• Journal of the Chungcheong Mathematical Society
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• v.23 no.3
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• pp.589-598
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• 2010

Generalizing normally quasi-ordered spaces, we introduce a concept of regularly quasi-ordered spaces and study their categorical properties. We obtain well behaved reflective subcategories of the category Rqos of regularly quasi-ordered spaces and continuous isotones, namely the full subcategory of Rqos determined by $T_0$-objects among others, and this result can be extended to that in the category Nqos of normally quasi-ordered spaces and continuous isotones.

• Journal of Elementary Mathematics Education in Korea
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• v.22 no.1
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• pp.1-24
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• 2018

This study included eleven elementary pre-service teachers who participated in the first and second teaching practices held by J Education College in 2015. After the pre-service teachers were encouraged to self-reflect on their mathematics teaching using a reflective survey sheet of mathematics teaching expertise, their uses of mathematics teaching expertise were analyzed according to the times of their mathematics practice instructions. The results are as follows: First, as the frequency of their mathematics teaching increased, the pre-service teachers' uses of mathematics teaching expertise increased, especially greatly with seven of them. However, the number of subcategories where the teachers' uses of mathematics teaching expertise increased was different from at least two to seven depending on the teachers. Second, the pre-service teachers who performed mathematics teaching practices four times used more of mathematics teaching expertise than those who did two times or three times. Third, some pre-service teachers who taught two or three times never reached 90% of the total score of any subcategory, even in the subcategory where they showed increase in their uses of mathematics teaching expertise. Fourth, the subcategory of 'reflection before class - teaching perspective - understanding of mathematics subject knowledge' was analyzed as the most difficult one for the study participants, and the reason is, they think, that there are not enough materials on the historical back grounds of mathematical concepts.