The Mathematical Education (한국수학교육학회지시리즈A:수학교육)

Korean Society of Mathematical Education (한국수학교육학회)
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A textbook analysis of irrational numbers unit: focus on the view of process and object

무리수 단원에 대한 교과서 분석 연구: 과정과 대상의 관점으로

  • Oh, Kukhwan (Graduate school of Department of Mathematics Education, Seoul National University) ;
  • Park, Jung Sook (Yangjae High School) ;
  • Kwo, Oh Nam (Department of Mathematics Education, Seoul National University)
  • Received : 2016.07.15
  • Accepted : 2017.05.20
  • Published : 2017.05.31
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Abstract

The representation of irrational numbers has a key role in the learning of irrational numbers. However, transparent and finite representation of irrational numbers does not exist in school mathematics context. Therefore, many students have difficulties in understanding irrational numbers as an 'Object'. For this reason, this research explored how mathematics textbooks affected to students' understanding of irrational numbers in the view of process and object. Specifically we analyzed eight textbooks based on current curriculum and used framework based on previous research. In order to supplement the result derived from textbook analysis, we conducted questionnaires on 42 middle school students. The questions in the questionnaires were related to the representation and calculation of irrational numbers. As a result of this study, we found that mathematics textbooks develop contents in order of process-object, and using 'non repeating decimal', 'numbers cannot be represented as a quotient', 'numbers with the radical sign', 'number line' representation for irrational numbers. Students usually used a representation of non-repeating decimal, although, they used a representation of numbers with the radical sign when they operate irrational numbers. Consequently, we found that mathematics textbooks affect students to understand irrational numbers as a non-repeating irrational numbers, but mathematics textbooks have a limitation to conduce understanding of irrational numbers as an object.

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References

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