• The Mathematical Education
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• v.62 no.1
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• pp.1-21
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• 2023

The purpose of this study is to explore how the student, who interiorized three levels of units, constructed fractions as multipliers by analyzing her ways of conceiving improper fractions with three levels of units and coordinating two three-levels-of-units structures. Among the data collected from our teaching experiment with two 4th grade students meeting 13 times for three months, we focus on how Seyeon, one of the participating students, wrote numerical expressions in the form of "× fraction" for the given situations using her splitting operation for composite units. Given the importance of splitting operation for composite units for the construction of fractions as multipliers, implications for further research are discussed.

• Education of Primary School Mathematics
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• v.23 no.2
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• pp.87-116
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• 2020

The purpose of this study is to explore how units-coordination ability is related to understanding fraction concepts. For this purpose, a teaching experiment was conducted with one fourth grade student, Eunseo for four months(2019.3. ~ 2019.6.). We analyzed in details how Eunseo's units-coordinating operations related to her understanding of fraction changed during the teaching experiment. At an early stage, Eunseo with a partitive fraction scheme recognized fractions as another kind of natural numbers by manipulating fractions within a two-levels-of-units structure. As she simultaneously recognized proper fraction and a referent whole unit as a multiple of the unit fraction, she became to distinguish fractions from natural numbers in manipulating proper fractions. Eunseo with a reversible partitive fraction scheme constructed a natural number greater than 1, as having an interiorized three-levels-of-units structure and established an improper fraction with three levels of units in activity. Based on the results of this study, conclusions and pedagogical implications were presented.

• The Mathematical Education
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• v.61 no.1
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• pp.1-28
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• 2022

The purpose of this study is to explore how students' fractional knowledge is related to their solving of proportion problems. To this end, 28 clinical interviews with four middle-grade students, each lasting about 30~50 minutes, were carried out from May 2021 to August 2021. The present study focuses on two 7th grade students who exhibited their ability to coordinate three levels of units prior to solving whole number problems. Although the students showed interiorization of three levels of units in solving whole number problems, how they coordinated three levels of units were different in solving proportion problems depending on whether the problems required reasoning with whole numbers or fractions. The students could coordinate three levels of units prior to solving the problems involving whole numbers, they coordinated three levels of units in activity for the problems involving fractions. In particular, the ways the two students employed partitioning operations and how they coordinated quantitative unit structures were different in solving proportion problems involving improper fractions. The study contributes to the field by adding empirical data corroborating the hypotheses that students' ability to transform one three levels of units structure into another one may not only be related to their interiorization of recursive partitioning operations, but it is an important foundation for their construction of splitting operations for composite units.

• School Mathematics
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• v.14 no.1
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• pp.45-64
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• 2012

The purpose of the present study was to investigate middle grades (Grade 5-7) mathematics teachers' knowledge of partitive fraction division. The data were derived from a part of 40-hour professional development course on fractions, decimals, and proportions with 13 in-service teachers. In this study, I attempted to develop a model of teachers' way of knowing partitive fraction division in terms of two knowledge components: knowledge of units and partitioning operations. As a result, teachers' capacities to deal with a sharing division problem situation where the dividend and the divisor were relatively prime differed with regard to the two components. Teachers who reasoned with only two levels of units were limited in that the two-level structure they used did not show how much of one unit one person would get whereas teachers with three levels of units indicated more flexibilities in solving processes.

• Journal of the Korean Society for Nondestructive Testing
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• v.32 no.6
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• pp.678-685
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• 2012

The objective of this study is to monitor the health status of harbor caissons which have potential foundation damage. To obtain the objective, the following approaches are performed. Firstly, a structural damage monitoring(SDM) method is designed for interlocked multiple-caisson structures. The SDM method utilizes the change in modal strain energy to monitor the foundation damage in a target caisson unit. Secondly, a finite element model of a caisson system which consists of three caisson units is established to verify the feasibility of the proposed method. In the finite element simulation, the caisson units are constrained each other by shear-key connections. The health status of the caisson system against various levels of foundation damage is monitored by measuring relative modal displacements between the adjacent caissons.

• Journal of Elementary Mathematics Education in Korea
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• v.23 no.3
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• pp.323-345
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• 2019

This study examines the introduction of fractions in the third grade mathematics textbooks focusing on stages of units coordination and suggests alternative activities to help students develop their understanding of fractions. As results, the sessions of introduction units in textbooks was well organized to allow students to construct more extensive fraction schemes (i.e., Part-whole fraction scheme → Partitive unit fraction scheme → Partitive fraction scheme). However, most of the activities in textbooks were related to stages 1 and 2 of units coordination. In particular, the operations and partitioning schemes (i.e., equi-partitioning and splitting schemes), which are key to the development of students' fraction knowledge, were not explicitly revealed. Fraction schemes also did not extend to the Iterative fraction scheme, which is central to the construction of improper fractions. Based on these results, this study is expected to provide implications for the introduction of fractions in textbooks focusing on stages of units coordination to teachers and textbook developers.

