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수학적 창의성과 개방형 문제(open ended problem)

  • Gwon, O-Nam;Jo, Yeong-Mi;Park, Jeong-Suk;Park, Ji-Hyeon;Kim, Yeong-Sil
    • Communications of Mathematical Education
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    • v.16
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    • pp.217-218
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    • 2003
  • 제7차 교육과정의 기본방향인 '21세기의 세계화 정보화 시대를 주도할 자율적이고 창의적인 한국인 육성'에서 볼 수 있듯이, 새로운 교육과정에서는 학생들의 창의력을 신장시키기 위한 방안으로 교과별 교육과정이나 재량활동 운영 등을 제시한 바 있다. 수학교육에서도 이러한 시대적 흐름에 발맞추어 수학적 창의력의 신장이 강조되고 있는 상황이다. 그동안 이론적인 측면과 실제적인 측면에서 수학적 창의성에 대한 성과가 축적되었다. 이론적인 측면에서 볼 때, Haylock(1987)등에 의해 창의력과 수학적 창의력의 구분되었으며, 특히 '수학적' 창의력에 대한 다양한 정의가 제안되었다. 실제적인 측면에서도 수학적 창의력을 측정하려는 평가 도구들이 그 동안 여러 가지로 개발하였다. 그러나, 이러한 수학적 창의력에 관한 전반적인 연구는 종국적으로 교실 수학수업에 반영되어야 함에도 불구하고, 그리 만족스럽지 못한 상황이다. 특히, 교실에서 수학수업을 실제로 담당하는 교사들이 수학적 창의력을 위한 수업을 하고자 하더라도 당장 가까이에서 구할 수 있는 교수 학습 자료가 여전히 부족한 상황이다. 물론 그 동안 교실 수학수업에서 사용할 수 있는 창의력 개발 프로그램이 전무한 것은 아니다. 그런데 그들 대부분은 게임이나 퍼즐을 이용한 것으로 그 수준이 단순 흥미유발에 그치고 있거나 소수의 영재아를 위한 소재를 중심으로, 특히 수학적 사고 과정을 따르기보다는, 시행착오를 거쳐 원하는 결과를 얻을 가능성이 많으며, 수학과의 연계성이 불분명한 채로 단순놀이에 그치는 경우가 적지 않아, 수업과 연관되어 창의력의 신장이라는 측면에서 볼 때, 적용하기 어려운 사례가 많다. 이러한 상황을 개선하는 데 기여하고자, 현재 교과교육공동연구 지원사업의 하나로 한국 학술 진흥재단의 지원을 받아, '개방형 문제(open-ended problems)'를 중심 소재로 한 '수학적 창의성'을 신장하기 위한 교수학습 프로그램을 개발하여, 중학교 1학년을 대상으로 연구를 진행하고 있다. 개방형 문제라 함은 명백한 정의가 어렵지만 Pehkeon(1995)는 개방형문제의 정의를 명백히 하기위한 시도로서 그 반대로 닫힌 문제에 대한 정의로부터 시작하여, 어떤 문제가 닫혀있다고 하는 것은 그 문제의 출발 상황과 목표 상황이 닫혀 있는 것, 즉 명백히 설명되어있을 때라면 개방형 문제는 이와 반대의 개념임을 시사하였다. Silver(1995)는 개방형 문제를 문제 자체가 다른 해석이 가능하거나 서로 다를 인정할만한 답을 가질 수 있는 문제 또는 풀이과정이 다양한 문제, 자연스럽게 다른 문제들을 제안하거나 일반화를 제시할 수 있는 문제라고 정의하였다. 따라서 개방형 문제란 출발상황이나 목표 상황의 일부가 닫혀있지 않을 때를 말하고 문제의 조건을 만족하는 해답이 여러 가지로 존재하는 문제를 뜻한다. 수학적 창의력을 개발하는 데, 다른 문제 유형보다도, 개방형 문제가 유리하다는 점은 이미 여러 학자들에 의해 주장되어왔다. 미국 국립영재교육센터(NRCG/T)는 기존의 사지선다형이나 단답형 문제와 질문들은 학생들의 사고 능력에 관한 정보를 거의 알려주지 못하기 때문에 한 가지 이상의 답을 요구하는 ‘open-ended' 또는 ’open-response' 문제와 질문을 가지고 수학 분야에서의 창의적 사고 능력과 표현능력을 측정해야 한다고 하였고, 개방형 문제가 일반적으로 정답이 하나인 문제보다 고차원적인 사고를 요구하게 하는 문제 형태라고 하였다. 본 연구에서는 이러한 근거를 바탕으로 개방형 문제의 유형을 다양한 답이 존재하는 문제, 다양한 해결 전략이 가능한 문제, 답이 없는 문제, 문제 만들기, 일반화가 가능한 문제 등으로 보고, 수학적 창의성 중 특히 확산적 사고에 초점을 맞추어 개방형 문제가 확산적 사고의 요소인 유창성, 독창성, 유연성 등에 각각 어떤 영향을 미치는지 20주의 프로그램을 개발, 진행하여 그 효과를 검증하고자 한다. 개방형 문제를 활용한 수학적 창의력 신장 프로그램을 개발하고 현장 학교에 실험 적용하여 그 효과를 분석하고자 하는 본 연구는 창의력 신장에 비중을 두는 수학과 교수-학습 과정에 실제적인 교수 학습 자료를 제공하는 것뿐만 아니라 교사들에게는 수학교실에서 사용 가능한 실제적인 활용방안을, 학생들에게는 주어진 문제를 여러 가지 각도에서 생각하면서 다양한 사고를 경험하는 기회를 가질 수 있어, 수학을 보는 학생들의 태도에도 긍정적인 변화를 가져올 수 있을 것이라 기대한다.

