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사치의 욕망을 심미적으로 전도(顚倒)시키는 회화표현에 대한 연구
Every misfortune originates from greed. Watching daily news reports, we frequently see that many accidents begin from one's greed, bringing misfortune to themselves and people in their surroundings. We shame those people while watching the news but, although it is not reported through the mass media, we curse and hurt other people because of our greeds. However, at the same time, such greed is the evidence of our existence and the eternal energy of life. My most personal and endless desire relates to private space that is pleasant and comfortable. It may be a desire of extravagance, and it is an excessive desire, not a condition necessary for living. However, my ceaseless craving for private space lead to abhorrence towards the present space along with mental pain. This is the most inferior desire that is considered as an operation of mental consumption most uncalled for in my life. Therefore, appropriate measure for interception of personal desires impeding happiness of life is needed. The common desires are caused by one's inner elements. However, I believe that the primary cause which stimulate and encourage to discriminate such desires is fetishism of today. Nowadays, advertisements that are sensationally sophisticated, provocative phrases of overflowing magazines, produced photographs of advertisements, marts that are becoming bigger, show-windows of shopping departments and etc are stimulants of our senses, being seen, heard, touched and felt irrespective of time and space. Out of all such stimulants, to me, who is over-obsessive about private spaces, pictures of spaces that are made to look comfortable mostly arouse the desire of extravagance and bring constant dissatisfaction toward the space in which I am present. Photography of today lies in the territory of art, and at the same time, it is a tool of recording facts and also a form of play. We are living at an era where it is flooding with images and visual elements have become important. The photographs of advertisements which have been produced to look attractive has their purpose on the viewers, thereby stimulating our desires. They accomplish their duty of alluring consumers because photographs confirm the fact that they 'really exist'. My works from 2006 to 2007 adopted scenes of produced photographs that urge desires. Objects in the scenes which stimulate desires are edited into individual photographs and undergo through process of becoming unreal by turning into paintings. The view point which observes the materials can be distinguished from the works of other artists who reflect time by adopting commercial images within prosperity of material production and consumption. The choice of colors and the method of expression used in my work possess the element of deleting the temptation factor of objects and emancipating from its original purpose. Color is the most dangerous element of temptation, therefore, the original magnificent colors are removed. Paintings are expressed in black, which means temperance, death and limitless space, with white, the part which have been erased, or blue, which means depression, sorrow and coldness, with white, the part which have been erased. The white part of the hollow-looking objects that have come to the front plays the role of something similar to a depressant. The plane surface which is filled with