오국환 Kukhwan Oh , 박정숙 Jung Sook Park , 권오남 Oh Nam Kwon

DOI: JANT Vol.56(No.2) 131-145, 2017

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.