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The Relationships between Mathematically Gifted Students and Regular Students in Perfectionism and the Affective Traits (중등 영재학생과 일반학생의 완벽주의 성향과 수학교과에 대한 정의적 특성과의 관계)

  • Whang, Woo-Hyung;Lee, Yu-Na
    • Communications of Mathematical Education
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    • v.23 no.1
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    • pp.1-38
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    • 2009
  • This study investigates the relationships of perfectionism and the affective traits(academic self-concept, learning attitude, interest, mathematical anxiety, learning habits) in mathematics between the gifted students and the regular students in Korean Middle Schools. The findings of this study can be used for the understanding of the gifted students, and as data or resources for counsellors when they advise the gifted students on enhancing study strategies and developing future courses. This study was investigated by measuring the relationships between perfectionism and the affective traits on mathematics between two groups. Here, the correlation analysis, t-test, and regression analysis of the SPSS for Window 12.0 Program were applied to measure the differences of both groups. Therefore, there were no differences in perfectionism between the gifted students and the regular students. But the self-oriented perfectionism of the gifted students appeared higher compare with regular students. The affective traits in mathematics of the gifted students appeared more positive compare with regular students. There were a few correlations between the perfectionism and the affective traits in mathematics at two group all. however the self-oriented perfectionism and the affective traits in mathematics showed to correlation. There were several suggestions based on the results of this study. First, the results showed that professional assistance is needed for the gifted students so that their perfectionism flows positively into developing their gifts. Secondly, the results suggested that specialized mathematical program reflecting on the affective traits of the gifted students in mathematics should be offered.Lastly, tthe results of this study suggested a researcher regarding relevance with perfectionism and affective traits regarding subject shall be performed more. The result of research shall be included to contents of training for the gifted students and their parents.