black or blue is erased with oil when it is in sticky and fluid condition. This process repeats the thought of erasing the object of desire, which needs to be erased in the mind, thereby hypnotizing my self, and the limited time of work extricates me from other earthly thoughts. Objects shown as a result appear strong without the seductive elements, free from the original purpose known as promotion for consumption. The erased part is empty but as it clearly reveals itself, it signifies as something similar to portraits. It resembles actual objects, however, it is changed into another false image, different from the real one. Eyes that head toward the object slide and bounce off from the smooth surface but there is no sense of deprivation, frustration or inferiority which we feel when facing with photographs of advertisements. The scenes that have become unreal are no longer objects of seductive possession but achieves independent meaning as an object of aesthetic. This thesis studied on the methods of expression and elements needed to converting the original purpose, which stimulate desires, into aesthetic objects by portrait-fying the objects, and self-hypnosis of controling and emptying infinite desires through the process of painting the produced scenes that are encouraging. Through this process, I hope to construct my own unique world of art. 모든 불행은 욕심으로부터 시작된다. 연일 보도되는 뉴스를 보면 많은 사건들이 욕심에서 시작되어 본인과 주변 사람들까지 불행하게 만드는 것을 흔히 볼 수 있다. 우리는 뉴스를 보면서 그들을 탓하지만 보도되지 않을 뿐 우리는 늘 욕심 때문에 누군가를 미워하고, 상처를 주고받는다. 그러나 동시에 이러한 욕심은 살아있다는 증거이기도 하며 영원히 계속되는 삶의 에너지이기도 하다. 본인의 욕심 중 가장 사사로우면서도 끊임없는 욕망은 쾌적하고 안락한 개인적 공간에 대한 것이다. 이것은 사치의 욕구라고도 할 수 있으며 이는 삶을 살아가기 위한 필수조건이 아닌 여분의 욕구이다. 그러나 본인의 개인적 공간에 대한 끊임없는 갈망은 정신적인 고통과 함께 현재의 공간에 대한 증오로까지 이어져 오고 있다. 이것은 본인의 삶에서 가장 불필요한 정신적 소모 작용으로 여겨지는 저급한 욕망이다. 그렇기에 사사로운 욕망이 삶의 행복을 저해하는 것을 막기 위해서 우리는 적절한 대책이 필요하다. 세속적 욕망의 원인은 사람들의 내면에도 그 요인이 있지만 그것을 자극하고 부추기며 차이를 느끼게 하는 현 시대의 물신(物神)주의가 가장 원색적인 요인이라고 여겨진다. 놀라울 정도로 세련된 광고와 넘쳐나는 매거진의 자극적 문구, 연출된 사진 광고, 점점 대형화 되는 마트나 백화점의 쇼윈도 등 요즈음의 광고는 장소와 시간에 관계없이 보여지고, 들려지고, 만져지고, 느껴지는 오감(五感)자극제이다. 그 중에서도 개인적 공간에 유독 집착하는 본인에게 안락한 공간을 연출한 사진은 가장 사치의 욕망을 불러일으키며 현재 자신이 가지고, 속한 공간에 대한 끊임없는 불만족을 유발시킨다.. 오늘날의 사진은 예술의 한 영역이기도 하고 사실을 기록하기 위한 도구이기도 하며 놀이이기도 하다. 우리는 시각적인 요소가 매우 중요해진 이미지의 홍수 시대 속에서 살아가고 있다. 특히 매력적으로 연출된 광고 사진은 그 목적이 보는 사람을 유혹하는데 있는 만큼 우리의 욕망을 자극한다. 그것은 사진이 가진 ‘실제로 존재함’을 확신시켜주는 이유로 소비자를 유혹하라는 본연의 임무를 충실히 달성해 낸다. 2006년부터 2007년으로 이어지는 본인의 작품들은 욕망을 부추기는 연출된 장면의 사진을 차용하고 있다. 욕망을 자극하는 장면 속의 대상은 독사진(獨寫眞)의 형태로 편집되어 비실재(非實在)적으로 전도(顚倒)되는 회화화(繪畵化) 과정을 거친다. 물질의 생산과 소비의 풍요로움 속에서 상품이미지를 차용하여 시대를 반영한 다른 작가들의 작품들과는 물질을 바라보는 시각에서 차이를 두고 있다. 본인의 작품은 색의 선택과 표현기법에서 대상의 유혹적 요소를 삭제시키고 본래 목적으로부터 해방시키기 위한 요소를 가진다. 색은 가장 위험한 유혹의 요소이므로 화려한 본래의 색채는 배제된다. 작품은 절제와 죽음, 무한한 공간의 의미를 가지는 검정색과 지워낸 자리의 흰색 또는 우울함, 슬픔과 차가움의 푸른색과 지워낸 자리의 흰색으로 표현된다. 대상이 드러난 텅 빈 느낌의 흰색은 진정제와 같은 역할을 한다. 검정색 또는 파란색으로 가득 채워진 화면은 물감이 끈적끈적하고 유동적인 상태에서 기름으로 지워진다. 이 과정은 마음에서 지워내야 할 욕망의 대상을 지워낸다는 생각을 반복하게 됨으로써 자기 최면을 걸고, 한정된 작업 시간은 다른 잡념으로부터 벗어나게 한다. 결과적으로 드러난 대상은 유혹적 요소를 잃은 경건한 모습으로 소비의 촉 진이라는 본래의 목적으로부터 벗어나 있다. 지워낸 자리는 비어있지만 또렷하게 드러나면서 마치 초상화와 같은 의미를 가진다. 실재하는 대상과 닮았지만 실제와는 다른 허상으로 변화된 것이다. 대상을 향한 시선은 매끈한 표면에서 미끄러지고 튕겨져 나오지만 광고사진을 대할 때 느끼는 박탈감이나 좌절, 열등감은 없다. 허상이 된 장면들은 더 이상 유혹적인 소유의 대상이 아닌 심미적 대상으로 독립적 의미를 가지게 된다. 본 논문은 본인을 자극하는 연출된 장면을 회화화(繪畵化) 하는 과정을 통해 무한한 욕망을 조절하고 비워내는 자기최면을 걸고, 대상의 초상화화(肖像畵化)를 통해 욕망을 자극하는 본래의 목적으로부터 심미적 대상으로 전도(顚倒) 시키고자 하는 표현 기법과 요소에 대하여 연구하였다. 이러한 과정을 통해 본인의 독자적인 작품세계를 구축하고자 한다.
