• Journal of Elementary Mathematics Education in Korea
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• v.22 no.4
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• pp.369-384
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• 2018

Multiplication is able to be described by using repeated addition, a Cartesian product, a scalar operation, rectangular array and area in many various context. Multiplication in various problem situations is learned by various of the teaching method and the order of teaching more than any other mathematical concepts and operations in elementary school. Nevertheless, the context of multiplication leaves further room for improvement. The purpose of this study is to examine the similarities and differences between the conceptual aspects of multiplication through the literature and to analyze the appropriateness of the teaching method and the order of teaching through textbook analysis. As a result of the study, it was found that multiplication of a scalar operation was introduced too early and did not properly reflect of meaning of multiplication as a scalar operation. There is also a need to use the concept of the rectangular array or area as a meaning of multiplication two quantities.

• School Mathematics
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• v.11 no.1
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• pp.17-37
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• 2009

Concept and model of multiplication is not single. Concepts of multiplication can be classified into three cases: repeated addition, times idea, pairs set. Models of multiplication can be classified into four cases: measurement, rectangular pattern, combinatorial problem, number line. Among diverse cases of multiplication's concept and model, which case does elementary mathematics education lay stress on? This question is a controvertible didactical point. In this thesis, (1) mathematical and didactical analysis of multiplication's concept and model is performed, (2) a concrete program of teaching multiplication which is based on times idea is contrived, (3) With this new program, the teaching experiment is performed and its result is analyzed. Through this study, I obtained the following results and suggestions. First, the degree of testee's understanding of times idea is not high. Secondly, a sort of test problem which asks the testee to find times value is more easy than the one to find multiplicative resulting value. Thirdly, combinatorial problem can be handled as an application of multiplication. Fourthly, the degree of testee's understanding of repeated addition is high. In conclusion, I observe the fact that this new program which is based on times idea could be a alternative program of teaching multiplication which could complement the traditional method.

• Geotechnical Engineering
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• v.11 no.3
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• pp.37-42
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• 1995

The laboratory hydraulic conducti vita tests with rigid wall permeameter were performed to study the effects of waste leachate on the permeability of a marine clay. The marine clay and waste leachate for this study were sampled from Kimpo Wastefills, and the hydraulic gradients applied to the clay specimens aTe relatively high from 37.5 to 225. The test results show that the permeability of a marine clay is increased with increasing the concentration of leachate and with decreasing the hydraulic gradient. And also both the liquid limit and the plasticity index of the marine clay miRed with waste leachate decrease with increasing the concentration of leachate.

• Journal of Elementary Mathematics Education in Korea
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• v.20 no.2
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• pp.283-309
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• 2016

The purpose of this study is to investigate gifted students in elementary mathematics how they understand of situations involving multiplication and concepts of multiplication. For this purpose, first, this study analyzed the teacher's guidebooks about introducing the concept of multiplication in elementary school. Second, we analyzed multiplication problems that gifted students posed. Third, we interviewed gifted students to research how they understand the concepts of multiplication. The result of this study can be summarized as follows: First, the concept of multiplication was introduced by repeated addition and times idea in elementary school. Since the 2007 revised curriculum, it was introduced based on times idea. Second, gifted students mainly posed situations of repeated addition. Also many gifted students understand the multiplication as only repeated addition and have poor understanding about times idea and pairs set.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.41 no.10
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• pp.51-56
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• 2004

We propose and fabricate an 1${\times}$2 asymmetric optical switch by TOE using SOI wafer based on silicon which has very large TOE figure and it is a good material for optical devices. SOI wafer consists of 3 layers; upper Si layer for device(waveguide;core, n=3.5), buried oxide layer for insulator(clad, n=1.5) and Si substrate layer. We designed 1${\times}$2 asymmetric y-branched single mode optical waveguide switch by BPM simulation and metal heater by heat transfer simulation. Fabricated switch shows about 3.5 watts of power consumption and over 20dB of crosstalk between output channels.

• Journal of Elementary Mathematics Education in Korea
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• v.19 no.4
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• pp.501-525
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• 2015