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Skin-Whitening and UV-Protective Effects of Angelica gigas Nakai Extracts on Ultra High Pressure Extraction Process (초고압 추출 공정에 의한 당귀 추출물의 미백 및 자외선 차단 효과)

  • Kim, Cheol-Hee;Kwon, Min-Chul;Han, Jae-Gun;Na, Chun-Su;Kwak, Hyeong-Geun;Choi, Geun-Pyo;Park, Uk-Yeon;Lee, Hyeon-Yong
    • Korean Journal of Medicinal Crop Science
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    • v.16 no.4
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    • pp.255-260
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    • 2008
  • This study was performed to investigate the enhancement of UV-protection activities and skin-whitening effects from Angelica gigas Nakai extracts on ultra high pressure extraction process. Extraction at $60^{\circ}C$ treated by ultra high pressure for 15 minute and associated with ultrasofication (HPE15) was showed more than double yield, compare conventional extraction, as 12.24% (w/w) from A. gigas. Extracts of HPE15 reduced expression of MMP-1 on UV-irradiated CCD-986sk cells as 122.2% and revealed high inhibitory potency on tyrosinase as 69.4% by adding samples. Extracts of HPE15 from A. gigas showed strong inhibition effect on melanin production test by Clone M-3 cells as 82.4% by adding extracts. From the preliminary observations, we considered that the extracts from A. gigas could be potent natural materials for skin-whitening agent, and could be used as a potential anti-aging agent for the photo-damaged skin.

The Quantitative Analysis of Photos and Illustrations in the Practical Arts (Technology.Home Economics)Textbook Based on A Gender Equity Perspective (양성평등적 관점에 기초한 실과(기술.가정)교과서의 사진 및 삽화 계량 분석)

  • Choi, Young-Sun;Yoon, In-Kyung
    • Journal of Korean Home Economics Education Association
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    • v.20 no.1
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    • pp.85-100
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    • 2008
  • This study attempted to analyze the contents of Practical Arts(Technology Home Economics)Textbooks written by the 7th national curriculum in a gender equity education. The objective of this study was to suggest some improvements which should be solved in terms of gender equity in Practical Arts, Technology and Home Economics education through analyzing their teaching and learning contents. Quantitative analysis were carried out for the objective of this study, Practical Arts(Technology Home Economics)Textbooks were divided into Technology and Home Economics fields. The pictures and illustration were analyzed in terms of sexual discrimination considering the social status and role. The analysis results were as follows. First, there were few cases of sexual discrimination in the texts. On the other hand, there were some cases of sexual discrimination in the pictures and illustration. Considering the results of some studies carried out in the 6th national curriculum, many problems raised in a gender equity education standpoint in the studies were solved. However, there were some cases of sexual discrimination which should be improved in the textbooks written by the 7th national curriculum. Second, there were few cases of sexual discrimination in Practical Arts textbooks. On the contrary many problems in terms of gender equity education were found in the textbooks of Technology and Home Economics. This result may be caused by the characteristics of Technology and Home Economics. The traditional viewpoint toward Technology and Home economics Textbook needs to be changed. In other words, their textbooks have to include practical contents for the positive sense of value and right sexual roles in terms of gender equity education. The contents of Practical Arts(Technology Home economics)Textbooks should be designed considering the articulation among the subjects and grades especially in terms of gender equity education.

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Screening of the Antimicrobial and Antitumor Activity of Xanthium strumarium L.Extract (한국산 도꼬마리 추출물로부터 항균.항암물질의 탐색)