Chromium methionine chelate가 3T3-L1 지방전구세포의 증식, 분화와 transcription factor발현에 미치는 영향
Cr은 glucose tolerance factor로서 당대사뿐만 아니라 결과적으로 혈중지방대사물질의 변화와 체지방의 변화와 같은 지방대사에 영향하는 것으로 보고되고 있다. 하지만 Cr이 어떻게 지방 대사에 영향 하는지에 대하여서는 알려진 바가 없다. 따라서 본 연구에서는 우선 세포수준에서 지방세포의 증식과 분화에 미치는 영향을 알아보기 위하여 Cr이 3T3-L1 지방전구세포의 분화에 미치는 영향을 규명하고자 하였다. 3T3-L1 지방전구세포는 생쥐(mouse)의 배아(embryo)로부터 분리한 세포로, 이들이 지방세포로 분화하기 때문에 지방세포분화를 연구하는데 널리 사용되어 왔다. 본 연구에서는 3T3-L1 지방전구세포를 Dulbecco's modified Eagle's medium(DMEM) 배양액에 10% bovine serum(BCS)를 섞어서 배양용기에 꽉 찬 상태까지 배양했고, 세포 seeding 6일 후에 호르몬(insulin, dexamethasone, isobutyl - methylzanthine) 을 처리해서 세포분화를 유도했다. 그 후 3T3-L1 지방전구세포의 분화는 glycerol-3-phosphate dehydrogenase 활성도에 의해 측정했고, Oil red O 염색으로 세포 내 지질방울의 형태변화를 관찰하였고 지방전구세포의 증식은 MTT 방법을 통해 세포 수를 측정하였다. 아울러 지방세포로 분화시 분화를 조절하는 대표적인 전사인자인 PPARγ, C/EBPα와 지방특이지표유전자인 FAS, LPL, aP2의 mRNA 발현량을 측정하였다. 본 연구에 사용한 Cr은 50ppb Cr-Met와 Cr-Pic를 사용하였으며 세포를 seeding하고 이틀 뒤부터 첨가하였다. 본 연구 결과, Cr 첨가는 3T3-L1 지방전구세포에 대한 지방세포의 증식과 분화에는 차이가 나타내지 않았다. 또한 전사인자와 지방특이유전자의 mRNA 발현량도 Cr 무첨가 대조구와 유의적인 차이가 없었다. 따라서 본 연구는 Cr의 지방대사 조절은 지방세포의 증식과 분화와는 연관성이 높지 않음을 증명하였다. 따라서 Cr에 의한 지방대사 조절의 기전은 오히려 지방의 축적량 조절과 관련되어 있다고 판단된다. Chromium has emerged as an essential trace mineral in nutrition. Chromium has a role in carbohydrate and lipid metabolism. A number of studies have evaluated the effect of Cr on glucose tolerance and insulin regulation that associated with lipid metabolism. However, the exact mechanism of lipid metabolism is not known yet. This in vitro study investigated the effect of chromium on the proliferation, differentiation and expression of transcription factor in 3T3-L1 preadipocyte. 3T3-L1 cell is a well-established cell line derived from mice embryo and the differentiate into adipocyte. This cell was plated in Dulbecco's modifed Eagle's medium(DMEM) plus 10% bovine serum(BCS). After six days, the cell was plated, and induced to differentiate by hormone treatment (day0) [insulin, dexamethasone and isobutyl-methylzanthine]. Differentiation of the 3T3-L1 cells were determined by glycerol-3-phosphate dehydrogenase (GPDH) activity and was monitored morphologically with Oil red O staining. Proliferation of the 3T3-L1 cell was determined by MTT assay. And, expression of transcription