This study analyzes arithmetic word problem of multiplication and division in the mathematics textbooks and workbooks of 3rd grade in elementary school according to 2009 revised curriculum. And we analyzes type of the problem solving ability which 4th graders prefer in the course of arithmetic word problem solving and the problem solving ability as per the type in order to seek efficient teaching methods on arithmetic word problem solving of students. First, in the mathematics textbook and workbook of 3rd grade, arithmetic word problem of multiplication and division suggested various things such as thought opening, activities, finish, and let's check. As per the semantic element, multiplication was classified into 5 types of cumulated addition of same number, rate, comparison, arrayal and combination while division was classified into 2 types of division into equal parts and division by equal part. According to result of analysis, the type of cumulated addition of same number was the most one for multiplication while 2 types of division into equal parts and division by equal part were evenly spread in division. Second, according to 1st test result of arithmetic word problem solving ability in the element of arithmetic operation meaning, 4th grade showed type of cumulated addition of same number as the highest correct answer ratio for multiplication. As for division, 4th grade showed 90% correct answer ratio in 4 questionnaires out of 5 questionnaires. And 2nd test showed arithmetic word problem solving ability in the element of arithmetic operation construction, as for multiplication and division, correct answer ratio was higher in the case that 4th grade students did not know the result than the case they did not know changed amount or initial amount. This was because the case of asking the result was suggested in the mathematics textbook and workbook and therefore, it was difficult for students to understand such questions as changed amount or initial amount which they did not see frequently. Therefore, it is required for students to experience more varied types of problems so that they can more easily recognize problems seen from a textbook and then, improve their understanding of problems and problem solving ability.

• The Journal of the Petrological Society of Korea
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• v.6 no.3
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• pp.244-244
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• 1997

The Janggunbong area(this study area) at the central-south part in the North Sobaegsan Massif, Korea, consists mainly of Precambrian(Wonnam and Yulri Formations)-Paleozoic [Joseon Supergroup(Jangsan Quarzite, Dueumri Formation and Janggum Limestone) and Pyeongan Group(Jaesan and Dongsugok Formations)] metasedimentary rocks and Mesozoic granitoid(Chunyang granite.) This study is to interpret geological structure of the North Sobaegsan Massif in the Jang-gunbong area by analysing rock-structure and microstructure of the constituent rocks. It indicates that its geological structure was formed at least by four phases of deformation after the formation of gneissosity(S0) in the Wonnam Formation and bedding plane(S0) in the Paleozoic metasedimentary rocks. The first phase deformation(D1) formed tight isoclinal fold(F1). Its axial plane(S1) strikes east-west and steeply dips north. Its axis (L1) subhorizontally plunges east-west. The second phase deformation(D2), which was related to ductile shear deformation, formed stretching lineation(L2) and shear foliation(S2). The sense of the shear movement indicates dextral strike-slip shearing(top-to-the east shearing). The third phase deformation(D3) formed open inclined fold(F3). Its axial plane(S3) strikes east-west and moderately or gently dips north. Its axis(L3) subhorizontally plunges east-west. The F3 fold reoriented the original north-dipping S1 foliation and D2 shear sense into south-dipping S1 foliation(top-to-the west shear sense on this foliation) at its a limb. The four phase of deformation(D4) formed asymmetric-type open inclined fold(F4) of NE-vergence with NW striking axial plane(S4) and NW-NNW plunging axis(L4). The F4 fold partly reoriented pre-D4 structural elements with east-west trend into those with north-south trend. Such reorientation is recognized mainly in the Paleozoic metasedimentary rocks.

• The Journal of the Petrological Society of Korea
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• v.6 no.3
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• pp.224-259
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• 1997

The Janggunbong area(this study area) at the central-south part in the North Sobaegsan Massif, Korea, consists mainly of Precambrian(Wonnam and Yulri Formations)-Paleozoic [Joseon Supergroupuangsan Quarzite, Dueumri Formation and Janggun Limestone) and Pyeongan Group (Jaesan and Dongsugok Formations)l metasedimentary rocks and Mesozoic granitoid(Chunyang granite). This study is to interpret geological structure of the North Sobaegsan Massif in the Janggunbong area by analysing rock-structure and microstructure of the constituent rocks. It indicates that its geological structure was formed at least by four phases of deformation after the formation of gneissosity(S0) in the Wonnam Formation and bedding plane(S0) in the Paleozoic metasedimentary rocks. The first phase deformation(D1) formed tight isoclinal fold(F1). Its axial plane(S1) strikes east-west and steeply dips north. Its axis(L1) subhorizontally plunges east-west. The second phase deformation(D2), which was related to ductile shear deformation, formed stretching lineation(L2) and shear foliation(S2). The sense of the shear movement indicates dextral strike-slip shearing(topto-the east shearing). The third phase deformation(D3) formed open inclined fold(F3). Its axial plane(S3) strikes east-west and moderately or gently dips north. Its axis(L3) subhorizontally plunges east-west. The F3 fold reoriented the original north-dipping S1 foliation and D2 shear sense into south-dipping S1 foliation(top-to-the west shear sense on this foliation) at its a limb. The four phase of deformation(D4) formed asymmetric-type open inclined fold(F4) of NE-vergence with NW striking axial plane(%) and NW-NNW plunging axis(L4). The F4 fold partly reoriented pre-D4 structural elements with east-west trend into those with north-south trend. Such reorientaion is recognized mainly in the Paleozoic metasedimentary rocks.