• 제목/요약/키워드: problem solving methods

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Student difficulties in constructed-response mathematics assessments: A case study of writing activities for low-performing first-year high school students (수학 서술형 평가의 어려움과 지도 방안: 고교 1학년 노력형 학생의 쓰기 활동 사례 연구)

  • Mihui Bae;Woong Lim
    • The Mathematical Education
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    • 제63권1호
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    • pp.1-18
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    • 2024
  • This study aims to analyze low-performing high school students' difficulties in constructed response (CR) mathematics assessments and explore ways to use writing activities to support student learning. The participants took CR assessments, engaged in guided writing activities across 15 lessons, and provided responses to our interviews. The study identified 20 types of student difficulties, which were sorted into two main categories: "mathematical difficulties" and "CR difficulties." The difficult nature of mathematics as a school subject included a lack of understanding of mathematical concepts, students' difficulty with mathematical symbols and notations, and struggles with word problems. Challenges specific to CR assessments included students' difficulties arising from the testing conditions unlike those of multiple-choice items, and included issues related to constructing appropriate responses and psychological barriers. To address these challenges in CR assessments, the study conducted guided writing activities as an intervention, through which six themes were identified: (1) internalization of mathematical concepts, (2) mathematical thinking through relational understanding, (3) diverse problem-solving methods, (4) use of mathematical symbols, (5) reflective thinking, and (6) strategies to overcome psychological barriers.

Analyses of the precision and strategies for representing the magnitude of fractions and decimals on the number line among 6th graders (초등학교 6학년의 분수와 소수의 크기에 대한 수직선 표상의 정확성 및 사용 전략 분석)

  • Jinyoung Heo;Soo-hyun Im
    • The Mathematical Education
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    • 제63권3호
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    • pp.393-409
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    • 2024
  • The number line model, which intuitively marks numerical magnitudes in space, is widely utilized to help in understanding the magnitudes that fractions and decimals represent. The study analyzed 6th graders' understanding of fractions and decimals, their problem solving strategies, and whether individual differences in the flexibility of various strategy uses are associated with the accuracy of numerical representation, calculation fluency, and overall mathematical achievement. As a result of the study, students showed relatively lower accuracy in representing fractions and decimals on a number line compared to natural numbers, especially for fractions with odd denominators compared to even denominators, and for two-digit decimals compared to three-digit decimals. Regarding strategy use, students primarily used benchmark, segmentation, and approximation strategies for fractions, and benchmark, rounding, and transformation strategies for decimals sequentially. Lastly, as students used various representation strategies for fractions, their accuracy in representing fractions and their overall mathematical achievement scores showed significantly better outcomes. Taken together, we suggest the need for careful instruction on different interpretations of fractions, the place value of decimals, and the meaning of zero in decimal places. Moreover, we discuss instructional methods that integrate the number line model and its diverse representation strategies to enhance students' understanding of fractions and decimals.

Ensemble Learning with Support Vector Machines for Bond Rating (회사채 신용등급 예측을 위한 SVM 앙상블학습)