factor(PPARγ, C/EBPα) and fat specific marker gene(FAS, LPL, aP2) in 3T3-L1 preadipocyte were also measured. There were no (p>0.05) significant differences on proliferaton and differentiation in 3T3-L1 preadipocyte among Cr treatment. There were either no (p>0.05) differences on expression of transcription factor and fat specific marker gene in 3T3-L1 preadipocyte among Cr treatment. According to the results of this study, it can be concluded there could be no effect of Cr on proliferation, differentiation in 3T3-L1 preadipocyte. Therefor it could be suggested that the action of Cr in lipid metabolism was associated with adiposity than proliferation and differentiation of adipocyte.
단결정 세라믹 브라켓 베이스의 표면 처리에 의한 bonding/debonding 특성제어 및 효과
심미에 대한 환자 및 술자의 기대가 증가함에 따라 교정 영역에서 세라믹 브라켓의 사용이 많아지고 있다. 이에 따라 세라믹 브라켓의 장점을 활용하고 단점을 극복하기 위한 재료의 개발이 지속적으로 이루어지고 있다. 본 연구는 강도와 투명도가 우수한 세라믹 브라켓의 디본딩 특성 개선 및 향상을 위한 것으로 디본딩 특성 향상을 위해 제안된 표면 처리의 효과 및 영향에 대하여 표면 처리 면적을 인자로 고찰하였다. 이 실험의 목적은 브라켓의 개발 과정 중 새로운 베이스 처리 방법을 사용한 단결정 세라믹 브라켓의 임상에서의 활용 가능성을 알아보는 것이다. 연구에 사용한 세라믹 브라켓은 사파이어 단결정 소재를 출발 원료로 하여 절삭 및 연마공정을 통하여 준비하였고, 기계적 유지 구조를 부여하기 위한 표면 처리를 시행하였다. 베이스 그래뉼 코팅은 그래뉼 분산 및 도포, 융착 열처리 공정을 통해 이루어졌다. 표면 처리 면적에 따른 전단 결합 강도를 알아보기 위하여 그래뉼 분사 면적을 단계적으로 조절하여 8 종류의 브라켓을 제작하였다(0, 20, 30, 40, 50, 60, 80, 100%). 레진 인공 치아 88개와 통상적 치료 과정에서 발거된 상악 소구치 88개를 각 8군으로 분류하였다. 치관의 협면 중앙에 레진 인공 치아는 샌드블라스팅, 자연 치아는 37% 인산 산부식으로 전처리 하였다. 제작된 8개 군의 브라켓 베이스 표면에 adhesive agent, adhesive resin paste 적용 후 치면에 접착, 여분의 레진을 제거하고 광중합 하였다. 브라켓의 접착면이 전단력 측정 기구의 작용 방향과 평행이 되도록 치근 부위를 레진 몰드에 고정하였다. 전단 결합 강도 측정기의 cross head speed는 0.5mm/min 으로 설정하였다. 브라켓 제거 후 분리된 치아 표면을 관찰하였다. 잔여 레진의 양을 ARI 지수로 기록하고, 브라켓 파절 여부 및 자연 치아의 표면 손상 여부를 조사하였다. 실험 결과 전단 결합 강도는 자연 치아의 경우 50% 군에서 8.09±2.66 MPa, 60% 군에서 8.68±2.87 MPa 로, 임상적으로 적용 가능한 브라켓의 접착 강도를 얻을 수 있었다. ARI 측정 결과 레진 인공 치아와 자연 치아에서 유사한 분리 양상을 보였으며, 표면 처리 면적이 넓을수록 잔여 레진의 양이 감소하였다. 브라켓 파절은 불특정한 4개의 시편에서 발생하였다. 자연 치아의 표면 손상 관찰 결과, 전단 결합 강도가 과도하게 나타난 80%와 100% 군에서 일부 치아의 에나멜 손상이 관찰되었다. 세라믹 브라켓의 제작 과정에서 다양한 요소의 조절을 통해 특성을 제어할 수 있다. 그 중에서 표면 처리 면적 비율 조절로 접착 강도 및 디본딩 양상을 알아보는 실험을 시행하였다. 이 실험에서는 50, 60% 군이 임상적으로 활용 가능한 범위내의 전단 결합 강도 및 디본딩 양상을 나타내었다. 표면 처리 면적을 세분화한 부가적인 실험이 가능하며, 다양한 인자 조절을 통해 임상에 활용 가능한 우수한 성질의 세라믹 브라켓 개발이 가능할 것이다.
