• The Mathematical Education
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• v.61 no.1
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• pp.1-28
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• 2022

The purpose of this study is to explore how students' fractional knowledge is related to their solving of proportion problems. To this end, 28 clinical interviews with four middle-grade students, each lasting about 30~50 minutes, were carried out from May 2021 to August 2021. The present study focuses on two 7th grade students who exhibited their ability to coordinate three levels of units prior to solving whole number problems. Although the students showed interiorization of three levels of units in solving whole number problems, how they coordinated three levels of units were different in solving proportion problems depending on whether the problems required reasoning with whole numbers or fractions. The students could coordinate three levels of units prior to solving the problems involving whole numbers, they coordinated three levels of units in activity for the problems involving fractions. In particular, the ways the two students employed partitioning operations and how they coordinated quantitative unit structures were different in solving proportion problems involving improper fractions. The study contributes to the field by adding empirical data corroborating the hypotheses that students' ability to transform one three levels of units structure into another one may not only be related to their interiorization of recursive partitioning operations, but it is an important foundation for their construction of splitting operations for composite units.

• Journal of the Korean housing association
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• v.1 no.1
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• pp.27-35
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• 1990

In the course of modernization coupled with industrialization and urbanization. Maru or wooden floor and Teachong or great hall of Han-ok or traditional Korean housing has experienced functional as well as physical changes to a remarkable degree. The author made an analysis of the transfiguration of Maru/Taechong space(M/T) with relation to: 1)Madang or yard. 2)Anbang or inner room, 3)Hyon-kwan or vestibule. 1) In relation to Madang, interiorization of M/T by way of setting sliding glass doors has begun to appear. 2) In connection with Anbang, division of role/function is being observed as far as family entertainment and reception of intimate friends is concerned. 3) Owing to wider acceptance of Hyon-kwan space as a buffer zone system, the advent of Keo-sil or living room is thought to be facilitated. The analysis, however, does not say that Keo-sil of modernized Korean housing might well be interpreted as the mere extension type of M/T of the vernacular housing.

• Journal of Educational Research in Mathematics
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• v.23 no.2
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• pp.237-252
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• 2013

The philosophy of science of Bachelard is introduced mainly with epistemological obstacles in the discussions within mathematics education. In his philosophy, epistemological obstacles are connected with the dialectical developments of science. Science progresses through generalization of concepts and theories by negating things which were recognized as obvious. These processes start with ruptures against the existing knowledge. Epistemological obstacles are failure in keeping distance with the existing knowledge when reorganization is needed. This concept means that there are the inherent difficulties in the processes of concept formation. Finally I compare the view of Bachelard on the developments of science and the 'interiorization-condensation-objectification' scheme of reflexive abstraction in mathematics education and discuss the inherent difficulties in the learning mathematics.

• The Mathematical Education
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• v.57 no.3
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• pp.231-246
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• 2018

In this paper, we applied Sfard's reification theory to analyze the secondary students' level of conceptualization with regard to the formula of quadratic equation. Through the generation and development of mathematical concepts from a historical perspective, Sfard classified the formulation process into three stages of interiorization, condensation, and reification, and proposed levels of formulation. Based on this theory, we constructed a test tool reflecting the reversibility of the nature of manipulation of Piaget's theory as a criterion of content judgement in order to grasp students' conceptualization level of the formula of quadratic equation. By applying this tool, we analyzed the conceptualization level of the formula of quadratic equation of the $9^{th}$ and $10^{th}$ graders. The main results are as follows. First, approximately 45% of $9^{th}$ graders can not memorize the formula of quadratic equation, or even if they memorize, they do not have the ability of accurate calculation to apply for it. Second, high school curriculum requires for students to use the formula of the quadratic equation, but about 60% of $10^{th}$ graders have not reached at the level of reification that they can use the formula of quadratic equation. Third, as a result of imaginarily correcting the error of the previous concept, there was a change in the levels of $9^{th}$ graders, and there was no change in $10^{th}$ graders.

• Parasites, Hosts and Diseases
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• v.29 no.2
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• pp.121-128
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• 1991

The degree of attraction of Toxoplasma gondii to vertebrate cells varies with cell type and cell phase. Human promyelocytic leukemia cells, HL-60, were synchronized by double thymidine block method and co-cultured with Toxoplasma for 1 hr at each cell stage to investigate the cell cycle specific susceptibility of parasites to host cells. For 30 hr the average number of Texoplasma that invaded was a little changed except at 3 hr from G1/S phase boundary which concurred with the peak point of DNA synthesis. At 3 hr which is a relatively short interval compared to whole S phase, modification of cells by parasitic invasion was most remarkable. The number of Toxoplasma that penetrated was increased to more than sin times. The shape of the cells became sludgy and almost indiscernible by strong accessibility of parasites only for an hour of mfd-S phase. The same auctuation was also observed at the second peak of S phase but weakly. This suggests that there be surface molecules concerning with the attachment of Texoplasma to the host cells, which is expressed at special point of S phase. further studies on the specific protein or similar molecules related could be carried out using synchronized HL-60 cells.