• Journal of the Korean School Mathematics Society
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• v.20 no.2
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• pp.141-161
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• 2017

As it's important to understand the order of operation in the mixed calculation of natural number and perform it, mathematics curriculums and textbooks focused that students can calculate with understanding the order of operation and its principles. For attaining the implications of teaching about the mixed calculations, this study analyzed the problem solving abilities and error types of 67 elementary students and 57 pre-service teachers using questionnaire which was developed in this study and composed of numeric expressions and word problems. The conclusions drawn from this study were as follows: Students were revealed the correct rates(86.2% and 73.5%) in numeric expressions and word problems, but they were showed the paradigmatic error types-the errors of the order of operation and the composition of numeric expression from word problems. Even though the correct rates of the preservice teachers were extremely high, the result of problem solving processes required that it's needed to be interested in teaching the principles of the order of operation in the mixed calculations. In addition, subjects were revealed the problems about using parentheses and equal sign.

• Journal of the Korean School Mathematics Society
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• v.10 no.4
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• pp.471-485
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• 2007

In this study, a 27 class hour prescribed program for the fourth grade students is to be developed and applied by extracting the contents associated with basic operations studied prior to the fourth grade level of mixed calculations. After analyzing the results of the research, the following conclusions are obtained. First, the prescribed program for mixed calculations brought about the improvement in the mixed calculation problem solving ability of the students. Second, applying the prescribed program for mixed calculation resulted in an increase in students' interest and concentration on problem solving. In synthesis of the above conclusions, the development and application of the prescribed program for mixed calculation improved the students' concentration on the problem and the students' problem solving ability.

• Education of Primary School Mathematics
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• v.21 no.3
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• pp.289-307
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• 2018

Although mixed calculation of natural numbers is important in that it completes arithmetic calculation of natural numbers in elementary school, few studies have been conducted regarding its instruction methods. Given this, this study analyzed Korean mathematics textbooks (from the fifth textbooks to the 2009 revised textbooks) along with Japanese and Singaporean textbooks in terms of the parentheses and the order of operations regarding mixed calculation of natural numbers. The results of this study showed that there were differences in introducing the parentheses and representing them in an explicit way per textbooks. In the Korean textbooks, the order of operations was presented mostly with the real-life contexts but it was not always in a diagrammatic representation. In contrast, in the Singaporean textbooks, the order of operations was presented without the real-life contexts and the use of calculators was emphasized. In the Japanese textbooks, the order of operations was presented with the real-life contexts and a hierarchy of operations was emphasized. Based on these results, this study suggested several implications of textbook development and instructional methods regarding mixed calculations of natural numbers.

• Journal of Educational Research in Mathematics
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• v.22 no.4
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• pp.477-494
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• 2012

This study is to review the content organization and developmental ways of the unit on the mixed calculations and explore the alternatives on the basis of students' responsive examples and error patterns with relation to the mixed calculations, mnemonics of PEMDAS and historical context with relation to the order of operations. Then I analyzed the textbook and manual for teachers of the unit of mixed calculations of fourth grade and improvement about teaching the mixed calculations. First, I pointed out illogical connection between practical problem and rules of order of operations. Second, I suggested constructing a textbook by considering conventional character of order of operations. Third, I pointed out the importance of structural understanding of an expression of mixed calculations and various strategies with relation to teaching and learning. This study is suggestive for textbook development of the mixed calculations.

• Proceedings of the Korea Water Resources Association Conference
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• 2010.05a
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• pp.198-201
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• 2010

지형이 불규칙한 자연하천에 대해 2차원 격자를 구성할 경우, 사각형 격자만을 사용한다면 지류와 본류의 합류부분에서 격자의 처리가 어려운 문제가 발생할 수 있으며, 삼각형 격자만을 사용하여 지형을 처리한다면 격자수가 많아져 계산시간이 다소 많이 소요되는 어려움이 존재할 수 있다. 혼합격자의 적용이 가능하다면 이러한 어려움은 어느정도 극복할 수 있다. 본 연구에서는 1차정확도 기법인 HLLC 기법을 적용하고, 지형이 복잡한 자연하천에 대한 격자처리의 유연성을 위해 삼각형 및 사각형 격자 그리고 이 두 격자가 혼용된 혼합격자의 적용이 가능한 2차원 유한체적모형을 개발하였다. 그리고 개발모형을 수리모형 실험을 통해 얻어진 실험자료가 존재하는 실험하도 및 실제 자연하천에서의 댐 붕괴에 대해 적용하여 결과를 비교하였다.

• Proceedings of the Korea Water Resources Association Conference
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• 2015.05a
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• pp.75-75
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• 2015