  • 김현수;유대식;이인선;김용원;여수환
    • KSBB Journal
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    • v.18 no.1
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    • pp.55-61
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    • 2003
  • To isolate and purify the antimicrobial and antitumor agents in Xanthium strumarium L. hydrothermal extract. The crude extract was extracted in ether or ethylacetate under neutral, acidic, and alkali conditions. The antimicrobial activity of each extract was tested against 16 strains of bacteria, 2 strains of yeast, and 2 strains of fungus. The ether neutral extract (XE-N) exhibited the strongest growth inhibition upon the 8 strains of gram-positive bacteria, 6 strains of gram-negative bacteria and Cryptococcus neoformans. Fluorescein diacetate (FDA) testing of XE-N and XEA-N showed growth inhibition of the 3 strains of E. coli, S. aureus and C. albicans even at 30 ng/mL, with the exception of p. aeruginosa. XE-N-S1 and XE-N-S3 from neutral ether extract (XE-N), XE-N-S3 from the acidic ether extract (XE-A), and XEA-N-S1 from ethylacetate (XEA-N) were purified as antimicrobial and antitumor agents. However all purified compounds decomposed with the exception of XE-N-S1. The results upon the antitumor activities of the crude extract and of its purified compounds, showed that XE-N-S1 had the best antitumor activity against HeLa cells. In terms of antitumor activity against HepG2 cells, XE-N-S1 and XE-N-S3 were superior, and against HT29 cells XE-N and XE-N-Sl were good, against Saos2, NCI H522, NCI H1703, Clone M3 cells XE-N-51 was very good, and against LN CAP cells XE-N-S3 was the best. Comparing of cellular toxicities various extracts and purified compounds with the existing antitumor agents, XE-A, XEA-A and XEA-B had the lowest toxicity, and XE-B had a lower toxicity than etoposide. XE-N-S1 and XE-N-S3 showed higher toxicities than etoposide, and the toxicity of XE-A-S3 was higher than that of etoposide, and lower than that of csplatin.

Anti-wrinkle Activity of $\beta$-carotene Extracted & Purified from Recombinant Escherichia coli (재조합 대장균으로부터 추출.정제된 베타-카로틴의 주름개선 활성)

  • Jo, Ji-Song;Ku, Bo-Mi;Kang, Sang-Soo;Lee, Jae-Ran;Kim, You-Geun;Lee, He;Kim, Sung-Bae;Kim, Seon-Won;Kim, Chang-Joon;Chung, In-Young
    • KSBB Journal
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    • v.23 no.6
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    • pp.513-518
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    • 2008
  • This paper described the extraction/purification of $\beta$-carotene from recombinant E.coli and evaluation of anti-wrinkle activity of purified $\beta$-carotene. No significant differences in extraction yields were observed when hexane or isobutyl acetate was used. However, extraction from wet-cell cake resulted in 2-fold higher amount of $\beta$-carotene than that from dry cells. Disruption of 5 g-wet cells by ultrasonic homogenizer, acetone dehydration, extraction with isobutyl acetate resulted in 36 mg of $\beta$-carotene corresponding to 61.2% of recovery. The formation and separation of $\beta$-carotene crystal improved the purity. 633 mg of $\beta$-carotene crystal with 93% purity was obtained from 223 g/L of wet-cell cake harvested from 2.5-L fed-batch culture broth. The cultures of normal human primary fibroblast were performed to investigate the effect of $\beta$-carotene on cytotoxicity as MTT assay and anti-wrinkle activity as collagen synthesis assays. $1.7{\mu}M$ of $\beta$-carotene was found to be optimal concentration at which 1.4-fold higher amount of collagen was synthesized than that in absence of $\beta$-carotene. This indicates that highly purified $\beta$-carotene can be obtained from recombinant E.coli by applying simple method with less toxic solvent and can be used in functional cosmetics as anti-wrinkle agent.

Optimization of TDA Recycling Process for TDI Residue using Near-critical Hydrolysis Process (근임계수 가수분해 공정을 이용한 TDI 공정 폐기물로부터 TDA 회수 공정 최적화)

