• Structural Engineering and Mechanics
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• v.27 no.1
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• pp.63-75
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• 2007

The code provisions on lap splices are critically assessed in the light of 203 beams without transverse reinforcement and 278 beams with transverse reinforcement. For comparison, the provisions given in the ACI 318, Eurocode 2, and TS 500 Codes are considered. The ACI Committee 408 recommended provision and a new proposal are also taken into account throughout the assessment. The comparison with real beam tests where the splice region was subjected to constant moment indicates that current provisions in the Codes do not agree acceptably with test results. The steel stress prediction graphs calculated by means of the Code provisions show high scatter and remain unsafe especially for test data without transverse reinforcement. Both the recent recommended provision by ACI Committee 408 and a new design expression proposed by the author have much less scatter with fewer unsafe predictions. The simplified design provision proposed by ACI Committee 408 does not yield similar results to that of the advanced design provision proposed by the same committee and therefore it could conveniently be replaced with the simpler equation proposed by the author.

• East Asian mathematical journal
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• v.37 no.2
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• pp.265-288
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• 2021

In the 2015 revised mathematics curriculum, the system of equations is first introduced in 'Variables and Expressions' of [Middle School Grades 1-3]. Then, It is constructed that after learning the linear function in 'Functions', the relationship between the graphs of two linear functions and the systems of linear equations are learned so that students could improve the geometric representation of the systems of equations. However, in of Elective-Centered Curriculum Common Courses, Instruction is limited to algebraic manipulation when teaching and learning systems of quadratic equations. This paper presented the teaching and learning method that can improve students' mathematical connection through various representations by providing geometric representations in parallel using GeoGebra, a mathematics learning software, with algebraic solutions in the teaching and learning situation of simultaneous quadratic equations.

• Journal of applied mathematics & informatics
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• v.41 no.2
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• pp.287-293
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• 2023

In this paper, the Augmented graph Es(τ) of the inverse graph Gs(τ) of a cyclic group (τ,◦) was studied. The Augmented inverse graph was constructed by applying the method of Mycielski's construction. The dimension of Augmented inverse graph and different properties of the graph were investigated. Later the chromatic number of Augmented inverse graph was discussed and the relation between the maximum degree of the graph and the chromatic number was established. In the Mycielski's construction, the properties of the key node 'u' in Es (τ) were established based on cardinality of the cyclic group (τ,◦) and also proved that the Augmented inverse graph Es(τ) was a triangle free graph.

• Archives of Plastic Surgery
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• v.35 no.5
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• pp.514-520
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• 2008

Purpose: Many attempts have been made to describe ideal facial proportions for over two thousands year and constantly lasted till now. Dr. Marquardt has derived supposedly ideal facial proportions from the facial golden mask using golden ratio of 1 : 1.618. On the other hand, facial reducing surgeries such as mandible angle reduction are popularized in Asia because the width of mid and lower face of Korean is recognized to be wider. The purpose is to analyze characters of Korean university students' faces in horizontal plane and establish the objective data for facial width distributions and clinical applications. Methods: We applied the facial golden mask to the photographs in 1000 cases, compared the width of mid and lower face between the facial golden mask and Korean university students' faces. And we first calculated the horizontal ratio(HR) of middle and lower face each for using comparative scale of width, facial golden mask. We divided 1,000 cases into 3 groups by degrees of HR and analyzed data of HR on each groups. Using calculated horizontal ratio, we newly invented the cumulative frequency of distribution graphs in Korean university students' faces. Results: Mean data of HR were over 1.0 in all groups, which means that Korean university students' faces are typically wider than facial golden mask in horizontal planes. And this study was statistically significant(p- value < 0.05). Clinically using the cumulative frequency distributions of Korean university students' face width, we can easily explain changes of facial width to patient after facial reducing surgery and describe the changes into objective data. Conclusion: This study concludes thatKorean university students' faces are wider than facial golden mask is significantly true and the cumulative frequency of distribution graphs are expected to be widely used for comparison of results in facial reducing surgery.

• Journal of Educational Research in Mathematics
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• v.25 no.1
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• pp.1-19
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• 2015

This paper aims to explore what we can improve in the curriculum, teaching-learning, and evaluation on the bases of the analyses of multiple-choice items set in National Assessment of Educational Achievement. For this goal, by using the distribution curves of the responses percentages, we will grasp the features of educational achievement which appear to students through an in-depth analysis about not only item itself but also the contents included in particular distracters. These analyses provide more information than the descriptive statistical values such as the mean of correct answer percentage and the discrimination of whole group and the mean of responses percentages of replies of subgroups. Because the distribution curves of the responses percentages reveal the transition from the lowest to the highest educational achievement very well. From these analyses we acquire the implications about the concept of prime factor or prime factorization, ratio(proportion) such as velocity, linear function, volume of cone, properties of solid figure, and probabilities of empty event and total event.

