• Title/Summary/Keyword: Mathematical concept

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A Study on the Development of a Simulation Model for Predicting Soil Moisture Content and Scheduling Irrigation (토양수분함량 예측 및 계획관개 모의 모형 개발에 관한 연구(I))

  • 김철회;고재군
    • Magazine of the Korean Society of Agricultural Engineers
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    • v.19 no.1
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    • pp.4279-4295
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    • 1977
  • Two types of model were established in order to product the soil moisture content by which information on irrigation could be obtained. Model-I was to represent the soil moisture depletion and was established based on the concept of water balance in a given soil profile. Model-II was a mathematical model derived from the analysis of soil moisture variation curves which were drawn from the observed data. In establishing the Model-I, the method and procedure to estimate parameters for the determination of the variables such as evapotranspirations, effective rainfalls, and drainage amounts were discussed. Empirical equations representing soil moisture variation curves were derived from the observed data as the Model-II. The procedure for forecasting timing and amounts of irrigation under the given soil moisture content was discussed. The established models were checked by comparing the observed data with those predicted by the model. Obtained results are summarized as follows: 1. As a water balance model of a given soil profile, the soil moisture depletion D, could be represented as the equation(2). 2. Among the various empirical formulae for potential evapotranspiration (Etp), Penman's formula was best fit to the data observed with the evaporation pans and tanks in Suweon area. High degree of positive correlation between Penman's predicted data and observed data with a large evaporation pan was confirmed. and the regression enquation was Y=0.7436X+17.2918, where Y represents evaporation rate from large evaporation pan, in mm/10days, and X represents potential evapotranspiration rate estimated by use of Penman's formula. 3. Evapotranspiration, Et, could be estimated from the potential evapotranspiration, Etp, by introducing the consumptive use coefficient, Kc, which was repre sensed by the following relationship: Kc=Kco$.$Ka+Ks‥‥‥(Eq. 6) where Kco : crop coefficient Ka : coefficient depending on the soil moisture content Ks : correction coefficient a. Crop coefficient. Kco. Crop coefficients of barley, bean, and wheat for each growth stage were found to be dependent on the crop. b. Coefficient depending on the soil moisture content, Ka. The values of Ka for clay loam, sandy loam, and loamy sand revealed a similar tendency to those of Pierce type. c. Correction coefficent, Ks. Following relationships were established to estimate Ks values: Ks=Kc-Kco$.$Ka, where Ks=0 if Kc,=Kco$.$K0$\geq$1.0, otherwise Ks=1-Kco$.$Ka 4. Effective rainfall, Re, was estimated by using following relationships : Re=D, if R-D$\geq$0, otherwise, Re=R 5. The difference between rainfall, R, and the soil moisture depletion D, was taken as drainage amount, Wd. {{{{D= SUM from { {i }=1} to n (Et-Re-I+Wd)}}}} if Wd=0, otherwise, {{{{D= SUM from { {i }=tf} to n (Et-Re-I+Wd)}}}} where tf=2∼3 days. 6. The curves and their corresponding empirical equations for the variation of soil moisture depending on the soil types, soil depths are shown on Fig. 8 (a,b.c,d). The general mathematical model on soil moisture variation depending on seasons, weather, and soil types were as follow: {{{{SMC= SUM ( { C}_{i }Exp( { - lambda }_{i } { t}_{i } )+ { Re}_{i } - { Excess}_{i } )}}}} where SMC : soil moisture content C : constant depending on an initial soil moisture content $\lambda$ : constant depending on season t : time Re : effective rainfall Excess : drainage and excess soil moisture other than drainage. The values of $\lambda$ are shown on Table 1. 7. The timing and amount of irrigation could be predicted by the equation (9-a) and (9-b,c), respectively. 8. Under the given conditions, the model for scheduling irrigation was completed. Fig. 9 show computer flow charts of the model. a. To estimate a potential evapotranspiration, Penman's equation was used if a complete observed meteorological data were available, and Jensen-Haise's equation was used if a forecasted meteorological data were available, However none of the observed or forecasted data were available, the equation (15) was used. b. As an input time data, a crop carlender was used, which was made based on the time when the growth stage of the crop shows it's maximum effective leaf coverage. 9. For the purpose of validation of the models, observed data of soil moiture content under various conditions from May, 1975 to July, 1975 were compared to the data predicted by Model-I and Model-II. Model-I shows the relative error of 4.6 to 14.3 percent which is an acceptable range of error in view of engineering purpose. Model-II shows 3 to 16.7 percent of relative error which is a little larger than the one from the Model-I. 10. Comparing two models, the followings are concluded: Model-I established on the theoretical background can predict with a satisfiable reliability far practical use provided that forecasted meteorological data are available. On the other hand, Model-II was superior to Model-I in it's simplicity, but it needs long period and wide scope of observed data to predict acceptable soil moisture content. Further studies are needed on the Model-II to make it acceptable in practical use.

