• Title/Summary/Keyword: mathematical learning potential

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A study on the Learning Polyhedra using 'Polyhedron' ('Polyhedron'을 활용한 다면체 학습에 관한 연구)

  • Kwon Sung-Yong
    • The Mathematical Education
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    • v.45 no.2 s.113
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    • pp.191-204
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    • 2006
  • Computer technology has a potential to change the contents of school mathematics and the way of teaching mathematics. But in our country, the problem whether computer technology should be introduced into mathematics classroom or not was not resolved yet. As a tool, computer technology can be used by teachers who are confident of the effectiveness and who can use it skillfully and can help students to understand mathematics. The purpose of this study was to investigate the effective way to introduce and utilize computer technology based on the status quo of mathematics classroom setting. One possible way to utilize computer technology in mathematics classroom in spite of the lack of computer and the inaccessibility of useful software is using domain specific simulation software like 'Polyhedron'. 'Polyhedron', as we can guess from the name, can be used to explore regular and semi regular polyhedra and the relationship between them. Its functions are limited but it can visualize regular polyhedra, transform regular polyhedra into other polyhedra. So it is easier to operate than other dynamic geometry software like GSP. To investigate the effect of using this software in mathematics class, three classes(one in 6th grade from science education institute for the gifted, two in 7th grade) were chosen. Activities focused on the relationship between regular and semi regular polyhedra. After the class, several conclusions were drawn from the observation. First, 'Polyhedron' can be used effectively to explore the relationship between regular and semi regular polyhedra. Second, 'Polyhedron' can motivate students. Third, Students can understand the duality of polyhedra. Fourth, Students can visualize various polyhedra by reasoning. To help teachers in using technology, web sites like NCTM's illuminations and NLVM of Utah university need to be developed.

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Correlation Analysis between Soil Shear Strength Parameters and Cone Index Using Artificial Neural Networks - 1 (인공신경망을 적용한 지반 전단강도정수와 콘지수 사이의 상관관계 분석 1)

  • Moon, In-Jong;Kim, Young-Uk
    • Journal of the Korea Academia-Industrial cooperation Society
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    • v.16 no.3
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    • pp.2234-2241
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    • 2015
  • This study has been undertaken to develop a relationship between the shear strength coefficients and the cone index. The theoretic mathematical equations for the relationship were rigorously investigated, and then a Artificial Neural Network(ANN) analysis was adapted to enhance the reliability of the investigation. The theoretical investigation involved various assumptions resulting in the significant error involvement of geotechnical behaviors of ground. Therefore, a model using the ANN has been learned to enhance the prediction of the cone index form the shear strength parameters. Site investigation reports from various construction fields were used for ANN model learning. The results of the study show that the model predicts the cone index from the shear strength parameters of soils very well. The further study that is undertaking has a potential promise of the generalized prediction technique for the cone index from the soil parameters.

An analysis of students' engagement in elementary mathematics lessons using open-ended tasks (개방형 과제를 활용하는 초등 수학 수업에서 학생의 참여 분석)

  • Nam, Inhye;Shin, Bomi
    • The Mathematical Education
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    • v.62 no.1
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    • pp.57-78
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    • 2023
  • Students' engagement in lessons not only determines the direction and result of the lessons, but also affects academic achievement and continuity of follow-up learning. In order to provide implications related to teaching strategies for encouraging students' engagement in elementary mathematics lessons, this study implemented lessons for middle-low achieving fifth graders using open-ended tasks and analyzed characteristics of students' engagement in the light of the framework descripors developed based on previous research. As a result of the analysis, the students showed behavioral engagement in voluntarily answering teacher's questions or enduring difficulties and performing tasks until the end, emotional engagement in actively expressing their pleasure by clapping, standing up and the feelings with regard to the topics of lessons and the tasks, cognitive engagement in using real-life examples or their prior knowledge to solve the tasks, and social engagement in helping friends, telling their ideas to others and asking for friends' opinions to create collaborative ideas. This result suggested that lessons using open-ended tasks could encourage elementary students' engagement. In addition, this research presented the potential significance of teacher's support and positive feedback to students' responses, teaching methods of group activities and discussions, strategies of presenting tasks such as the board game while implementing the lessons using open-ended tasks.

Estimation of Greenhouse Tomato Transpiration through Mathematical and Deep Neural Network Models Learned from Lysimeter Data (라이시미터 데이터로 학습한 수학적 및 심층 신경망 모델을 통한 온실 토마토 증산량 추정)

