초등학생의 분수와 분수 연산에 대한 이해 양상
Examining how elementary students understand fractions and operations1
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This study examines how elementary students understand fractions with operations conceptually and how they perform procedures in the division of fractions. We attempted to look into students’ understanding about fractions with divisions in regard to mathematical proficiency suggested by National Research Council (2001). Mathematical proficiency is identified as an intertwined and interconnected composition of 5 strands- conceptual understanding, procedural fluency, strategic competence, adaptive reasoning, and productive disposition. We developed an instrument to identify students’ understanding of fractions with multiplication and division and conducted the survey in which 149 6th-graders participated. The findings from the data analysis suggested that overall, the 6th-graders seemed not to understand fractions conceptually; in particular, their understanding is limited to a particular model of part-whole fraction. The students showed a tendency to use memorized procedure-invert and multiply in a given problem without connecting the procedure to the concept of the division of fractions. The findings also proposed that on a given problem-solving task that suggested a pathway in order for the students to apply or follow the procedures in a new situation, they performed the computation very fluently when dividing two fractions by multiplying by a reciprocal. In doing so, however, they appeared to unable to connect the procedures with the concepts of fractions with division.
Abstract
This study examines how elementary students understand fractions with operations conceptually and how they perform procedures in the division of fractions. We attempted to look into students’ understanding about fractions with divisions in regard to mathematical proficiency suggested by National Research Council (2001). Mathematical proficiency is identified as an intertwined and interconnected composition of 5 strands- conceptual understanding, procedural fluency, strategic competence, adaptive reasoning, and productive disposition. We developed an instrument to identify students’ understanding of fractions with multiplication and division and conducted the survey in which 149 6th-graders participated. The findings from the data analysis suggested that overall, the 6th-graders seemed not to understand fractions conceptually; in particular, their understanding is limited to a particular model of part-whole fraction. The students showed a tendency to use memorized procedure-invert and multiply in a given problem without connecting the procedure to the concept of the division of fractions. The findings also proposed that on a given problem-solving task that suggested a pathway in order for the students to apply or follow the procedures in a new situation, they performed the computation very fluently when dividing two fractions by multiplying by a reciprocal. In doing so, however, they appeared to unable to connect the procedures with the concepts of fractions with division.
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