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Development and Application of Integrative STEM (Science, Technology, Engineering and Mathematics) Education Model Based on Scientific Inquiry (과학 탐구 기반의 통합적 STEM 교육 모형 개발 및 적용)

  • Lee, Hyonyong;Kwon, Hyuksoo;Park, Kyungsuk;Oh, Hee-Jin
    • Journal of The Korean Association For Science Education
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    • v.34 no.2
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    • pp.63-78
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    • 2014
  • Integrative STEM education is an engineering design-based learning approach that purposefully integrates the content and process of STEM disciplines and can extend its concept to integration with other school subjects. This study was part of fundamental research to develop an integrative STEM education program based on the science inquiry process. The specific objectives of this study were to review relevant literature related to STEM education, analyze the key elements and value of STEM education, develop an integrative STEM education model based on the science inquiry process, and suggest an exemplary program. This study conducted a systematic literature review to confirm key elements for integrative STEM education and finally constructed the integrative STEM education model through analyzing key inquiry processes extracted from prior studies. This model turned out to be valid because the average CVR value obtained from expert group was 0.78. The integrative STEM education model based on the science inquiry process consisted of two perspectives of the content and inquiry process. The content can contain science, technology, engineering, and liberal arts/artistic topics that students can learn in a real world context/problem. Also, the inquiry process is a problem-solving process that contains design and construction and is based on the science inquiry. It could integrate the technological/engineering problem solving process and/or mathematical problem solving process. Students can improve their interest in STEM subjects by analyzing real world problems, designing possible solutions, and implementing the best design as well as acquire knowledge, inquiry methods, and skills systematically. In addition, the developed programs could be utilized in schools to enhance students' understanding of STEM disciplines and interest in mathematics and science. The programs could be used as a basis for fostering convergence literacy and cultivating integrated and design-based problem-solving ability.

A Study on the Problem of Organic Image in the 20th Post-paintings (20세기 후기회화에 있어서 유기 이미지의 문제)