최지영 인하대학교 교육대학원 2010 국내석사
We prove that finite dimensional euclidean space ℝ is complete with respect to both usual metric(euclidean metric) and square metric. Moreover, we prove that infinite dimensional euclidean space ℝ is complete with respect to the uniform metric. We study the compactness of metric space and prove the main theorem called Ascoli Theorem. 우리는 유한차원 유클리드 공간인 ℝ에 usual metric(euclidean metric) 과 square metric이 주어져 있을 때 완전함을 증명한다. 또한 무한차원 유클리드 공간인 ℝ도 unifom metric에 대하여 완전함을 보인다. 우리는 거리공간의 compact성에 대해 공부하고 Ascoli 정리라 불리는 주요한 정리를 증명한다.
장마전선상의 하층제트 유입으로 인한 집중호우에 관한 연구
In general, heavy rainfall in Korea is mostly associated with inflow of 850hPa low-level jet. It transports abundant heat and moisture flux to the Changma front. In this study, synoptic characteristics of heavy rainfall in Korea from a case study is examined by classifying heavy rainfall cases with synoptic patterns, in particular distribution of upper- and low-level jets, western North Pacific high, and moisture flux. The surface and upper-level weather charts including auxiliary analysis chart and radar and satellite images obtained from the Korea Meteorological Administration, and 500hPa geopotential heights from NCEP/NCAR are used and then KLAPS is applied to understand the local atmospheric structure associated with heavy rainfall. Results show that maximum frequency in 60 heavy rainfall cases with more than 150mm/day appears in the Changma type of 43 cases (a proportion in relation to a whole is 52%) including the combined Changma types with typhoon and cyclone. As indicated in previous studies, most heavy rainfall cases are related to inflow of low-level jet. In addition, synoptic characteristics based on the analyses of weather charts, radar and satellite images, and KLAPS in heavy rainfall case of 12 July, 2009 reveal that the atmospheric vertical structure in particular equivalent potential temperature favorable for effective inflow of warm and moist southwesterly into the Changma front is linked to large potential instability and the strong convergence accompanied with low-level jet around Suwon contributes to atmospheric upsliding along the Changma front, producing heavy rainfall.