• Journal of the Korean Chemical Society
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• v.66 no.3
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• pp.243-250
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• 2022

The purpose of this study was to investigate the inscription of North Korean Higher-Level Middle School 1 chemistry textbooks in the era of North Korean leader Kim Jong-un to understand North Korean chemistry education. The types and functions of inscription for each unit of the North Korean Higher-Level Middle School 1 Chemistry textbook were analyzed and compared with the inscription of the 'Chemistry I' textbook in South Korea. Inscriptions were analyzed by constructing an analysis frame based on previous studies. The analysis results were as follows. First, as for the types of inscription used in North Korean textbooks, photographs and illustrations were used the most, and graphs were used the least. Second, the functions of inscription used in North Korean textbooks had many exploratory and exemplary functions, and decorative functions were used the least. Third, there was no significant difference in type and function of textbook inscriptions from North and South Korea. The results of this study may be helpful in understanding North Korean chemistry education.

• Communications of Mathematical Education
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• v.30 no.2
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• pp.199-223
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• 2016

The purpose of this study is to investigate how first and second graders in middle school take in integrated understanding about the concept of function. The data was collected through the questionnaire conducted by the first and second-year students at A, B middle school in Cheongju. The questionnaire consisted of 14 questions related to the extent of understanding a concept of function, the ability to express function and to translate function. The results are summarized as follows. First, the percentage of correct answer made a difference according to the types of representation. Questions leading students to translate a task into a table or an equation showed quite high correct response rates. However, questions asking students to translate a task into graphs showed high incorrect responses. Second, the result shows that students have the different viewpoints depending on their grades when they have to determine whether the suggested situation belongs to function. The first-year students tended to consider function as the concept of 'definition'. On the other hand, the second-year students emphasized 'equation' of function. Finally, only a few students can distinguish the various situations and representations into the definition of function. This result shows that students didn't get the integrated understanding of the concept of function.

• The Mathematical Education
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• v.56 no.3
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• pp.281-300
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• 2017

This study analyzed the difficulties of middle school students in computer simulation of the law of large numbers through eye movement analysis. Some students did not attend to the simulation results and could not make meaningful inferences. It is observed that students keep the existing concept even though they observe the simulation results which are inconsistent with the misconceptions they have. Since probabilistic intuition influence student's thinking very strongly, it is necessary to design a task that allows students to clearly recognize the difference between their erroneous intuitions and simulation results. In addition, we could confirm through eye movements analysis that students could not make meaningful observations and inferences if too much reasoning was needed even though the simulation included a rich context. It is necessary to use visual representations such as graphs to provide immediate feedback to students, to encourage students to attend to the results in a certain intentional way to discover the underlying mathematical structure rather than simply presenting experimental data. Some students focused their attention on the visually salient feature of the experimental results and have made incorrect conclusion. The simulation should be designed so that the patterns of the experimental results that the student must discover are not visually distorted and allow the students to perform a sufficient number of simulations. Based on the results of this study, we suggested that cumulative relative frequency graph showing multiple results at the same time, and the term 'generally tends to get closer' should be used in learning of the law of large numbers. In addition, it was confirmed that eye-tracking method is a useful tool for analyzing interaction in technology-based probabilistic learning.

• Tunnel and Underground Space
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• v.7 no.2
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• pp.100-107
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• 1997

In case of a fire outbreak in a uni-directional road tunnel, the flow of traffic immediately behind the fire disaster will be stalled all the way back to the entrance of the tunnel. Furthermore, when the vehicle passengers try to flee away from the fire toward the entrance of the tunnel, the extremely hot fume that propagates in the same direction will be fatal to the multitudes evacuating, but may also cause damage to the ventilation equipments and the vehicles, compounding the evacuation process. This paper will present the 3-dimensional modelling analysis of the preventive measures of such a fume propagation in the same direction as the evacuating passengers. For the analysis, the fire hazard was assumed to be a perfect combustion of methane gas injected through the 1 m X 2 m nozzle in the middle of the tunnel, and the product of $CO_2$ as the indicator of the fume propagation. From the research results, when the fire hazard occurred in middle of the 400 m road tunnel, the air density decreased around the fire point, and the maximum temperatures were 996 K and 499 K at 210 m and 350 m locations, respectively, 60 seconds after fire disaster occurred, when the fumes were driven out only towards the exit-direction of the tunnel. By tracing the increase of $CO_2$ level over 1% mole fraction, the minimum longitudinal ventilation velocity was found to be 2.40 m/sec. Furthermore, through Analysis of the temperature distribution graphs, and observation of the cross-sectional distribution of $CO_2$ over 1% mole fraction, it was found that the fume did not mix with the air, but rather moved far in a laminar flow towards exit of the tunnel.

• Communications of Mathematical Education
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• v.27 no.2
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• pp.99-119
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• 2013

This study investigated the schemes to apply key competencies to middle school math teaching. Key competencies (KCs, hereafter), however, have been discussed only at the national-level general curriculum. Through the survey with mathematics educators, we selected key competencies that can be better developed through mathematics subject. We investigate ways to apply key competencies into math teaching and learning with the math-talented students who usually lack interpersonal skills and communication skills. Along with KC goals, we selected graphs (or graphing skills in math contents) as learning goals, and we designed and implemented competency-based instruction for the gifted. Through participant observation of math teaching and learning, we identified students' improvement in interpersonal skills and communication skills. We also identified students' skill development in other key competencies such as creativity, problem solving, information processing skills, etc., which can be developed through mathematics teaching and learning. Through this study, we found out that key competencies can be developed through mathematics teaching and we need in-depth studies on this matter.