• Journal of Elementary Mathematics Education in Korea
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• v.15 no.1
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• pp.39-56
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• 2011

In 7th grade textbooks, the distributive property is generalized as in algebraic forms, and it seems that the students have not so good grip on this property. To get a good stock of knowledge on that generalized property, full understanding of it in concrete context should take precedence. This study would aim to propose some educational implications for better understanding of that property, through analysing the contents of it comparatively in Korean and Japanese elementary textbooks.

• Journal of Educational Research in Mathematics
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• v.27 no.3
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• pp.451-467
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• 2017

This study examined how the distributive principles(DP) works in our elementary school textbooks and work books to figure out the implications for developing the elementary mathematics curriculum and textbooks. For this purpose, Chinese and Japanese elementary textbooks were reviewed and five criteria for the analysis of Korean textbooks and workbooks were prepared by the review. The analysis showed that Korean textbooks and work books are inefficient to handle DP in many ways. Based on these findings, this study suggested that the DP should be codified into the curriculum and explicitly dealt with in elementary math textbooks.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.36 no.7
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• pp.651-657
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• 2008

A new approach for maximizing torque capability of low efficient reaction wheel assembly is addressed in this paper. At first, to find out a solution in constrainted field, weighted pseudo-inverse and momentum minimized allocation are suggested instead of a general control allocation called pseudo-inverse. The second method is a structural manner to enlarge torque capability of specific axis by changing installed skew angle of wheels. Two proposed methods are applied to large angle maneuvers of satellite. Improvement of control performance and feasibility for applying to commercial satellite attitude control are demonstrated by numeric simulations.

• Journal of Educational Research in Mathematics
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• v.21 no.3
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• pp.239-259
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• 2011

This study investigated the elementary school students' ability on the algebraic reasoning as generalized arithmetic. It analyzed the written responses from 648 second graders, 688 fourth graders, and 751 sixth graders using tests probing their understanding of the properties of whole number operations. The result of this study showed that many students did not recognize the properties of operations in the problem situations, and had difficulties in applying such properties to solve the problems. Even lower graders were quite successful in using the commutative law both in addition and subtraction. However they had difficulties in using the associative and the distributive law. These difficulties remained even for upper graders. As for the associative and the distributive law, students had more difficulties in solving the problems dealing with specific numbers than those of arbitrary numbers. Given these results, this paper includes issues and implications on how to foster early algebraic reasoning ability in the elementary school.

• Journal of Elementary Mathematics Education in Korea
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• v.23 no.1
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• pp.143-168
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• 2019

Along with the significance of algebraic thinking in elementary school, it has been recently emphasized that the properties of number and operations need to be explored in a meaningful way rather than in an implicit way. Given this, the purpose of this study was to analyze how third graders could understand the properties of operations in multiplication after they were taught such properties through a reconstructed unit of multiplication. For this purpose, the students from three classes participated in this study and they completed pre-test and post-test of the properties of operations in multiplication. The results of this study showed that in the post-test most students were able to employ the associative property, commutative property, and distributive property of multiplication in (two digits) × (one digit) and were successful in applying such properties in (two digits) × (two digits). Some students also refined their explanation by generalizing computational properties. This paper closes with some implications on how to teach computational properties in elementary mathematics.

• Journal of Elementary Mathematics Education in Korea
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• v.21 no.1
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• pp.1-22
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• 2017

The properties of arithmetic are considered as essential to understand the principles of calculation and develop effective strategies for calculation in the elementary school level, thanks to agreement on early algebra. Therefore elementary students' misunderstanding of the properties of arithmetic might cause learning difficulties as well as misconcepts in their following learning processes. This study aims to provide elementary teachers a part of pedagogical content knowledge about the properties of arithmetic and to induce some didactical implications for teaching the properties of arithmetic in the elementary school level. To do this, elementary school mathematics textbooks since the period of the first curriculum were analyzed. These results from analysis show which properties of arithmetic have been taught, when they were taught, and how they were taught. Based on them, some didactical implications were suggested for desirable teaching of the properties of arithmetic.