  • Han, Joo Hee;Han, Kee Do;Jeong, Chang Mo;Do, Seung Hoe;Sin, Yeong Ho
    • Korean Chemical Engineering Research
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    • v.44 no.6
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    • pp.650-658
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    • 2006
  • The recycling of TDA from solid waste of TDI plant(TDI-R) by near-critical hydrolysis reaction had been studied by means of a statistical design of experiment. The main and interaction effects of process variables had been defined from the experiments in a batch reactor and the correlation equation with process variables for TDA yield had been obtained from the experiments in a continuous pilot plant. It was confirmed that the effects of reaction temperature, catalyst type and concentration, and the weight ratio of water to TDI-R(WR) on TDA yield were significant. TDA yield decreased with increases in reaction temperature and catalyst concentration, and increased with an increase in WR. As a catalyst, NaOH was more effective than $Na_2CO_3$ for TDA yield. The interaction effects between catalyst concentration and temperature, WR and temperature, catalyst type and reaction time on TDA yield had been defined as significant. Although the effect of catalyst concentration on TDA yield at $300^{\circ}C$ as subcritical water was insignificant, the TDA yield decreased with increasing catalyst concentration at $400^{\circ}C$ as supercritical water. On the other hand, the yield increased with an increase in WR at $300^{\circ}C$ but showed negligible effect with WR at $400^{\circ}C$. The optimization of process variables for TDA yield has been explored with a pilot plant for scale-up. The catalyst concentration and WR were selected as process variables with respect to economic feasibility and efficiency. The effects of process variables on TDA yield had been explored by means of central composite design. The TDA yield increased with an increase in catalyst concentration. It showed maximum value at below 2.5 of WR and then decreased with an increase in WR. However, the ratio at which the TDA yield showed a maximum value increased with increasing catalyst concentration. The correlation equation of a quadratic model with catalyst concentration and WR had been obtained by the regression analysis of experimental results in a pilot plant.

Effect of Culture Medium Strength, Plant Growth Regulators and Ethylene Inhibitors for Adventitious Bud Induction from Mature Zygotic Embryo in Larix kaempferi (낙엽송 (Larix kaempferi) 성숙배로부터 부정아 유도를 위한 배지농도, 식물생장조절물질 및 에틸렌 억제제 효과)

  • Kim, Yong Wook
    • Journal of Korean Society of Forest Science
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    • v.103 no.1
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    • pp.72-79
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    • 2014
  • Adventitious buds were produced from the cultures of mature zygotic embryos of Larix kaempferi with the highest frequency in Quoirin & Lepoivre (LP) medium containing 1.0 mg/L zeatin (76.1%). The effective treatments for inducing adventitious shoots growth above 2 mm were shown in Litvay (LM) medium with 0.5 mg/L zeatin (75.2%) or LP medium with 2.0 mg/L zeatin (70.2%), respectively. In experiment with half strength salts medium for induction of the adventitious buds, the effective treatments were obtained from 1/2LP medium with 1.0 (83.3%) or 2.0 mg/L (81.7%) zeatin, respectively. However, the best adventitious shoot growth more than 2 mm appeared in 1/2LM medium with 1.0 mg/L zeatin (66.7%). In experiment with half strength salts medium for induction of the adventitious buds, the effective treatments were obtained from 1/2LP medium with 1.0 (83.3%) or 2.0 mg/L (81.7%) zeatin, respectively. However, the best adventitious shoot growth more than 2 mm appeared in 1/2LM medium with 1.0 mg/L zeatin (66.7%). In experiment of subsequent treatment with various cytokinins for induction of the adventitious buds, the best one (52.9%) was obtained from 1.0 mg/L zeatin for 2weeks, and then subcultured to the medium with 1.0 mg/L thidiazuron (TDZ). The effect of ethylene synergist or inhibitor on adventitious buds induction was examined. The highest rate (34.6%) of adventitious buds marked from the treatments of 1.0 mg/L zeatin+2.0 mg/L MGBG (methylglyoxal bis-[guanylhydrazone]). And the highest no. of adventitious buds(1.5/explant) was shown in the medium with 1.0 mg/L zeatin+2.0 mg/L $CoCl_2$.