  • Kim, Myoung-Jong
    • Journal of Intelligence and Information Systems
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    • 제18권2호
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    • pp.29-45
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    • 2012
  • Bond rating is regarded as an important event for measuring financial risk of companies and for determining the investment returns of investors. As a result, it has been a popular research topic for researchers to predict companies' credit ratings by applying statistical and machine learning techniques. The statistical techniques, including multiple regression, multiple discriminant analysis (MDA), logistic models (LOGIT), and probit analysis, have been traditionally used in bond rating. However, one major drawback is that it should be based on strict assumptions. Such strict assumptions include linearity, normality, independence among predictor variables and pre-existing functional forms relating the criterion variablesand the predictor variables. Those strict assumptions of traditional statistics have limited their application to the real world. Machine learning techniques also used in bond rating prediction models include decision trees (DT), neural networks (NN), and Support Vector Machine (SVM). Especially, SVM is recognized as a new and promising classification and regression analysis method. SVM learns a separating hyperplane that can maximize the margin between two categories. SVM is simple enough to be analyzed mathematical, and leads to high performance in practical applications. SVM implements the structuralrisk minimization principle and searches to minimize an upper bound of the generalization error. In addition, the solution of SVM may be a global optimum and thus, overfitting is unlikely to occur with SVM. In addition, SVM does not require too many data sample for training since it builds prediction models by only using some representative sample near the boundaries called support vectors. A number of experimental researches have indicated that SVM has been successfully applied in a variety of pattern recognition fields. However, there are three major drawbacks that can be potential causes for degrading SVM's performance. First, SVM is originally proposed for solving binary-class classification problems. Methods for combining SVMs for multi-class classification such as One-Against-One, One-Against-All have been proposed, but they do not improve the performance in multi-class classification problem as much as SVM for binary-class classification. Second, approximation algorithms (e.g. decomposition methods, sequential minimal optimization algorithm) could be used for effective multi-class computation to reduce computation time, but it could deteriorate classification performance. Third, the difficulty in multi-class prediction problems is in data imbalance problem that can occur when the number of instances in one class greatly outnumbers the number of instances in the other class. Such data sets often cause a default classifier to be built due to skewed boundary and thus the reduction in the classification accuracy of such a classifier. SVM ensemble learning is one of machine learning methods to cope with the above drawbacks. Ensemble learning is a method for improving the performance of classification and prediction algorithms. AdaBoost is one of the widely used ensemble learning techniques. It constructs a composite classifier by sequentially training classifiers while increasing weight on the misclassified observations through iterations. The observations that are incorrectly predicted by previous classifiers are chosen more often than examples that are correctly predicted. Thus Boosting attempts to produce new classifiers that are better able to predict examples for which the current ensemble's performance is poor. In this way, it can reinforce the training of the misclassified observations of the minority class. This paper proposes a multiclass Geometric Mean-based Boosting (MGM-Boost) to resolve multiclass prediction problem. Since MGM-Boost introduces the notion of geometric mean into AdaBoost, it can perform learning process considering the geometric mean-based accuracy and errors of multiclass. This study applies MGM-Boost to the real-world bond rating case for Korean companies to examine the feasibility of MGM-Boost. 10-fold cross validations for threetimes with different random seeds are performed in order to ensure that the comparison among three different classifiers does not happen by chance. For each of 10-fold cross validation, the entire data set is first partitioned into tenequal-sized sets, and then each set is in turn used as the test set while the classifier trains on the other nine sets. That is, cross-validated folds have been tested independently of each algorithm. Through these steps, we have obtained the results for classifiers on each of the 30 experiments. In the comparison of arithmetic mean-based prediction accuracy between individual classifiers, MGM-Boost (52.95%) shows higher prediction accuracy than both AdaBoost (51.69%) and SVM (49.47%). MGM-Boost (28.12%) also shows the higher prediction accuracy than AdaBoost (24.65%) and SVM (15.42%)in terms of geometric mean-based prediction accuracy. T-test is used to examine whether the performance of each classifiers for 30 folds is significantly different. The results indicate that performance of MGM-Boost is significantly different from AdaBoost and SVM classifiers at 1% level. These results mean that MGM-Boost can provide robust and stable solutions to multi-classproblems such as bond rating.

Detorque force and surface change of coated abutment screw after repeated closing and opening (코팅된 지대주 나사의 반복 착탈 후 풀림력과 표면변화에 대한 연구)

