• Title/Summary/Keyword: statistical problem solving

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Transforming mathematics education with AI: Innovations, implementations, and insights

  • Sheunghyun Yeo;Jewoong Moon;Dong-Joong Kim
    • The Mathematical Education
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    • v.63 no.2
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    • pp.387-392
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    • 2024
  • The use of artificial intelligence (AI) in mathematics education has advanced as a means for promoting understanding of mathematical concepts, academic achievement, computational thinking, and problem-solving. From a total of 13 studies in this special issue, this editorial reveals threads of potential and future directions to advance mathematics education with the integration of AI. We generated five themes as follows: (1) using ChatGPT for learning mathematical content, (2) automated grading systems, (3) statistical literacy and computational thinking, (4) integration of AI and digital technology into mathematics lessons and resources, and (5) teachers' perceptions of AI education. These themes elaborate on the benefits and opportunities of integrating AI in teaching and learning mathematics. In addition, the themes suggest practical implementations of AI for developing students' computational thinking and teachers' expertise.

An Analysis of Methods for Teaching Bar and Line Graphs in Elementary Mathematics Textbooks (초등 수학 교과서의 막대그래프와 꺾은선그래프 지도에 대한 분석)

  • Kim, Somin;Lee, Jong-hak
    • Journal of the Korean School Mathematics Society
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    • v.23 no.3
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    • pp.259-276
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    • 2020
  • The purpose of this study was to identify how didactic transposition (teaching and learning methods) has occurred and developed in the teaching of graphs in elementary school mathematics textbooks for third and fourth graders according to the previous and current curricula. In this study, we analyzed the lesson units on bar graphs and line graphs in mathematics textbooks for each curriculum, from the fifth curriculum to the 2015 revised curriculum. We also investigated the implication of statistics education deriving from didactic transposition (teaching and learning methods). We found that the timing of teaching bar and line graphs was rarely changed as the curriculum has changed. In addition, the use of technology was not actively implemented in school statistics, although the curriculum emphasized the use of technology in statistical education. Lastly, the textbooks did not address the variability and distribution of data and the sample or sampling process, which are significant statistical concepts. Based on the findings of this study, we suggest how to teach statistical graphs and what to consider for the next mathematics textbook.

A Study on Knowledge for the Teaching of Variability and Reasoning about Variation (변이성과 변이 추론의 지도를 위한 지식)

  • Ko, Eun-Sung;Lee, Kyeong-Hwa
    • Journal of Educational Research in Mathematics
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    • v.20 no.4
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    • pp.493-509
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    • 2010
  • Researchers have suggested that educators have to focus their attention on variability and reasoning about variation as means of developing students' statistical thinking in school mathematics. This paper investigated knowledge for the teaching of variability and reasoning about variation; what are sources of variability, how to cope with variability, what are types of variability, how to recognize variability, and the relationship between statistical problem solving and variability. The results involve: discussion on the sources of variability and how to cope with variability promotes students' awareness of different types of variability and students' motivation in the following steps in the statistical activity; emphasis on reasoning about variation in teaching representation of data accords with objectives of statistics education; reexamination of curriculum for statistics education is needed, which has a content-oriented arrangement.

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Concrete Class Plan for a Statistical Project of 5th Graders in Elementary School Using Infographics (인포그래픽을 활용한 초등학교 5학년 통계 프로젝트 수업의 구체화 방안)

  • Kim, Ji Hye;Song, Sang Hun
    • Journal of Elementary Mathematics Education in Korea
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    • v.23 no.1
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    • pp.75-92
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    • 2019
  • The 2015 revised mathematics curriculum encourages students to use graphs in newspapers and the Internet as materials when teaching graphs, and to experience a series of statistical problem-solving processes that collect, classify, organize, graph and interpret data. The graphs that the students learn through traditional textbooks were a single type of graphs. In particular, the graphs of the 5th and 6th grade groups were only increased in numbers, but the basic concepts were repeated in the 3rd and 4th grades. Fortunately, from the 2009 revision curriculum, it is possible to select the graph suitable for the situation while comparing the characteristics of some graphs. In most cases, the graphs used in the real world are presented in the form of a compounded infographics. The purpose of this study is to analyze and analyze the manifestations of information processing competence elements emphasized in the 2015 revised curriculum through the statistical project class using the informal graphic in the fifth grade of elementary school. And we suggested a concrete class plan.