• Korean Journal of Soil Science and Fertilizer
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• v.7 no.1
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• pp.1-4
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• 1974

The application of the Distribution Law to soil-pesticide systems yielded the following empirical implications : 1) The amount of the pesticide adsorbed by a soil is negatively proportional to the soil water content. 2) At a given soil water content the amount adsorbed is proportional to the Kd of the soil. 3) The effect of soil water content on the amount of the pesticide adsorbed diminishes with increasing magnitude of the Kd.

• Communications of Mathematical Education
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• v.35 no.4
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• pp.505-525
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• 2021

In this study, we investigated how multiplication by 2-digit numbers had been taught in elementary mathematics textbooks of Korea, Japan, Singapore, and USA. As a result of analysis, we found as follows. Korean textbooks do not teach the multiplication by 10 and the multiplication by power of 10, but Japanese, Singapore, and US textbooks explicitly teach related content. In the '×tens' teaching, Japanese and American textbooks teach formally the law of association of multiplication applied in the process of calculating the partial product of multiplication. The standard multiplication algorithm generally followed a standard method of recording partial product result according to the law of distribution, but the differences were confirmed in the multiplication model, the teaching method of the law of distribution, and the notation of the last digit '0'. Based upon these results, we suggested some proposals for improving the multiplication teaching.

• Education of Primary School Mathematics
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• v.22 no.3
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• pp.181-203
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• 2019

Even though the properties of operations in multiplication serve a fundamental basis of conceptual understanding the multiplication with whole numbers for elementary students, there has been lack of research in this field. Given this, the purpose of this study was to analyze instructional methods related to the properties of operations in multiplication (i.e., commutative property of multiplication, associative property of multiplication, distributive property of multiplication over addition) in a series of mathematics textbooks of Korea, Japan, and the US. The overall analysis was conducted in the following two aspects: (a) when and how to deal with the properties of multiplication in three instructional context (i.e., introduction, application, generalization), and (b) what models use to represent the properties of multiplication. The results of this showed that overall similarities in introducing the properties of multiplication .in (one digit) ${\times}$ (one digit) as well as emphasizing the divers representation. However, subtle but meaningful differences were analyzed in applying and generalizing the properties of multiplication. Based on these results, this paper closes with some implications on how to teach the properties of operations in multiplication properties in elementary mathematics.

• Proceedings of the Korea Water Resources Association Conference
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• 2023.05a
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• pp.103-103
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• 2023

질량 및 에너지 보존 법칙은 수문현상을 포함한 자연 현상의 기본 법칙이다. 유역에서 물의 질량 보존은 강수량 P가 유출량 Q, 증발산량 E, 그리고 육역저수량변화 ΔS로 분할되는 것(P=Q+E+ΔS)을 의미하며 열 에너지 보존은 순복사에너지 R_n이 잠열 λE, 현열 H, 그리고 지열 G로 분할되는 것(R_n=λE+H+G)을 의미한다. 유역에서 물과 에너지의 분배 과정은 E로 연결되어 있으며 이 두 과정을 포괄적으로 이해하는 것은 기후 및 지표환경의 변화를 예측하고 대비하는데 중요하다. 이 연구에서는 미국 전역의 400여개 유역에 대한 정보를 제공하는 Model Parameter Estimation Project(MOPEX) 데이터를 이용하여 유역의 기후 조건에 따라 물과 에너지의 분배가 어떻게 달라지는지 Budyko 평면에서 분석했다. 장기간에 대해 ΔS와 G는 무시할 수 있다는 가정하에 건조한 유역일수록 P, Q, 그리고 E 모두 작게 나타나는데 P와 Q의 감소폭이 훨씬 크기 때문에 E의 P에 대한 비는 크게 나타났다. 또한 건조한 유역일수록 E는 작고 R_n이 크기 때문에 H가 크게 나타났으며 H가 큰 유역일 수록 유역의 최대 기온과 최저 기온의 차이가 크게 나타났다. 이러한 변화는 동일한 유역내에서 물과 에너지 분배의 시간적 변화로도 나타나고 있다.