The Surgical Outcome for Gastric Submucosal Tumors: Laparoscopy vs. Open Surgery (위 점막하 종양에 대한 개복 및 복강경 위 절제술의 비교)

  • Lim, Chai-Sun;Lee, Sang-Lim;Park, Jong-Min;Jin, Sung-Ho;Jung, In-Ho;Cho, Young-Kwan;Han, Sang-Uk
    • Journal of Gastric Cancer
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    • v.8 no.4
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    • pp.225-231
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    • 2008
  • Purpose: Laparoscopic gastric resection (LGR) is increasingly being used instead of open gastric resection (OGR) as the standard surgical treatment for gastric submucosal tumors. Yet there are few reports on which technique shows better postoperative outcomes. This study was performed to compare these two treatment modalities for gastric submucosal tumors by evaluating the postoperative outcomes. We also provide an analysis of the learning curve for LGR. Materials and Methods: Between 2003.4 and 2008.8, 103 patients with a gastric submucosal tumor underwent either LGR (N=78) or OGR (n=25). A retrospective review was performed on a prospectively obtained database of 103 patients. We reviewed the data with regard to the operative time, the blood loss during the operation, the time to the first soft diet, the postoperative hospital stay, the tumor size and the tumor location. Results: The clinicopatholgic and tumor characteristics of the patients were similar for both groups. There was no open conversion in the LGR group. The mean operation time and the bleeding loss were not different between the LGR group and the OWR group. The time to first soft diet (3.27 vs. 6.16 days, P<0.001) and the length of the postoperative hospital stay (7.37 vs. 8.88 days, P=0.002) were shorter in the LGR group compared to the OGR group. The tumor size was bigger in the OGR group than that in the LGR group (6.44 vs. 3.65 cm, P<0.001). When performing laparoscopic gastric resection of gastric SMT, the surgeon was able to decrease the operation time and bleeding loss with gaining more experience. We separated the total cases into 3 periods to compare the operation time, the bleeding losses and the complications. The third period showed the shortest operation time, the least bleeding loss and the fewest complications. Conclusion: LGR for treating a gastric submucosal tumor was superior to OGR in terms of the postoperative outcomes. An operator needs some experience to perform a complete laparoscopic gastric resection. Laparoscopic resection could be considered the first-line treatment for gastric submucosal tumors.

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Molecular Cytogenetic Characterization of Supernumerary Marker Chromosomes by Chromosomal Microarray (염색체 마이크로어레이를 이용한 표지염색체의 분자세포유전학적 특성)

  • Bae, Mi-Hyun;Yoo, Han-Wook;Lee, Jin-Ok;Hong, Maria;Seo, Eul-Ju
    • Journal of Genetic Medicine
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    • v.8 no.2
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    • pp.119-124
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    • 2011
  • Purpose: Supernumerary marker chromosome (SMC) could be associated with various phenotypic abnormalities based on the chromosomal origin of SMCs. The present study aimed to determine the genomic contents of SMCs using chromosomal microarray and to analyze molecular cytogenetic characterizations and clinical phenotypes in patients with SMCs. Materials and Methods: Among patients with SMCs detected in routine chromosomal analysis, SMCs originating from chromosome 15 were excluded from the present study. CGH-based oligonucleotide chromosomal microarray was performed in 4 patients. Results: The chromosomal origins of SMCs were identified in 3 patients. Case 1 had a SMC of 16.1 Mb in 1q21.1-q23.3. Case 2 showed 21 Mb gain in 19p13.11-q13.12. Case 3 had a 4.5 Mb-sized SMC rearranged from 2 regions of 2.5 Mb in 22q11.1-q11.21 and 2.0 Mb in 22q11.22-q11.23. Conclusion: Case 1 presented a wide range of phenotypic abnormalities including the phenotype of 1q21.1 duplication syndrome. In case 2, Asperger-like symptoms are apparently related to 19p12-q13.11, hearing problems and strabismus to 19p13.11 and other features to 19q13.12. Compared with cat-eye syndrome type I and 22q11.2 microduplication syndrome, anal atresia in case 3 is likely related to 22q11.1-q11.21 while other features are related to 22q11.22-q11.23. Analyzing SMCs using high-resolution chromosomal microarray can help identify specific gene contents and to offer proper genetic counseling by determining genotype-phenotype correlations.