  • Jang, Jong-Suk;Kim, Hee-Jung;Chung, Chae-Heon
    • The Journal of Korean Academy of Prosthodontics
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    • 제46권5호
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    • pp.500-510
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    • 2008
  • Statement of problem: Recently researches about WC/C (Tungsten Carbide/Carbon) or TiN (Titanium Nitride) coating on abutment screws are going on. It decreases friction coefficient, resistance against corrosion and withdrawal of physical fragility when the coating is applied to the metal surfaces. It is reported that coated abutment screws improved abrasion, adaptability and detorque force. Purpose: This study is about the effects of coated abutment screws on loosening of screw and for the purpose of solving the loosening phenomenon of abutment screws which is clinical problem. Material and methods: Detorque force and surface changes are compared when 10 times of repeated closing and opening are applied to both uncoated titanium abutment screws (Group A) and coated abutment screws with WC/C (Group B) and TiN (Group C). Each group was made up of 10 abutment screws. Results: 1. Before repeated closing and opening, Somewhat rough surface with regular direction was observed in Group A. Coated granules were observed in group B and group C and overall coated layer appeared in regular and smooth form. 2. Before repeated closing and opening, The coated surface showed bigger and thicker size of coated granules in Group C than Group B. 3. After repeated closing and opening, abrasion and deformation of abutment screw surface was observed in Group A and Group B. Exfoliation phenomenon was observed in Group B. 4. Group A showed biggest range of decrease when the weight changes of abutment screws were measured before and after repeated closing and opening. Group C showed less weight changes than Group B but there was no statistical difference between two groups. 5. Group B and Group C showed higher average detorque force than Group A and there was statistical difference. 6. Group A showed more prominent decrease tendency of average detorque force than Group B and Group C. Conclusion: Coated abutment screws with WC/C or TiN did not show prominent surface changes than uncoated titanium abutment screws even though they were repeatedly used. And they showed excellent resistance against friction and high detorque force. Thus it is considered that adaptation of WC/C or TiN coating on abutment screws will improve the screw loosening problem.

A Study on Shape Optimization of Plane Truss Structures (평면(平面) 트러스 구조물(構造物)의 형상최적화(形狀最適化)에 관한 구연(究研))

  • Lee, Gyu won;Byun, Keun Joo;Hwang, Hak Joo
    • KSCE Journal of Civil and Environmental Engineering Research
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    • 제5권3호
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    • pp.49-59
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    • 1985
  • Formulation of the geometric optimization for truss structures based on the elasticity theory turn out to be the nonlinear programming problem which has to deal with the Cross sectional area of the member and the coordinates of its nodes simultaneously. A few techniques have been proposed and adopted for the analysis of this nonlinear programming problem for the time being. These techniques, however, bear some limitations on truss shapes loading conditions and design criteria for the practical application to real structures. A generalized algorithm for the geometric optimization of the truss structures which can eliminate the above mentioned limitations, is developed in this study. The algorithm developed utilizes the two-phases technique. In the first phase, the cross sectional area of the truss member is optimized by transforming the nonlinear problem into SUMT, and solving SUMT utilizing the modified Newton-Raphson method. In the second phase, the geometric shape is optimized utilizing the unidirctional search technique of the Rosenbrock method which make it possible to minimize only the objective function. The algorithm developed in this study is numerically tested for several truss structures with various shapes, loading conditions and design criteria, and compared with the results of the other algorithms to examme its applicability and stability. The numerical comparisons show that the two-phases algorithm developed in this study is safely applicable to any design criteria, and the convergency rate is very fast and stable compared with other iteration methods for the geometric optimization of truss structures.

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Three-Dimensional High-Frequency Electromagnetic Modeling Using Vector Finite Elements (벡터 유한 요소를 이용한 고주파 3차원 전자탐사 모델링)

  • Son Jeong-Sul;Song Yoonho;Chung Seung-Hwan;Suh Jung Hee
    • Geophysics and Geophysical Exploration
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    • 제5권4호
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    • pp.280-290
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    • 2002
  • Three-dimensional (3-D) electromagnetic (EM) modeling algorithm has been developed using finite element method (FEM) to acquire more efficient interpretation techniques of EM data. When FEM based on nodal elements is applied to EM problem, spurious solutions, so called 'vector parasite', are occurred due to the discontinuity of normal electric fields and may lead the completely erroneous results. Among the methods curing the spurious problem, this study adopts vector element of which basis function has the amplitude and direction. To reduce computational cost and required core memory, complex bi-conjugate gradient (CBCG) method is applied to solving complex symmetric matrix of FEM and point Jacobi method is used to accelerate convergence rate. To verify the developed 3-D EM modeling algorithm, its electric and magnetic field for a layered-earth model are compared with those of layered-earth solution. As we expected, the vector based FEM developed in this study does not cause ny vector parasite problem, while conventional nodal based FEM causes lots of errors due to the discontinuity of field variables. For testing the applicability to high frequencies 100 MHz is used as an operating frequency for the layer structure. Modeled fields calculated from developed code are also well matched with the layered-earth ones for a model with dielectric anomaly as well as conductive anomaly. In a vertical electric dipole source case, however, the discontinuity of field variables causes the conventional nodal based FEM to include a lot of errors due to the vector parasite. Even for the case, the vector based FEM gave almost the same results as the layered-earth solution. The magnetic fields induced by a dielectric anomaly at high frequencies show unique behaviors different from those by a conductive anomaly. Since our 3-D EM modeling code can reflect the effect from a dielectric anomaly as well as a conductive anomaly, it may be a groundwork not only to apply high frequency EM method to the field survey but also to analyze the fold data obtained by high frequency EM method.