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Direction-of-Arrival Estimation Using Linear Prediction Method in Conjunction with Signal Enhancement Approach (신호부각법과 결합된 선형예측방법을 이용한 도래각 추정)

  • 오효성
    • The Journal of Korean Institute of Electromagnetic Engineering and Science
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    • v.10 no.6
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    • pp.959-967
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    • 1999
  • In this paper, we propose a Linear Prediction Method(LPM) in conjunction with signal enhancement for solving the direction-of-arrival estimation problem of multiple incoherent plane waves incident on a uniform linear array. The basic idea of signal enhancement is that of finding the covariance matrix of given rank that lies closest to a given estimated matrix in Frobenius norm sense. It is well known that LPM has a high-resolution performance in general applications, while it provides a lower statistical performance in lower SNR environment. To solve this problem, the LPM combined with signal enhancement approach is herein proposed. Simulation results are illustrated to demonstrate the better performance of the proposed method than conventional LPM.

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Application of Resampling Method based on Statistical Hypothesis Test for Improving the Performance of Particle Swarm Optimization in a Noisy Environment (노이즈 환경에서 입자 군집 최적화 알고리즘의 성능 향상을 위한 통계적 가설 검정 기반 리샘플링 기법의 적용)

  • Choi, Seon Han
    • Journal of the Korea Society for Simulation
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    • v.28 no.4
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    • pp.21-32
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    • 2019
  • Inspired by the social behavior models of a bird flock or fish school, particle swarm optimization (PSO) is a popular metaheuristic optimization algorithm and has been widely used from solving a complex optimization problem to learning a artificial neural network. However, PSO is difficult to apply to many real-life optimization problems involving stochastic noise, since it is originated in a deterministic environment. To resolve this problem, this paper incorporates a resampling method called the uncertainty evaluation (UE) method into PSO. The UE method allows the particles to converge on the accurate optimal solution quickly in a noisy environment by selecting the particles' global best position correctly, one of the significant factors in the performance of PSO. The results of comparative experiments on several benchmark problems demonstrated the improved performance of the propose algorithm compared to the existing studies. In addition, the results of the case study emphasize the necessity of this work. The proposed algorithm is expected to be effectively applied to optimize complex systems through digital twins in the fourth industrial revolution.

Study of The Area of Nursing Need by the Family Developmental Stage (가족발달단계에 따른 간호요구영역에 관한 연구)

