The Mathematical Education (한국수학교육학회지시리즈A:수학교육)

Korean Society of Mathematical Education (한국수학교육학회)
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An Analysis of Students' Understanding of Operations with Whole Numbers and Fractions

자연수와 분수 연산에 대한 학생들의 이해 분석

  • Received : 2011.10.10
  • Accepted : 2012.02.20
  • Published : 2012.02.28
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Abstract

The purpose of the study was to investigate how students understand each operations with whole numbers and fractions, and the relationship between their knowledge of operations with whole numbers and conceptual understanding of operations on fractions. Researchers categorized students' understanding of operations with whole numbers and fractions based on their semantic structure of these operations, and analyzed the relationship between students' understanding of operations with whole numbers and fractions. As the results, some students who understood multiplications with whole numbers as only situations of "equal groups" did not properly conceptualize multiplications of fractions as they interpreted wrongly multiplying two fractions as adding two fractions. On the other hand, some students who understood multiplications with whole numbers as situations of "multiplicative comparison" appropriately conceptualize multiplications of fractions. They naturally constructed knowledge of fractions as they build on their prior knowledge of whole numbers compared to other students. In the case of division, we found that some students who understood divisions with whole numbers as only situations of "sharing" had difficulty in constructing division knowledge of fractions from previous division knowledge of whole numbers.

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References

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