• Journal for History of Mathematics
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• v.26 no.1
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• pp.33-56
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• 2013

This is a literature study about the concept of 'Division into Equal Parts' in middle school geometry. First, we notice that the concept of the division into equal parts in middle school geometry is given in four themes, which are those of line segments, angles, arches and areas. Second, we investigate and analyse the historical backgrounds of these four kinds of divisions into equal parts. Third, the possibility of extension in terms of method and concept was researched. Through the result of this study, we suggest that it is desirable to use effective utility of history in mathematical teaching and learning in middle school.

• The Mathematical Education
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• v.50 no.3
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• pp.309-327
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• 2011

In this paper, we extended the division algorithm for the integers to the finite decimals. Though the remainder for the finite decimals is able to be defined as various ways, the remainder could be defined as 'the remained amount' which is the result of the division and as "the remainder" only if 'the remained amount' is decided uniquely by certain conditions. From the definition of "the remainder" for the finite decimal, it could be inferred that 'the division by equal part' and 'the division into equal parts' are proper for the division of the finite decimal concerned with the definition of "the remainder". The finite decimal, based on the unit of measure, seemed to make it possible for us to think "the remainder" both ways: 1" in the division by equal part when the quotient is the discrete amount, and 2" in the division into equal parts when the quotient is not only the discrete amount but also the continuous amount. In this division context, it could be said that the remainder for finite decimal must have the meaning of the justice and the completeness as well. The theorem of the division algorithm for the finite decimal could be accomplished, based on both the unit of measure of "the remainder", and those of the divisor and the dividend. In this paper, the meaning of the division algorithm for the finite decimal was investigated, it is concluded that this theory make it easy to find the remainder in the usual unit as well as in the unusual unit of measure.

• 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.

• Journal of Educational Research in Mathematics
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• v.21 no.1
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• pp.1-16
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• 2011

This study is to review division of whole numbers which is dealt in the revised elementary mathematics textbook and manual for teacher. The textbook and manual for teachers are most important documents to teach mathematics. And they are important to the would-be teachers who study the elementary mathematics with such documents. Therefore the textbook and manual for teachers should have no errors. But I found they have some errors and problems regarding division of whole numbers. In this paper, I discuss the problems and suggest the alternative plans.

• The Mathematical Education
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• v.50 no.3
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• pp.337-354
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• 2011

The purpose of the study was to investigate how students understand multiplication and division of fractions and how their understanding influences the solutions of fractional word problems. Thirteen students from 5th to 6th grades were involved in the study. Students' understanding of operations with fractions was categorized into "a part of the parts", "multiplicative comparison", "equal groups", "area of a rectangular", and "computational procedures of fractional multiplication (e.g., multiply the numerators and denominators separately)" for multiplications, and "sharing", "measuring", "multiplicative inverse", and "computational procedures of fractional division (e.g., multiply by the reciprocal)" for divisions. Most students understood multiplications as a situation of multiplicative comparison, and divisions as a situation of measuring. In addition, some students understood operations of fractions as computational procedures without associating these operations with the particular situations (e.g., equal groups, sharing). Most students tended to solve the word problems based on their semantic structure of these operations. Students with the same understanding of multiplication and division of fractions showed some commonalities during solving word problems. Particularly, some students who understood operations on fractions as computational procedures without assigning meanings could not solve word problems with fractions successfully compared to other students.

• Journal of Digital Convergence
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• v.14 no.9
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• pp.325-329
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• 2016

Facial authentication has the limelight because it has less resistance and it is hard to falsify among various biometric identification. The algorithm of facial authentication can bring about huge difference in accuracy and speed by the algorithm construction. Along with face-extracted data by tracing and extracting pupil, the thesis studied algorithm which extracts data to improve error rate and to accurately authenticate face. It detects face by cascade, selects as significant area, divides the facial area into 4 equal parts to save the coordinate of object. Also, to detect pupil from the eye, the binarization is conducted and it detects pupil by Hough conversion. The core coordinate of detected pupil is saved and calculated to conduct facial authentication through data matching. The thesis studied optimized facial authentication algorithm which accurately calculates facial data with pupil trace.