  • 최부옥
    • Journal of Korean Academy of Nursing
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    • v.7 no.2
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    • pp.43-59
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    • 1977
  • The Community Health Service considers the family as a service unit and places the emphasis of its service on the health problems and the nursing needs of the family rather than the individual. From the conceptual point of view that tile community health service is both health maintenance and health promotion of the family, the community health nurse should have a knowledge of the growth and development of the family and be responsible for the comprehensive support of normal family development. The community health nurse often is in a position to make a real contribution to normal family development. In order to investigate the relationship between the areas of nursing need and family development, the following objectives were established 1. To discover the general characteristics of the study population by the stage of family development. 2. To discover specific nursing needs in relation to the family developmental stage, and to determine the intensity of the nursing needs and the ability of the family to cope with these needs. 3. To discover overall family health nursing problems in relation to the family developmental stage and determine the intensity of the nursing need and the problem solving ability of family. Definitions : The family developmental stages as classified by Dually were used stage 1. Married couples(without children) stage 2. Childbearing Families (oldest child birth to 30 months of age) stage 3. Families with preschool children (oldest child 2½-to 6 years) stage 4. Families with schoolchildren (oldest child 6 to 13 years). stage 5. Families with teenagers (oldest child 13 to 20 years) stage 6. Families as launching centers (first child gone to last child′s leaving home). stage 7. Middle- aged parents (empty nest to retirement) stage 8. Aging family member (retirement to death of both spouses) The areas of nursing need were defined as those used in the study, "A Comprehensive Study about Health and Nursing Need and a Social Diagram of the Community", by tile Nursing research Institute and Center for population. and Family Planning, July 1974. The study population defiled and selected were 260 nuclear families ill two myron of Kang Hwa Island. Percent, mean value and F- test were utilized in tile statistical analysis of the study result. Findings : 1. General characteristics of the study population by tile family developmental stage ; 1)The study population was distributed by the family developmental stage as follows : stage 1 : 3 families stage 2 : 13 families stage 3 : 24 families stage 4 : 41 families stage 5 : 50 families stage 6 : 106 families stage 7 : 13 families stage 8 : 10 families 2) Most families had 4 or 5 members except for those in stage, 1, 7, and 8. 3) The parents′ present age was older in the higher developmental stage and their age at marriage was also younger in the higher developmental stages. 4) The educational level of parents was primarily less than elementary school irrespective of the developmental stage. 5) More than half of parents′ occupations were listed as laborers irrespective of the developmental stage, 6) More than half of the parents were atheists irrespective of the developmental stage. 7) The higher the developmental stage(from stage 2 to stage 6 ), the wider the distribution of children′s ages. 8) More than half of the families were of middle or lower socio-economic level. 2. Problems in specific areas of nursing need by family developmental stage, the intensity of nursing need and the problem solving ability of the family : 1) As a whole, many problems, irrespective of the developmental stage, occurred in tile areas of Housing and Sanitation, Eating Patterns, Housekeeping, Preventive Measures and Dental care. Problems occurring ill particular stages included the following ; stage 1 : Prevention of Accident stage 2 : Preventive Vaccination, Family Planning. stage 3 : Preventive Vaccination, Maternal Health, Family Planning, Health of Infant and Preschooler. stage 4, 5 : Preventive Vaccination, Family Planning, Health of School Children. stage 6 : Preventive Vaccination, Health of School Children. 2) The intensity of the nursing need in the area of Acute and Chronic Diseases was generally of moderate degree or above irrespective of the developmental stages except for stage 1. Other areas of need listed as moderate or above were found in the following stages: stage 1 : Maternal Health stage 3 . Horsing and Sanitation, Prevention of Accident. stage 4 . Housing and Sanitation. stage 5 : Housing and Sanitation, Diagnostic and Medical Care. stage 6 : Diagnostic and Medical care stage 7 : Diagnostic and Medical Care, Housekeeping. stage 8 : Housing and Sanitation, Prevention of Accident, Diagnostic and Medical Care, Dental Care, Eating Patterns, Housekeeping. 3) Areas of need with moderate problem solving ability or less were as follows : stage 1 : Diagnostic and Medical Care, Maternal Health. stage 2 : Prevention of Accident, Acute and Chronic Disease, Dental Care. stage 3 : Housing and Sanitation, Acute and Chronic Disease, Diagnostic and Medical Care, Preventive Measure, Dental Care, Maternal Health, Health of Infant and preschooler, Eating Patterns. stage 4 : Housing and Sanitation, Prevention of Accident, Diagnostic and Medical Care, Preventive Measure, Dental Care, Maternal Health, Health of New Born, Health of Infant and Preschooler, Health of school Children, Eating Patterns, Housekeeping. stage 5 . Housing and Sanitation, Prevention of Accident, Acute and Chronic Disease, Diagnostic and Medical Care, Preventive Measure, Dental Care, Preventive Vaccination, Maternal Health, Eating Patterns. stage 7, 8 : Housing and Sanitation, Prevention of Accident, Acute and Chronic Disease, Diagnostic and Medical Care, Preventive Measures, Dental Care, Preventive Vaccination, Eating Patterns , Housekeeping. Problem occurrence, the degree of nursing need and the degree of problem solving ability 1 nursing need areas for the family as a whole were as follows : 1) The higher the stages(except stage 1 ), the lower the rate of problem occurrence. 2) The higher the stage becomes, the lower the intensity of the nursing need becomes. 3) The higher the stages (except stages 7 and 8), the higher. the problem solving ability. Conclusions ; 1) When the nursing care plan for the family is drawn up, depending upon the stage of family development, higher priority should be give to nursing need areas ① at which problems were shown to occur ② where the nursing need is shown to be above moderate degree and ③ where the problem solving ability was shown to be of moderate degree. 2) The priority of the nursing service should be Placed ① not on those families in the high developmental stage but on those families in the low developmental stage ② and on those areas of need shown in stages 7 and 8 where the degree nursing need was high and the ability to cope low.