  • Park Ji-Sook
    • Journal of Science of Art and Design
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    • v.3
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    • pp.145-177
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    • 2001
  • The artist's interest has been captivated by ecological phenomena in Nature. Her keen captivation has then been focused into plastic art depicting the image of primitive life. The wide sweep of her work encompasses the totality of nature which consists of the human's subconscious power and imagination which she then portrays by organic images. These organic images are in contrast to scientific, mathematical and logical inference and consciousness. This research examines the character of the organic images in modern art by her analysis of some representative works by others. The image is an essential concept in the art which appeared in very different ways and in different perspectives. The image in the artwork appears to be the realistic expression until the early part of the 20th Century. Well into the 20th Century, it began being expressed in various ways such as combined images by imagination which is combined or rejected in the story of artwork. It also began being expressed by transferred images by changed original conditions. It is the main purpose of this research is to study of various expressions of organic images in the artwork of the Post-Modernism era. The character and meaning of organic image painting helps people to approach the human instinct more easily to find out the natural essence. It is also an objective of the organic image to tenderise our human sensibilities, thus helping us to regain vitality and recover our poor humanity in the barren wilderness of modern society. 'Life communion with nature' is a meeting point and common ground for Oriental Philosophy and organic image painting. Through this research, organic image painting is characterised in the four following ways : 1st) Organic image painting seeks regularity and perfection of outer shapes, in contrast to disordered and deformed nature, resulting in organic and biotic formalistic mode of plastic art. 2nd) Organic image painting seeks the formative. 3rd) Organic image painting pursues the priceless dignity of life by researching the formatted arrangement and figure, which contains primitive power of life. 4th) Organic image painting makes crystal clear the power of human and nature, which is a historic and biological phenomenon. This, in turn, exposes the humanistic view of the world from modern society best characterised in lost self-understanding, isolation and materialism. The representative organic image painting artists are Elizabeth Murray, Kusama Yayoi, and Niki do Saint Phalle. Elizabeth Murray used shaped canvas and a round construction of relief works. Kusama Yayoi used Automatistic expressionism originating from the realms of unconsciousness and which is represented by the mass and shape of a water drop. Niki do Saint Phalle shows the transcendence of universal life and anti-life to respect the dignity of life and the eco-friendliness relationship of human and nature in the post-modernism in art history. This is accomplished by surrealistic, symbolic, fantastic and humoristic expression. These three artists' works express the spirit of the organic image in contemporary art. It contains the stream of nature and life to seek not only the state of materialism in the reality, but also the harmonized world of nature and human which has almost lost the important meaning in modern times. Finally, this organic image is the plastic language of the majestic life. It is the romantic idea that the intimacy of nature and the universe and Surrealism, which emphasizes the unconsciousness , is the source of truth and spirit. Also it is influenced by primitive art and abstract art. According to this research, the subject 'Research About Organic Images' is not only an important element in the plastic arts from primitive society to the present, but is also fundamental to an true understanding of Post-Modernism.

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Features of sample concepts in the probability and statistics chapters of Korean mathematics textbooks of grades 1-12 (초.중.고등학교 확률과 통계 단원에 나타난 표본개념에 대한 분석)

  • Lee, Young-Ha;Shin, Sou-Yeong
    • Journal of Educational Research in Mathematics
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    • v.21 no.4
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    • pp.327-344
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    • 2011
  • This study is the first step for us toward improving high school students' capability of statistical inferences, such as obtaining and interpreting the confidence interval on the population mean that is currently learned in high school. We suggest 5 underlying concepts of 'discretion of contingency and inevitability', 'discretion of induction and deduction', 'likelihood principle', 'variability of a statistic' and 'statistical model', those are necessary to appreciate statistical inferences as a reliable arguing tools in spite of its occasional erroneous conclusions. We assume those 5 concepts above are to be gradually developing in their school periods and Korean mathematics textbooks of grades 1-12 were analyzed. Followings were found. For the right choice of solving methodology of the given problem, no elementary textbook but a few high school textbooks describe its difference between the contingent circumstance and the inevitable one. Formal definitions of population and sample are not introduced until high school grades, so that the developments of critical thoughts on the reliability of inductive reasoning could not be observed. On the contrary of it, strong emphasis lies on the calculation stuff of the sample data without any inference on the population prospective based upon the sample. Instead of the representative properties of a random sample, more emphasis lies on how to get a random sample. As a result of it, the fact that 'the random variability of the value of a statistic which is calculated from the sample ought to be inherited from the randomness of the sample' could neither be noticed nor be explained as well. No comparative descriptions on the statistical inferences against the mathematical(deductive) reasoning were found. Few explanations on the likelihood principle and its probabilistic applications in accordance with students' cognitive developmental growth were found. It was hard to find the explanation of a random variability of statistics and on the existence of its sampling distribution. It is worthwhile to explain it because, nevertheless obtaining the sampling distribution of a particular statistic, like a sample mean, is a very difficult job, mere noticing its existence may cause a drastic change of understanding in a statistical inference.