• Journal of the Korean Data and Information Science Society
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• v.28 no.2
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• pp.383-393
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• 2017

When we deal with grouped statistical data, it is desirable to use a calculation method that gives as close value to the true value of a statistic as possible. In this paper, we suggested a new method to calculate the quantiles of grouped data. The main idea of the suggested method is calculating the data values by partitioning the pentagons, that correspond to the class intervals in the frequency polygon drawn according to the histogram, into parts with equal area. We compared this method with existing methods through simulations using some datasets from introductory statistics textbooks. In the simulation study, we simulated as many data values as given in each class interval using the inverse transform method, on the basis of the distribution that has the shape given by the frequency polygon. Using the sum of squares of differences from quantiles of the simulated data as a criterion, the suggested method was found to have better performance than existing methods for almost all quartiles and deciles.

• Korean Journal of Heritage: History & Science
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• v.53 no.3
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• pp.80-109
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• 2020

The Sacheonwangsa Temple in Silla is an esoteric temple that was founded provisionally in 670, and was completed in 679. This study attempted to elucidate the planning method of the Sacheonwangsa Temple based on the results of research on excavations and investigations into its construction processes and construction measures thereof. The research results are as follows. (1) In the site construction, assuming the size of one Bang (坊) on the south of Nangsan Mountain, after dividing the north-south width into three equal parts, there is a possibility that two of these parts were set to the flat portion. (2) In the 'Jochang (祖創, 670)', it is estimated that an area of 300 cheoks by 300 cheoks was postulated on the flat surface, and, as an initial conception, the mandala's plane design of the outer square 2 hasta (3 cheoks) and inner square 1 hasta (1.5 cheoks) was originally devised for the setting of 'Mudra (神印)', and an area 100 times greater has been set as the basis in the scale and layout planning of the central block. (3) During 'Gaechang (攺刱, ~679)', it is judged that because of the narrowness of the distance between the Pagoda and Geumdang Hall, which occurs when the center of the Geumdang Hall coincides with the center of 'the first stage of the foundation (先築基壇)', the scale and layout planning were adjusted from the initial conception. (4) The arrangement of the building was determined by dividing the fixed size of the central block (280 cheoks by 320 cheoks). Specifically, the east-west direction is set on the quartile's line of the east-west width of the central block, and in contrast, the north-south direction is based on the structural characteristics of the central block. It is presumed that the position of the transept was determined through the division and adjustment of the column spacing of the east-west corridor, then the Geumdang Hall and Altar were based on this. (5) The scale of the Geumdang Hall and Pagoda is determined by the petition of the division by the unit fraction starting from the quartile's line of the central block's east-west width. This planning is understood to be based on the self-similarity, which is rooted in the mandala's plane design as the model.

• Journal of Animal Science and Technology
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• v.64 no.1
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• pp.23-37
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• 2022