• Journal of the Korean School Mathematics Society
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• v.14 no.4
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• pp.477-490
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• 2011

The concept of pedagogical content knowledge (PCK) has been developed and expanded to identify essential components of mathematical knowledge for teaching (MKT) by Ball and her colleagues (2008). This study proposes an alternative perspective to view MKT focusing on key developmental understandings (KDUs) that carry through an instructional sequence, that are foundational for learning other ideas. In this study we provide constructive components of KDUs in fraction multiplication by focusing on the constructs of 'three-level-of-units structure' and 'recursive partitioning operation'. Expecially, our participating preservice elementary teacher, Jane, demonstrated that recursive partitioning operations with her length model played a significant role as a KDU in fraction multiplication.

• Journal of the Korea Institute of Building Construction
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• v.16 no.1
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• pp.87-96
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• 2016

More than half of Korea's urban population currently lives in multi-unit dwellings. This particular residence structure inevitably positions the living spaces of residents in close proximity to one another. Because of this proximity, the sounds of a particular household will transfer to other residents' units creating conflict between tenants. Efforts to alleviate this problem have been made in both the public and private sector. A prominent method of noise analysis between living units has been to make an actual sound measurement and obtain qualitative measurements from questionnaires. Although this method has been most widely used, such analysis requires a large amount of human effort and time. In addition, the questionnaire method fails to provide the objective information needed to accurately assess the noise situation. To overcome the inadequacies of this previous method, this study seeks to evaluate the applicability of an acoustic simulation method. Three types of living noises were analyzed to assess the noise levels passed between multi-unit dwellings. The acoustic simulation method was found to be more economical, efficient, and adaptable in information processing. The results of this study can be further applied to design and control living-noise through procedures such as acoustic absorption or space redesign.

• The Journal of Korean Academy of Prosthodontics
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• v.42 no.4
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• pp.425-442
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• 2004

Statement of problem: A difficulty in achieving a passive-fitting prosthesis can be overcome by individual crown restoation of multiple implants. But individualized crown has another difficulty in control of contact tightness and stress distribution. Purpose: This in vitro study is to evaluate the stress distribution and the magnitude in the supporting tissues around Endopore implants with different crown lengths, interproximal contact tightness, and the splinting effects. Material & methods: Three Endopore implants($4.1{\times}9mm$) were placed in the mandibular posterior edentulous area distal to the canine and photoelastic model was made with PL-2 resin(Measurements Group, Raleigh, USA). Restorations were fabricated in two crown lengths: 9, 13 mm. For non-splinted restorations, individual crowns were fabricated on three custom-milled titanium abutments. After the units were cemented, 4 levels of interproximal contact tightness were evaluated: open, ideal($8{\mu}m$ shim stock drags without tearing), medium($40{\mu}m$), and heavy($80{\mu}m$). For splinted restorations, 3-unit fixed partial dentures were fabricated. This study was examined under simulated non-loaded and loaded conditions(6.8 kg). Photoelastic stress analysis was carried out to measure the fringe order around the implant supporting structure. Results: 1. When restorations were not splinted, the more interproximal contact tightness was increased among the three implants, the more stress was shown in the cervical region of each implant. When crown length was increased, stresses tended to increase in the apex of implants but there were little differences in stress fringes. 2. When nonsplinted restorations were loaded on the first or third implant, stresses were increased in the apex and cervical region of loaded implant. Regardless of interproximal contact tightness level, stresses were not distributed among the three implants. But with tighter interproximal contact, stresses were increased in the cervical region of loaded first or third implant. 3. When the nonsplinted restorations were not loaded, there were little stresses on the supporting structure of implants, but low level stresses were shown in the splinted restorations even after sectioning and soldering. 4. With splinted restorations, there were little differences in stresses between different crown lengths. When splinted restorations were loaded, stresses were increased slightly on the loaded implant, but relatively even stress distribution occurred among the three implants. Conclusions: Splinting the crowns of adjacent implants is recommended for Endopore implants under the overloading situation.

• Journal of the Korean Society of Marine Environment & Safety
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• v.28 no.4
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• pp.601-609
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• 2022

Jack-up drilling rigs are mobile offshore platforms widely used in the offshore oil and gas exploration industry. These are independent, three-legged, self-elevating units with a cantilevered drilling facility for drilling and production. A typical jack-up rig includes a triangular hull, a tower derrick, a cantilever, a jackcase, living quarters and legs which comprise three-chord, open-truss, X-braced structure with a spudcan. Generally, jack-up rigs can only operate in water depths ranging from 130m to 170m. Recently, there has been an increasing demand for jack-up rigs for operating at deeper water levels and harsher environmental conditions such as waves, currents and wind loads. All static and dynamic loads are supported through legs in the jack-up mode. The most important issue by society is to secure the safety of the leg structure against collision that causes large instantaneous impact energy. In this study, nonlinear FE -analysis and verification of the requirement against collision for 35MJ recommended by DNV was performed using LS-Dyna software. The colliding ship used a 7,500ton of shore supply vessel, and five scenarios of collisions were selected. From the results, all conditions do not satisfy the class requirement of 35MJ. The loading conditions associated with chord collision are reasonable collision energy of 15M and brace collisions are 6MJ. Therefore, it can be confirmed that the identical collision criteria by DNV need to be modified based on collision scenarios and colliding members.