• School Mathematics
• /
• v.16 no.4
• /
• pp.763-782
• /
• 2014

The purpose of this study is to investigate mathematics content knowledge(MCK) of pre-service teachers about the area of a circle. 53 pre-service teachers were asked to perform four tasks based on the central ideas of measurement for the area of a circle. The results of this study are as follows. First, pre-service teachers had some difficulty in describing the meaning of the area of a circle. Quite a few of them didn't recognize the necessity of counting the number of area units. Secondly, pre-service teachers had insufficient content knowledge about the central ideas of measurement for the area of a circle such as partitioning, unit iteration, rearranging, structuring an array and approximation. Lastly, few pre-service teachers understood the concept of actual infinity. Most students regarded the rectangle as the figure having the approximation error instead of the limitation from rearranging the parts of a circle.

• Journal of the Korean Society for Railway
• /
• v.17 no.5
• /
• pp.342-348
• /
• 2014

Contact between wheel and rail leads to the creep phenomenon. Linear creep theory, assuming linear increase in the creep force vs creep, results in a critical speed at which the vibration of a railway vehicle goes to infinity. However, the actual creep force converges to a limited value, so that the vibration of a railway vehicle cannot increase indefinitely. In this study, the dynamics of a railway vehicle is investigated with a 6 DOF bogie model includingthe nonlinear creep curves of Vermeulen, Polach, and a newly calculated creep curve with strip theory. Strip theory considers the profiles of the wheel and rail. The results show that the vibration of a railway vehicle results in a limit-cycle over a specific running speed, and this limit-cycle becomes smaller as the slope of the creep-curve steepens. Moreover, a hunting phenomenon is caused due to flange contact, which restricts the magnitude of the limit-cycle.

• Sim-seong Yeon-gu
• /
• v.37 no.2
• /
• pp.149-183
• /
• 2022

The oracle of the I Ching, divination can be understood as 'synchronicity phenomenon' in analytic psychology. In order to experience divination actually, it requires a religious attitude that asks questions with a serious mind when a person is in trouble that consciousness reaches its limit. It is not just a passive attitude, but a modest, active attitude to ask what I can do now. The experience of the oracle of the I Ching connected to supra-consciousness is similar to 'active imagination'-talking with the archetype of collective unconsciousness-and is 'the process of finding the rhythm of Self-archetype, the absolute wisdom of unconsciousness.' One month before my father's death, I took care of him who couldn't communicate verbally and I divination with a question 'What can I do for my father and me now?' The I Ching's answer was hexagram 19 Lin 臨, nine at the beginning. It's message was '咸臨貞吉 joint approach. perseverance brings good fortune.' 志行正也 we must adhere perseveringly to what is right.' Through this phrase, I learned the attitude of waiting for life after death as if 'joyful obedient' to the providence of nature that spring comes after winter. And I found that keeping the touching emotion of meeting infinity (in analytical psychological terms, 'Self') with perseveration is to do the true meaning of life beyond popular money-mindedness. And six months before my father's death, I had a dream about the afterlife. In the process of interpreting that dream, I learned not only from the shock of the direct message that 'it is a truth that there is something after death,' but also the regeneration of the mind through introversion from the similarity between the closed ward and '黃泉'-chinese underworld through amplification. And I learned the importance of an open attitude to accept new things through the 'window to eternity' symbolized by the white iron gate. In my father's catholic funeral ritual, I had hope that the catholic doctrine 'Communio Sanctorum'-A spiral cycle in which the living and the dead help each other may be real as well as a symbol of the individuation process in which consciousness and unconsciousness interact in our minds. Through the consolation received through the funeral visit of many people I met in my life, I found the answer that the path to contact with infinity begins with loving the beings in front of me. I tried to understand this continuous experience by the perspective of analytical psychology.

• School Mathematics
• /
• v.19 no.2
• /
• pp.319-343
• /
• 2017

In this study, we hope to reveal specialized content knowledge(SCK) and its features necessary to analyze student's errors and difficulties about the concept of irrational numbers. The instruments and interview were administered to 3 in-service mathematics teachers with various education background and teaching experiments. The results of this study are as follows. First, specialized content knowledge(SCK) were characterized by the fixation to symbolic representation like roots when they analyzed the concentration and overlooking of the representations of irrational numbers. Secondly, we observed the centralization tendency on symbolic representation and the little attention to other representations as the standard of judgment about irrational numbers. Thirdly, In-service teachers were influenced by content of students' error when they analyzed the error and difficulties of students. Lately, we confirmed that the content knowledge about the viewpoint of procept and actual infinity of irrational numbers are most important during the analyzing process.