Thirty-six weaned piglets with an initial body weight (BW) of 8.43 ± 0.40 kg (28 days of age, ([Landrace × Yorkshire] × Duroc) were randomly assigned to 6 treatments for a 2-week feeding trial to determine the effects of different inorganic zinc (IZ), organic zinc (OZ) or combination of low crude protein diet (LP) and Mixed feed additive (MFA) on diarrhea score, nutrient digestibility, zinc utilization, blood profiles, organ weight, and fecal microflora in weaned piglet diet. The pigs were individually placed in 45 × 55 × 45 cm stainless steel metabolism cages in an environmentally controlled room (30 ± 1℃). The dietary treatments included a negative control (NC), positive control (PC; zinc oxide, 1,000 mg/kg), T1 (IZ : OZ, 850 : 150), T2 (IZ : OZ 700 : 300), T3 (IZ : OZ, 500 : 500), and T4 (LP + MFA [0.1% Essential oils + 0.08% Protease + 0.02% Xylanase]). The daily feed allowance was adjusted to 2.7 times the maintenance requirement for digestible energy (2.7 × 110 kcal of DE/kg BW^0.75). This allowance was divided into two equal parts, and the piglets were fed at 08 : 30 and 17 : 30 each day. Water was provided ad libitum through a drinking nipple. The diarrhea score was significantly increased (p < 0.05) in NC treatment compared with other treatments. The apparent total tract digestibility (ATTD) of dry matter (DM), nitrogen (N), and gross energy (GE) was significantly increased (p < 0.05) in the T2 treatment compared with the PC and NC treatments in week 1. In week 2, the ATTD of DM, N, and GE was significantly decreased (p < 0.05) in the NC treatment compared with other treatments. The T3 treatment had significantly higher (p < 0.05) ATTD and apparent ileal digestibility of zinc than the PC and T1 treatments. The Escherichia coli count in feces was significantly decreased in the T4 treatment compared with the NC and T2 treatments. The Lactobacillus count in feces was significantly increased in the T4 and T1 treatment compared with the T2 and T3 treatments. In conclusion, IZ : OZ 500 : 500 levels could improve nutrient digestibility and zinc utilization in weaned piglets, Moreover, MFA in LP diets could be used as a zinc alternative.

• Journal of Bio-Environment Control
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• v.28 no.4
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• pp.342-351
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• 2019

The optimum N concentrations incorporated as pre-planting nutrient charge fertilizer were determined for seedling raising using cylindrical paper pots. A root medium was formulated by blending of peat moss (particles smaller than 2.84 mm were 80-90%) and perlite (1 to 3 mm) with the ratio of 7:3 (v/v). The treatment N concentrations incorporated during the root medium formulation were adjusted to 0, 150, 250, 500, and $750mg{\cdot}L^{-1}$ and the concentrations of essential nutrients except N were equal in all treatments. After making of paper pots and putting into the 40-cell tray, the seeds of Chinese cabbage ('Chunmyeong Bom Baechu') and pak-choi ('Hanog cheonggyeongchae') were sown. During the raising of seedlings, weekly analysis of medium pH, EC and concentrations of inorganic elements were conducted. After 21 and 20 days after seed sowing of Chinese cabbage and pak-choi, the growth of the above-ground parts were measured and contents of inorganic elements in the plant tissues were analyzed. During the growing period, pH of the root media rose gradually and the EC decreased rapidly at week 3. The pH of root media at harvest was in the range of 5.3 to 5.9 in Chinese cabbage and 4.93 to 5.39 in pak-choi. Growth of the aboveground parts in terms of fresh and dry weight in both the plants were the highest in the $250mg{\cdot}L^{-1}$ N treatment and the lowest in the control treatment. The elevation of pre-planting N concentrations in root medium resulted in the increase of tissue N content and decrease of P, Ca, and Mg contents. The regression equation derived from the influence of varied pre-planting N concentrations on dry weight of above-ground tissue were $y=-0.0036x^2+0.0021x+0.0635$ ($R^2=0.9826$) in Chinese cabbage and $y=-0.16x^2+0.0009x+0.032$ ($R^2=0.991$) in pak-choi. When the low critical concentration of pre-plant N is taken at the point where dry weight of above-ground tissue is 10% less than maximum (0.40 g in Chinese cabbage and 0.16 g in pak-choi), those point are 0.36 g and 0.144 g per plant in Chinese cabbage and pak-choi, respectively. The lower critical N concentrations of root media calculated from the regression equations are $196mg{\cdot}L^{-1}$ for Chinese cabbage and $187mg{\cdot}L^{-1}$ for pak-choi. These results indicate that optimum pre-plant N concentrations for seedling raising using paper pots are in the range of 196 to $250mg{\cdot}L^{-1}$ for Chinese cabbage and 187 to $250mg{\cdot}L^{-1}$ for pak-choi.