ABSTRACT A Study on Expressional Features of 《MAUS》 by Art Spigelman Choi, Ji Young Department of cartoon Art Graduate School, Kong Ju National University Kong Ju. Korea (Supervised by Professor Lim, Cheong San) The cartoon asserted as the which is a 9th art and the authors whom it creates shouts in spite of the change of the recognition against the cartoon of the household furniture was not exchanged prominently. With the contents which is the possibility of putting in the form inside which is a cartoon it has a schedule one prejudice there is not a possibility of hiding with transfer. So far it is generality and in thought the cartoon raises an effect from one of amusement or education of the children or it comes to think with the industrial by-product, it has the recognition where is nearer the art than in the goods. Instant for raises the phase of the cartoon which it comes to think with the style which is low like from one territory of this application art the cartoon which refuses the normal recognition of the household furniture from the front is the 《MAUS》 of Art Spigelman. Spigelman won the literary work which is secluded with this work and to win Pulitzer Prize in 1992 the art value and a work characteristic of the cartoon and simultaneously official recognition it was received. As he receives Pulitzer Prize and in cartoon history to draw large stroke and recently 'the cartoon probably is art or not' when the discussion is meaningless. Mickey Mouse, Superman and so on the work which is 《MAUS》 from the American environment which represents commerce cartoon became the catalyst which converts the recognition against a cartoon. With this one bias cartoon it expected in cartoon of existing, slight, humour, satire, witticism and so on core psychological or history, philosophy and thought of the human being the what kind of art style than it will be able to express more finely it is because the fact is proven above aesthetics value. This study the representative work of the Spigelman which raises the phase of cartoon analyzed the structure quality of narrative quality and expression type of the expression contents regarding the 《MAUS》. Also with the art value as the tool of the art sublimation which confronts together in us it researched meaning of cartoon. First, in the works background of Spigelman, the thought background he sent an adolescence background investigated about hippie culture, counter culture that the times situation and environment creation scenery of the 1960-1970 《MAUS》. With creation process of the 《MAUS》 it investigates a different work tendency from tendency of work creation and the possibility of knowing the work world which the Spigelman is various and the change of the work tube it was. Regarding psychosis power healing of the Spigelman which is caused by with creation of the it analyzed the psychoanalysis objection of the Freud with character. And in order to complement the deficient point which leans in expression type analysis and with cartoon reference it arranged the concept regarding being understood of different style. The second, in narration characteristics of expression contents regarding 《MAUS》, studied fablic narration and analyzed true records and the fact that the past and actual simultaneous narration showed intensely in realism of 《MAUS》 through interviews in the narration of documentary, doublespeak. It was inserted from Frame formula configuration it did the contents form analysis regarding the 《The prisoner of a hell planet》 in whole story inside. The third, it researched the change process and a symbol characteristic of the character of the 《MAUS》 from structure quality of the expression type regarding 《MAUS》, and compared the external form quality of the animal character of the Disney and 《MAUS》. Cartoon theory of the Scott McClould with character movement and action of unit of six branch, the shape of unit and it will be various from the MAUS》 and it will be used, from the 《MAUS》 it will be able to investigate of six branch combination and the writing from the shape and function and cartoon of feature good intention atmosphere and the balloon. Art Spigelman the photograph which is a peculiar expression technique, it analyzes the unique to illustration and the map and form of the 《MAUS》 where the realism is strongly expressed. it will be able to investigate a structure completion degree. Spigelman leads 《MAUS》 and the Fascism of the Nazis calls and only to reconsider a next generation righteousness forgetfulness regarding the history mistake which is not the possibility of erasing it knows, with the influence where the weight of history goes mad to the individual company actuality of the existence it will not be able to dispose hereupon one it awakens. This discord of the individual company with an art on level of the history prosecution against the violence of silk Nazis end the thing knew and, with cartoon to draw the discontinuation of being understood of the father and it sublimated with point with the author who aims a new value it is same, with young generation resist why and, regarding being frank, it is treating it has the different work and a discrimination characteristic from point. This it is the work characteristic which 《MAUS》 excels which official recognition receiving Spigelman world-wide. Only the work of the Spigelman, it knows draws the pain of time and history merely even from our country in KOREA and plentifully there is a cartoon work. Yet, it saw it with the work of art and as the tool of the art sublimation which confronts the natural features which researches a cartoon questionable matter still did not become general in us. The next art result work characteristic human nature it expects the quality growth which in commerce expansion of cartoon the work research of the cartoon which the inside and outside of the country which it receives is various becomes the rubber and does not search for. * A thesis submitted to the committee of Graduate School, KongJu Natioal University in partial fulfillment of the requirements for the degree of Master of Arts Conferred in July 2007.
