• Journal of the Korean School Mathematics Society
• /
• v.25 no.4
• /
• pp.375-396
• /
• 2022

In this paper, to provide an idea for the 2022 revised mathematics curriculum by restructuring the content of the 2015 mathematics curriculum, the content elements of recurring decimals of textbooks, which showed differences in the curriculum of Korea and Japan, were analyzed. As a result of this study, in Korea, before the introduction of the concept of irrational numbers, repeating decimals were defined in the second year of middle school, and the relationship between repeating decimals and rational numbers was dealt with. In Japan, after studying irrational numbers in the third year of middle school, the terminology of repeating decimals is briefly dealt with. Then, when learning the concept of limit in the high school <Mathematics III> subject, the relationship between rational numbers and repeating decimals is dealt with. Based on the results of the study, in relation to the optimization of the amount of learning in the 2022 curriculum revision, implications for the introduction period of the circular decimal number, alternatives to the level of its content, and the teaching and learning methods were proposed.

• Journal of Educational Research in Mathematics
• /
• v.25 no.3
• /
• pp.263-279
• /
• 2015

The introduction of real numbers is one of the most difficult steps in the teaching of school mathematics since the mathematical justification of the extension from rational to real numbers requires the completeness property. The author elucidated what questions about real numbers can be unanswered as the "institutional didactic void" in school mathematics defining real numbers as the union of the rational and irrational numbers. The pre-service teachers' explanations on the extension from rational to real numbers and the raison d'$\hat{e}$tre of arbitrary non-recurring decimals showed the superficial and fragmentary understanding of real numbers. Connecting school mathematics to university mathematics via the didactic void, the author discussed how pre-service teachers could break the illusion of transparency about the real number.