fractions, and how the subjects' concept formation and schema in their problem solving competence proceed to carry out transformations. As a result, we can tell that precise recognition of primary concepts, schema, and transformed schema work as crucial factors when addition of fractions is associated with multiplication of fractions, and then that the schema and transformed schema that result from the connection among primary mathematic concepts and the precise recognition of the primary concepts play more important roles than any other factors in creative problem solving with respect to addition and multiplication of fractions.

#### Acknowledgement

Supported by : 세한대학교

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