An Analysis of Research Trends Related to Software Education for Young Children in Korea (유아의 소프트웨어 교육 관련 국내 최근 연구의 경향 분석)

  • Chun, Hui Young;Park, Soyeon;Sung, Jihyun
    • Korean Journal of Child Education & Care
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    • 제19권2호
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    • pp.177-196
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    • 2019
  • Objective: This study aims to analyze research trends related to software education for young children, focusing on studies published in Korea from 2016 to 2019 March. Methods: A total of 26 research publications on software education for young children, searched from Korea Citation Index and Research Information Sharing Service were identified for the analysis. The trend in these publications was classified and examined respectively by publication dates, types of publications, and the fields of study. To investigate a means of research, the analysis included key topics, types of research methods, and characteristics of the study variables. Results: The results of the analysis show that the number of publications on the topic of software education for young children has increased over the three years, of which most were published as a scholarly journal article. Among the 26 research studies analyzed, 16 (61.5%) are related to the field of early childhood education or child studies. Key topics and target subjects of the most research include the curriculum development of software education for young children or the effectiveness of software education on 4- and 5-year-old children. Most of the analyzed studies are experimental research designs or in the form of literature reviews. The most frequently studied research variable is young children's cognitive characteristics. For the studies that employ educational programs, the use of a physical computing environment is prevalent, and the most frequently used robot as a programming tool is "Albert". The duration of the program implementation varies, ranging from 5 weeks to 48 weeks. In the analyzed research studies, computational thinking is conceptualized as a problem-solving skill that can be improved by software education, and assessed by individual instruments measuring sub-factors of computational thinking. Conclusion/Implications: The present study reveals that, although the number of research publications in software education for young children has increased, the overall sufficiency of the accumulated research data and a variety of research methods are still lacking. An increased interest in software education for young children and more research activities in this area are needed to develop and implement developmentally appropriate software education programs in early childhood settings.

Multi-Variate Tabular Data Processing and Visualization Scheme for Machine Learning based Analysis: A Case Study using Titanic Dataset (기계 학습 기반 분석을 위한 다변량 정형 데이터 처리 및 시각화 방법: Titanic 데이터셋 적용 사례 연구)

  • Juhyoung Sung;Kiwon Kwon;Kyoungwon Park;Byoungchul Song
    • Journal of Internet Computing and Services
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    • 제25권4호
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    • pp.121-130
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    • 2024
  • As internet and communication technology (ICT) is improved exponentially, types and amount of available data also increase. Even though data analysis including statistics is significant to utilize this large amount of data, there are inevitable limits to process various and complex data in general way. Meanwhile, there are many attempts to apply machine learning (ML) in various fields to solve the problems according to the enhancement in computational performance and increase in demands for autonomous systems. Especially, data processing for the model input and designing the model to solve the objective function are critical to achieve the model performance. Data processing methods according to the type and property have been presented through many studies and the performance of ML highly varies depending on the methods. Nevertheless, there are difficulties in deciding which data processing method for data analysis since the types and characteristics of data have become more diverse. Specifically, multi-variate data processing is essential for solving non-linear problem based on ML. In this paper, we present a multi-variate tabular data processing scheme for ML-aided data analysis by using Titanic dataset from Kaggle including various kinds of data. We present the methods like input variable filtering applying statistical analysis and normalization according to the data property. In addition, we analyze the data structure using visualization. Lastly, we design an ML model and train the model by applying the proposed multi-variate data process. After that, we analyze the passenger's survival prediction performance of the trained model. We expect that the proposed multi-variate data processing and visualization can be extended to various environments for ML based analysis.