중등학교 수학교사들이 교과 내용 지도 시 어려움에 대한 실태조사 및 분석
최지영 공주대학교 교육대학원 2008 국내석사
A lot of teachers try to keep improving their teaching methods based on their teaching experiences. Actually, they enhance their mathematical ability and understanding while they teach students, or determine the success or failure of their instruction and change their view by observing how students respond to it. The purpose of this study was to examine what sort of teaching they found it difficult to do, what the reason was and how they resolved it in an effort to lay the foundation for configuring programs for mathematics education. The subjects in this study were teachers who took courses to be a certified first-grade regular teacher for secondary school, which were provided to teachers across the nation. After a survey was conducted, the answer sheets from 102 teachers were gathered. Open-ended questions were utilized in the survey to find out about what difficulties they usually had in teaching mathematics, what caused it and how they tackled it. The findings of the study were as follows: First, in the field of 'number and operation,' the teachers investigated had difficulties in teaching how to abstract mathematical things collectively and how to make new number systems, like positive number, rational number, real number or complex number, out of natural numbers, because of the cognitive disorder of students. And they made the use of Venn diagram in teaching set relationship and offered concrete number-manipulative activities. That allowed them to offer more efficient education. the teachers faced difficulties in teaching 'a log' that was a new concept, since it was elusive for students. They told them the history of log to make it more understand- able, but students didn't yet understand it. So they handled it just for form's sake after merely mentioning the necessity of it. Second, in the area of 'letter and expression,' the teachers faced difficulties because students weren't good at making concise mathematical sentences. In that situation, they provided concrete manipulative activities, asked gradual questions or gave clues so that students could solve the given problems. As students weren't given enough time to solve the given problems, they refrained themselves from doing time-consuming things. So they thought it was a shame not to take time to give lessons. The teachers found it hard to teach 'a series' as well, because students didn't understand the use of necessary signs and how to make a formula. And the teachers let them solve a lot of problems to make it easier for them to use signs. Third, in terms of 'regularity and function,' some of the teachers introduced function as corresponding relation since the current curriculum made it hard for them to let students grasp the definition of function. Those who considered it onerous to teach this field because they had to write many things on the blackboard made the use of mathematical engineering tools. And the teachers had a hard time in teaching trigonometrical function, and the reason was that it was taught at the end of semester, and that it made it difficult to catch the attention of students. The poor prerequisite learning of students was another reason. So the teachers taught it by reconstructing the textbooks at their option. in the area of 'interpreting,' the teachers had difficulties as students could not link the conceptions of real infinite and potential infinite. To iron out this problem, they gave examples to show how these things changed, and provided visual education to let students use their intuition in understanding it. As students weren't able to know the difference between infinite sequence and infinite series, the teachers instructed how to understand and use Σ sign so that they could realize the difference between the two. Fourth, the area of 'probability and statistics' was handled at the end of semester as well, which resulted in distracting students and giving a hard time to the teachers. They taught students to be aware of the necessity of probability and statistics by igniting their interest by selecting themes that intrigued them. Fifth, the greatest number of the teachers found it hard to teach the proof of geometry in the field of 'diagram' due to the poor intuition and logical thinking of students, since this field required the intuitive and logical abilities. They taught them to think in an efficient and refined manner by having them construct their own proof process in group, by filling out vacancies or by using proof cards. Sixth, in the area of 'measurement,' they raised a question about the necessity of education about approximate quantity. Furthermore, they weren't knowledgeable about it, and they considered it troublesome to teach simultaneous inequality because they had to make a separate graph whenever they handled each of relevant problems. But the use of engineering tools enabled them to make a graph more easily. The findings of the study are expected to assist teachers to make a better preparation for mathematics education and enhance the efficiency of their academic guidance. Also, the findings might contribute to mapping out more successful and effective teaching-learning programs. The development and generalization of diverse teaching methods and multiple manipulative teaching aids will allow teachers to take some pressure off, to boost the quality of teaching and to help students improve their mathematical thinking.