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A Case Study on Characteristics of the Mathematics Gifted Children (수학영재의 특성에 관한 사례연구)

  • Kim, Min-Jung;Ryu, Sung-Rim
    • Education of Primary School Mathematics
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    • v.10 no.1 s.19
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    • pp.41-56
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    • 2007
  • Related with the mathematics gifted children the situation of different case studies is the research which is limited in mathematics problem solving process of the most mathematics gifted children. The research which it sees hereupon observes from the scope which is wider the quality of the mathematics gifted children, before the hazard mathematics gifted children whom it sees enter into the mathematics gifted children education center unit life and life after studying living and dismissal of a class from the general school, namely for their general life it leads compared to attitude it observes the reporter it does a quality. For a what kind of interest in the mathematics gifted children, the research leads the family or general class, from the gifted children education center it has it considers encouragement, map and to give a help to good mathematics gifted children education activation, it does. It will reach and to respect with afterwards it set a same three research problem. First, before entering into the mathematics gifted children education center, are the mathematics gifted children what kind of quality? Second, Are the mathematics gifted children what kind of quality for general school hour? Third, Are the mathematics gifted children what kind of quality after dismissal of a class after hour? Being selected in the hazard gifted children education center which solves an up research problem, simple characteristic and approach ease characteristic, by the condition of the permission possibility back it selected 2 person gifted children school boxes which are coming and going. And, before entering into these mathematics gifted children education center, studying life from the general school, life after dismissal of a class it will extend at 1 years, various recording it will ask and it collected direct observation and interview it led against their quality it analyzed. It shared the result which it analyzes with emotional quality, studying conduct qualities, general qualities of the mathematics gifted children and qualities of mathematics gifted children parents. Studies level of the mathematics gifted children parents high facility when them are young from, the interest and helping out which it has were considerable, to advance with the direction where in order for always with great disaster them are proper the map it did. In general quality of the mathematics gifted children from young age the ability which finds a language and a possibility concept superiorly the ability which expresses the thought of oneself logically was superior, the competitive spirit was high, it liked it came reading, a leader role, to reveal a deepening school with the fact that it comes and goes. Also it will burn with their studying conduct quality and it will roll and it did deeply and it arranged knot eagerly, accomplishing which is superior from the field which is various it showed, the originality was superior, the subject attachment power was high quite, oneself it studies it has a devotion the possibility of knowing it was. And, the social characteristic of the friends and is good with their emotional quality and it does there is own reflection and an encouragement at any time and also a confidence, but just as good as the stress also it receives the possibility of knowing it was to him.

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Composition of Curriculums and Textbooks for Speed-Related Units in Elementary School (초등학교에서 속력 관련 단원의 교육과정 및 교과서 내용 구성에 관한 논의)

  • Jhun, Youngseok
    • Journal of Korean Elementary Science Education
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    • v.41 no.4
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    • pp.658-672
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    • 2022
  • The unique teaching and learning difficulties of speed-related units in elementary school science are mainly due to the student's lack of mathematical thinking ability and procedural knowledge on speed measurement, and curriculums and textbooks must be constructed with these in mind. To identify the implications of composing a new science curriculum and relevant textbooks, this study reviewed the structure and contents of the speed-related units of three curriculums from the 2007 revised curriculum to the 2015 revised curriculum and the resulting textbooks and examined their relevance in light of the literature. Results showed that the current content carries the risk of making students calculate only the speed of an object through a mechanical algorithm by memorization rather than grasp the multifaceted relation between traveled distance, duration time, and speed. Findings also highlighted the need to reorganize the curriculum and textbooks to offer students the opportunity to learn the meaning of speed step-by-step by visualizing materials such as double number lines and dealing with simple numbers that are easy to calculate and understand intuitively. In addition, this paper discussed the urgency of improving inquiry performance such as process skills by observing and measuring an actual object's movement, displaying it as a graph, and interpreting it rather than conducting data interpretation through investigation. Lastly, although the current curriculum and textbooks emphasize the connection with daily life in their application aspects, they also deal with dynamics-related content somewhat differently from kinematics, which is the main learning content of the unit. Hence, it is necessary to reorganize the contents focusing on cases related to speed so that students can grasp the concept of speed and use it in their everyday lives. With regard to the new curriculum and textbooks, this study proposes that students be provided the opportunity to systematically and deeply study core topics rather than exclude content that is difficult to learn and challenging to teach so that students realize the value of science and enjoy learning it.