오염원과 취수장이 동일 구간 내에 공존하는 국내하천의 특성상, 하천 평면 내에서 오염물의 거동 및 혼합 특성을 보다 정확하게 해석하기 위해서는 2차원 이송-분산 모형의 적용이 필요하다. 이를 위해서는 2차원 모형의 주요 매개변수인 종분산계수와 횡분산계수의 적절한 입력이 매우 중요하다. 하지만 국내외적으로 횡분산계수에 대한 연구는 많이 진행된 반면, 현재까지 종분산계수에 대한 연구는 충분히 이루어지지 않은 실정이다. 분산계수를 결정하는 방법에는 실측된 농도 자료의 유무에 따라 크게 두 가지로 분류된다. 실측된 농도 자료가 없는 경우, 이론식이나 경험식을 이용하는 방법이 있다. 반면에 추적자 실험 등을 수행하여 실측된 농도 자료가 있는 경우, 모멘트법 또는 추적법을 적용하여 농도-시간 분포 곡선으로부터 분산계수를 계산하는 것이다. 모멘트법은 임의 지점에서 농도의 횡분포를 통해 얻을 수 있는 2차 모멘트의 종방향 변화율이 횡분산계수와 비례한다는 원리를 이용한 것이며, 추적법은 상류부의 관측된 농도를 입력자료로 하여 하류부의 농도를 계산한 후 계산된 농도와 실측된 하류부 농도의 비교를 통해 분산계수를 산정하는 방법이다. 본 연구에서는 불규칙한 단면 형상을 가지는 자연하천에서의 2차원 종 횡분산계수를 산정하기 위해서 Baek & Seo(2010)가 제안한 2차원 유관추적법(2D Stream-tube Routing Procedure)을 적용하였다. 본 연구에서는 국내 자연하천 중 다양한 사행형태를 갖으며 수질오염 사고의 위험이 높은 구간을 선정하고, 추적자로서 Rhodamine WT를 이용하여 현장실험을 수행하였다. 실험에서 수집된 수리량 및 농도자료로부터 추적자의 2차원적 거동을 분석하였으며, 2차원 유관추적법을 적용하여 종분산계수를 산정하였다. 그 결과 하폭 대 수심비(W/H)와 마찰손실관련 무차원변수(U/U*)의 증가에 따라 종분산계수가 증가됨을 확인 할 수 있었다. 본 연구에서 산출된 종분산계수와 선행 연구에서 수집된 자료를 이용하여 추정식을 개발하였다. 차원해석을 통해 무차원 종분산계수에 영향을 미치는 무차원 인자를 선별하고 회귀분석을 이용하여 종분산계수 추정식을 유도하였다. 추정식을 이용하여 산정한 종분산계수의 범위는 Elder (1959)가 제안한 이론값보다 약 10배 정도로 크게 나타났다. 혼합 특성이 밝혀지지 않은 자연하천에 2차원 확산모형을 적용하고자 할 때 본 연구에서 개발된 추정식으로부터 계산된 종분산계수를 사용할 수 있을 것이다.

• Journal of Elementary Mathematics Education in Korea
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• v.20 no.2
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• pp.215-238
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• 2016

The 2015 national revised curriculum was notified officially the last year. The intent and direction of the revision caused more or less change for mathematical contents to be taught and is expected to cause a considerable change in math class. In the level of elementary school mathematics, it turned that several contents were deleted or moved to the upper grades because the revision focused especially both on reducing students' burden of learning and on fostering the mathematical key competences. This study aims to examine the relevance of the change through investigation of the national curriculums for elementary school mathematics since 1946. The mathematical contents to be analyzed in this study were mixed calculation of natural numbers, mixed calculation of fractions and decimal fractions, position and direction of objects, are/hectare and ton, the range of numbers and estimating, surface and volume of cylinders, pattern and correspondence, and direct/inverse proportionality, which were changed in any aspect relative to 2009 national revised curriculum. Based on the results of these analyses, the discussion will provide some suggestions for setting the direction of elementary mathematics curriculum.

• Journal of Elementary Mathematics Education in Korea
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• v.14 no.2
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• pp.377-399
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• 2010

Mixed calculations involving fractions and decimals covered in the unit 6-Na in elementary school math class cause students difficulties, leading them make lots of errors. If students fail to understand temporarily or partly what the teacher taught or lose confidence and continue to have difficulty due to a lack of understanding and skills of algorithm, though they properly understand the concept and principle of the learning content, it should be resolved through intensive teaching. For students suffering from this problem, a correct diagnosis and appropriate treatment are required. Therefore, this study developed a feedback program after diagnosing students' errors through evaluating them in order to continuously assist them to fully understand contents regarding mixed calculations involving fractions and decimals.

• East Asian mathematical journal
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• v.24 no.5
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• pp.547-564
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• 2008

The purpose of this study was to investigate 5th graders' performance for mixed operational problem. For this purpose. two kinds of studies were conducted: a descriptive study by pencil and paper tests(32 problems) and a clinical study by interviews. The conclusions drawn from the results obtained in this study were as follows: First, students were highly scored in pencil and paper tests(M=85.25%). But that score is not up to scratch. Because the problem was composed of simple calculations and if students calculate problems from only let side, they gel 75% right answer, etc. Second, most of students solved mixed operational problems by text-based way, but some students solved flexibly. There are several error types. The main error type is students' following the wrong order of calculations. Some students have obstacles to express their thought with numerical expressions. So they make errors. Third, students solve mixed operational problems with various strategies. For examples, they solve problems by describing calculation procedures, drawing lines to indicate the order of calculations, carrying out two numerical expressions, etc.

• Fire Science and Engineering
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• v.33 no.5
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• pp.1-6
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• 2019

The recent development of biofuel production technology facilitates the widespread use of bioethanol and biodiesel by mixing them with fossil fuels. However, the use of these new blended fuels in combustion could result in severe safety problems, such as fire and explosion. In this study, numerical simulation was performed on the well-stirred reactor (WSR) to simulate the autoignition temperature (AIT) in homogeneous combustion and clarify the effect of ethanol addition on the AIT, the most important property for assessing the potential for fire and explosion. Response surface methodology (RSM) was introduced as a design of experiment (DOE), enabling the AIT to be predicted and optimized systematically with respect to three independent variables: ethanol mole fraction, equivalence ratio, and pressure. The results show that the autoignition temperature primarily depends on the ethanol mole fraction and pressure, while the effects of the equivalence ratio are independent of the AIT. RSM accurately predicted the experimental AIT, indicating that this method can be used to effectively predict the key properties involved in fires and explosions.