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An Analysis on the Past Items of Probability and statistics in Secondary School Mathematics Teacher Certification Examination (수학과 중등임용 확률과 통계학 기출문항 분석)

  • Kim, Changil;Jeon, Youngju
    • Journal of the Korean School Mathematics Society
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    • v.20 no.4
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    • pp.387-404
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    • 2017
  • In this paper, in the last 4 years(2014~2017 school year), we classified the probability and statistical items based on the evaluation scope of the mathematics subject content knowledge which were presented by the Korea Institute for Curriculum and Evaluation, and the classified items were analyzed. As a result, First, in order to induce normalization of the probability and statistical curriculum, four assessment field should be evenly distributed. Second, integrated thinking and comprehensive analytical thinking assessment is required. Third, item an epilogue should be used to measure mathematical thinking and logical competence. Fourth, the ratio of the number of items in probability and statistics to the number of that was 7.7%~10.0%, and the ratio according to the item weighting was 5.0%~7.5%. Fifth, it maintains the policy of stabilizing a good the level of difficulty of the items. Finally, probability and statistical assessment should focus on measuring problem solving ability from an inductive point of view.

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Improvement of Search Efficiency in Optimization Algorithm using Self-adaptive Harmony Search Algorithms (매개변수 자가적응 화음탐색 알고리즘의 성능 비교를 통한 최적해 탐색 효율 향상)

  • Choi, Young Hwan;Lee, Ho Min;Yoo, Do Guen;Kim, Joong Hoo
    • Journal of the Korea Academia-Industrial cooperation Society
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    • v.19 no.1
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    • pp.1-11
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    • 2018
  • In various engineering fields, determining the appropriate parameter set is a cumbersome and difficult task when solving optimization problems. Despite the appropriate parameter setting through parameter sensitivity analysis, there are limits to evaluating whether the parameters are appropriate for all optimization problems. For this reason, kinds of a Self-adaptive Harmony searches have been developed to solve various engineering problems by the appropriate setting of algorithm's own parameters according to the problem. In this study, various types of Self-adaptive Harmony searches were investigated and the characteristics of optimization were categorized. Six algorithms with a differentiation of optimization process were applied and compared with not only the mathematical optimization problem, but also the engineering problem, which has been applied widely in the algorithm performance comparisons. The performance of each algorithm was compared, and the statistical performance indicators were used to evaluate the application results quantitatively.

A Study on Pre-Service Teachers' Understanding of Random Variable (확률변수 개념에 대한 예비교사의 이해)

  • Choi, Jiseon;Yun, Yong Sik;Hwang, Hye Jeang
    • School Mathematics
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    • v.16 no.1
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    • pp.19-37
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    • 2014
  • This study investigated the degree of understanding pre-service teachers' random variable concept, based on the attention and the importance for developing pre-service teachers' ability on statistical reasoning in statistics education. To accomplish this, the subject of this study was 70 pre-service teachers belonged to three universities respectively. The teachers were given to 7 tasks on random variable and requested to solve them in 40 minutes. The tasks consisted of three contents in large; 1) one was on the definition of random variables, 2) the other was on the understanding of random variables in different/diverse conditions, and 3) another was on problem solving relevant to random variable concept. The findings are as follows. First, while 20% of pre-service teachers understood the definition of random variable correctly, most teachers could not distinguish between random variable and variable or probability. Second, there was a significant difference in understanding random variables in different/diverse conditions. Namely, the degree of understanding on the continuous random variable was superior to that of discrete random variable and also the degree of understanding on the equal distribution was superior to that of unequality distribution. Third, three types of problems relevant to random variable concept dealt with in this study were finding a sample space and an elementary event, and finding a probability value. In result, the teachers responded to the problem on finding a probability value most correctly and on the contrary to this, they had the mot difficulty in solving the problem on finding a sample space.

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