  • Meanne P. Andes;Mi-young Roh;Mi Young Lim;Gyeong-Lee Choi;Jung Su Jung;Dongpil Kim
    • Journal of Bio-Environment Control
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    • v.32 no.4
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    • pp.384-395
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    • 2023
  • Since transpiration plays a key role in optimal irrigation management, knowledge of the irrigation demand of crops like tomatoes, which are highly susceptible to water stress, is necessary. One way to determine irrigation demand is to measure transpiration, which is affected by environmental factor or growth stage. This study aimed to estimate the transpiration amount of tomatoes and find a suitable model using mathematical and deep learning models using minute-by-minute data. Pearson correlation revealed that observed environmental variables significantly correlate with crop transpiration. Inside air temperature and outside radiation positively correlated with transpiration, while humidity showed a negative correlation. Multiple Linear Regression (MLR), Polynomial Regression model, Artificial Neural Network (ANN), Long short-term Memory (LSTM), and Gated Recurrent Unit (GRU) models were built and compared their accuracies. All models showed potential in estimating transpiration with R2 values ranging from 0.770 to 0.948 and RMSE of 0.495 mm/min to 1.038 mm/min in the test dataset. Deep learning models outperformed the mathematical models; the GRU demonstrated the best performance in the test data with 0.948 R2 and 0.495 mm/min RMSE. The LSTM and ANN closely followed with R2 values of 0.946 and 0.944, respectively, and RMSE of 0.504 m/min and 0.511, respectively. The GRU model exhibited superior performance in short-term forecasts while LSTM for long-term but requires verification using a large dataset. Compared to the FAO56 Penman-Monteith (PM) equation, PM has a lower RMSE of 0.598 mm/min than MLR and Polynomial models degrees 2 and 3 but performed least among all models in capturing variability in transpiration. Therefore, this study recommended GRU and LSTM models for short-term estimation of tomato transpiration in greenhouses.

Introduction of AI digital textbooks in mathematics: Elementary school teachers' perceptions, needs, and challenges (수학 AI 디지털교과서의 도입: 초등학교 교사가 바라본 인식, 요구사항, 그리고 도전)

  • Kim, Somin;Lee, GiMa;Kim, Hee-jeong
    • Education of Primary School Mathematics
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    • v.27 no.3
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    • pp.199-226
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    • 2024
  • In response to the era of transformation necessitating the introduction of Artificial Intelligence (AI) and digital technologies, educational innovation is undertaken with the implementation of AI digital textbooks in Mathematics, English, and Information subjects by 2025 in Korea. Within this context, this study analyzed the perceptions and needs of elementary school teachers regarding mathematics AI digital textbook. Based on a survey conducted in November 2023, involving 132 elementary school teachers across the country, the analysis revealed that the majority of elementary school teachers had a low perception of the introduction and need for mathematics AI digital textbooks. However, some recognized the potential for personalized learning and effective teaching support. Furthermore, among the core technologies of the AI digital textbook, teachers highly valued the necessity of learning diagnostics and teacher reconfiguration functions and had the most positive perception of their usefulness in math lessons, while their perception of interactivity was relatively low. These findings suggest the need for changing teachers' perceptions through professional development and information provision to ensure the successful adoption and use of mathematics AI digital textbooks. Specifically, providing concrete and practical ways to use the AI digital textbook, exploring alternatives to digital overload, and continuing development and research on core technologies.

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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    • v.18 no.2
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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.

Analysis of the Effectiveness of Big Data-Based Six Sigma Methodology: Focus on DX SS (빅데이터 기반 6시그마 방법론의 유효성 분석: DX SS를 중심으로)

  • Kim Jung Hyuk;Kim Yoon Ki
    • KIPS Transactions on Software and Data Engineering
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    • v.13 no.1
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    • pp.1-16
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    • 2024
  • Over recent years, 6 Sigma has become a key methodology in manufacturing for quality improvement and cost reduction. However, challenges have arisen due to the difficulty in analyzing large-scale data generated by smart factories and its traditional, formal application. To address these limitations, a big data-based 6 Sigma approach has been developed, integrating the strengths of 6 Sigma and big data analysis, including statistical verification, mathematical optimization, interpretability, and machine learning. Despite its potential, the practical impact of this big data-based 6 Sigma on manufacturing processes and management performance has not been adequately verified, leading to its limited reliability and underutilization in practice. This study investigates the efficiency impact of DX SS, a big data-based 6 Sigma, on manufacturing processes, and identifies key success policies for its effective introduction and implementation in enterprises. The study highlights the importance of involving all executives and employees and researching key success policies, as demonstrated by cases where methodology implementation failed due to incorrect policies. This research aims to assist manufacturing companies in achieving successful outcomes by actively adopting and utilizing the methodologies presented.

Development of Applied Music Education Program for Creative and Convergent Thinking-With a Focus on the Capstone design Class (창의·융합적 사고를 위한 실용음악 교육프로그램 개발-캡스톤디자인 수업을 중심으로)

  • Yun, Sung-Hyo;Han, Kyung-hoon
    • The Journal of the Convergence on Culture Technology
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    • v.10 no.4
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    • pp.285-294
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    • 2024
  • This study aims to enhance learners' creative and integrative thinking through the use of a practical music education program, facilitating high-quality artistic activities and the integration of various disciplines. To achieve this, a practical music education program incorporating the PDIE model was designed, and the content validity of the developed program was verified. Through this process, We have researched and described methodologies for multidisciplinary research that can be applied in practical music education. This paper focuses on the fourth session of the study, which deals with the creative and integrative education of practical music and mathematics. The mathematical theory of interest in this research is the Fibonacci sequence, fundamental to the golden ratio in art. The goal is to enable balanced and high-quality creative activities through learning and applying the Fibonacci sequence. Additionally, to verify the validity and effectiveness of the instructional plan, including the one used in the 15-week course, we have detailed the participants involved in the content validation, the procedures of the research, the research tools used, and the methods for collecting and analyzing various data. Through this, We have confirmed the potential of creative and integrative education in higher practical music education and sought to develop educational methodologies for cultivating various creative talents in subsequent research.