CHILDHOOD TRAUMA:RESILIENCE AND RISK FACTORS ON DEVELOPMENTAL TRAJECTORY (소아기 외상 : 발달경로에 따른 보호 및 위험인자)

  • Kim, Young-Shin
    • Journal of the Korean Academy of Child and Adolescent Psychiatry
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    • 제13권1호
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    • pp.15-23
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    • 2002
  • Knowledge regarding the resilience factors and risk factors of the childhood trauma on the developental trajectory is in its infancy due to the lack of prospective follow-up studies in the childhood trauma and limited understanding of the complex reciprocal interactions between childhood trauma, develop-ent and various aspects of children's environment. These difficulties in the conceptual framework and research methods in the childhood trauma are partly reflected in the inconsistencies, even controversies, of the results in the childhood trauma researches. Despite these difficulties, common aspects of the risk factors and resilience of the childhood trauma on the development can be identified from the previous studies. The resilience to the negative outcome on the development by childhood trauma includes:sex female before puberty, male after puberty or infancy), high socioeconomic status, no organic problem, easy temperament, no previous experience with early loss or separation, younger age at the trauma, better problem solving capacity, high self-esteem, internal locus of control, high coping skills, ability to identify interpersonal relationships, ability to play, sense of humor, having capable parents, having a warm relaionship with at least one of the parents, high education and participating in the organized religious activities. These commonalities of the results suggest that risk and resilient factors of the childhood trauma are interdependent, each factor has multiplicity in the impacts on the children's development according to the developmental stage of the child, family and children's other environment, trauma and stressor have diverse effects according to their intensity and risk and resilience factors could have synergistic or antagonistic effects to each other. To develop comprehensive understanding on the relationship between childhood trauma and developmental psychopathology, risk and resilience factors and to develop effective and efficient prevention and intervention, research on the effect of the stress on the neurodevelopment, on the individual differences of the response to the trauma including genetic factors and constitution, and on the brain plasticity should be accompanied in the future.

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Corporate Credit Rating based on Bankruptcy Probability Using AdaBoost Algorithm-based Support Vector Machine (AdaBoost 알고리즘기반 SVM을 이용한 부실 확률분포 기반의 기업신용평가)

  • Shin, Taek-Soo;Hong, Tae-Ho
    • Journal of Intelligence and Information Systems
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    • 제17권3호
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    • pp.25-41
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    • 2011
  • Recently, support vector machines (SVMs) are being recognized as competitive tools as compared with other data mining techniques for solving pattern recognition or classification decision problems. Furthermore, many researches, in particular, have proved them more powerful than traditional artificial neural networks (ANNs) (Amendolia et al., 2003; Huang et al., 2004, Huang et al., 2005; Tay and Cao, 2001; Min and Lee, 2005; Shin et al., 2005; Kim, 2003).The classification decision, such as a binary or multi-class decision problem, used by any classifier, i.e. data mining techniques is so cost-sensitive particularly in financial classification problems such as the credit ratings that if the credit ratings are misclassified, a terrible economic loss for investors or financial decision makers may happen. Therefore, it is necessary to convert the outputs of the classifier into wellcalibrated posterior probabilities-based multiclass credit ratings according to the bankruptcy probabilities. However, SVMs basically do not provide such probabilities. So it required to use any method to create the probabilities (Platt, 1999; Drish, 2001). This paper applied AdaBoost algorithm-based support vector machines (SVMs) into a bankruptcy prediction as a binary classification problem for the IT companies in Korea and then performed the multi-class credit ratings of the companies by making a normal distribution shape of posterior bankruptcy probabilities from the loss functions extracted from the SVMs. Our proposed approach also showed that their methods can minimize the misclassification problems by adjusting the credit grade interval ranges on condition that each credit grade for credit loan borrowers has its own credit risk, i.e. bankruptcy probability.