• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.26 no.3
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• pp.328-336
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• 2017

The exit surface of a lens is designed using a three-dimensional free-form expression in order to easily modify a curved surface. This enables the design of numerical values and mathematical things using three-dimensional free-form expression, and enhances precision because it can be fine-tuned via numerical control. The standard of "Classification of Luminaire Light Distribution" for outdoor lighting fixtures by IESNA is adopted in order to examine the correlation between three-dimensional free-form surface expression and lighting performance. The variation of light distribution type and range is analyzed using the values of maximum light intensity and 50% light intensity. The actual tolerance occurs owing to parameters such as the thickness of the lens, the distance between LEDs, and the movement of the center of the incident surface; the effects of changes in these parameters on the performance are compared and analyzed.

• Applied Science and Convergence Technology
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• v.25 no.6
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• pp.158-161
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• 2016

Debye temperature is an important thermodynamical factor in quantum dots (QDs); it can be used to determine the degree of homogeneity of a QD structure as well as to study the interdiffusion mechanism during growth. Direct estimation of the Debye temperature can be obtained using the Varshni relation. The Varshni relation is an empirical formula that can interpret the change of emission energy with temperature as a result of phonon interaction. On the other hand, phonons energy can be calculated using the Fan Expression. The Fan expression and Varshni relation are considered equivalent at a temperature higher than Debye temperature for InAs quantum dot. We investigated InAs quantum dot optically, the photoluminescence spectra and peak position dependency on temperature has been discussed. We applied a mathematical treatment using Fan expression, and the Varshni relation to obtain the Debye temperature and the phonon energy for InAs quantum dots sample. Debye temperature increase about double compared to bulk crystal. We concluded that the In/Ga interdiffusion during growth played a major role in altering the quantum dot thermodynamical parameters.

• Education of Primary School Mathematics
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• v.22 no.1
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• pp.65-82
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• 2019

In this study, students' multiplication expression method according to visual model was analyzed through paper test and eye tracking test. As a result of the paper-pencil test, students were presented with multiplication formula. In the group model (number of individual pieces in a group) ${\times}$ (number of group) in the array model (column) ${\times}$ (row), but in the array model, the proportion of students who answered the multiplication formula in the (row) ${\times}$ (column). From these results, we derived the appropriate model presentation method for multiplication instruction and the multiplication expression method for visual model.

• The Mathematical Education
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• v.56 no.1
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• pp.63-80
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• 2017

By analysing the examination papers from third grade high school students, we classified the errors occurred in the problem solving process of high school 'Geometry and Vectors' into several types. There are five main types - (A)Insufficient Content Knowledge, (B)Wrong Method, (C)Logical Invalidity, (D)Unskilled Expression and (E)Interference.. Type A and B lead to an incorrect answer, and type C and D cannot be distinguished by multiple-choice or closed answer questions. Some of these types are classified into subtypes - (B1)Incompletion, (B2)Omitted Condition, (B3)Incorrect Calculation, (C1)Non-reasoning, (C2)Insufficient Reasoning, (C3)Illogical Process, (D1)Arbitrary Symbol, (D2)Using a Character Without Explanation, (D3) Visual Dependence, (D4)Symbol Incorrectly Used, (D5)Ambiguous Expression. Based on the these types of errors, answers of each problem was analysed in detail, and proper ways to correct or prevent these errors were suggested case by case. When problems that were used in the periodical test were given again in descriptive forms, 67% of the students tried to answer, and 14% described flawlessly, despite that the percentage of correct answers were higher than 40% when given in multiple-choice form. 34% of the students who tried to answer have failed to have logical validity. 37% of the students who tried to answer didn't have enough skill to express. In lessons on curves of secondary degree, teachers should be aware of several issues. Students are easily confused between 'focus' and 'vertex', and between 'components of a vector' and 'coordinates of a point'. Students often use an undefined expression when mentioning a parallel translation. When using a character, students have to make sure to define it precisely, to prevent the students from making errors and to make them express in correct ways.

• East Asian mathematical journal
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• v.25 no.3
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• pp.321-341
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• 2009

The purpose of this study was to examine the effect of the manipulative materials in the Australian Maths 300 program by applying it to Korean Elementary Mathematics Education - based on parts of 'Probability and Statistics', and 'Symbol and Expression'. In order to this purpose, we select appropriate Maths 300's manipulate materials that could be used to obtain learning objectives within class time for each part, four lessons with the materials were taught at to third, fourth, and fifth grade students of elementary School. The effect of the teaching was analyzed by videotape and student opinion. The results of this study are the following: First, the manipulative tools were almost entirely lacking for the 'Probability and Statistics' section without a 'number of cases' unit. The tools presented in the 'Symbol and Expression' section were helpful in the games that were used for checking preceding learning. Second, the results of using the Math 300 manipulative materials in class showed that the students were eager to be involved in the activities using those materials and to find their own solutions in problem-solving questions that were suited to them; these led to them making their own questions. In response to questioning about the use of the manipulative materials, the students stated that it was easy and fun for them to use the manipulative materials, to solve the problems for themselves, and that they would like to continue practicing the activities in the future. Finally, Studies on the presentation of a variety of manipulative materials including those in this study that can used in problem-solving learning and other learning fields, and the methodology for the use of manipulative materials can be enhanced through further studies.

• Journal of the Korean School Mathematics Society
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• v.16 no.3
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• pp.561-582
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• 2013

Meanwhile, the meaning has been emphasized in mathematics. But the meaning of meaning had not been clearly defined and the meaning classification had not been reported. In this respect, the meaning was classified as expressive and cognitive. Furthermore, it was reclassified as mathematical situation and real situation. Based on this classification, we investigated how student recognizes the meaning when solving mathematical modeling problem. As a result, we found that the understanding of cognitive meaning in real situation is more difficult than that of the other meaning. And we knew that understanding the meaning in solving of equation, has more difficulty than in expression of equation. Thus, to help students understanding the meaning in the whole process of mathematical modeling, we have to connect real situation with mathematical situation. And this teaching method through unit and measurement, will be an alternative method for connecting real situation and mathematical situation.

• Journal of the Korean School Mathematics Society
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• v.19 no.1
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• pp.103-122
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• 2016

The purpose of this study was to analyze the sentences related with mathematical modeling in the third and fourth grade mathematics textbooks in accordance with changing of Korean mathematics curricula. In the preliminary analysis, the researchers used the criteria that Kim(2010) had analyzed Mathematics in Context[MiC], and analyzed South Korean textbooks from the perspective of mathematical modeling. The researchers revised them for the analysis criteria among South Korean elementary mathematics textbooks and employed them as the analysis framework of the present study. From the mathematical modeling perspective, the study reached the following conclusions in accordance with the change of textbooks from the 7th curriculum to the 2009 revised curriculum. The contexts of real-world situations presented in the textbooks are increased in all areas except Probability and Statistics areas, the methods of expression of mathematical model are diversified in all areas except Patterns area, and the communication types are also diversified and frequencies increased in all areas except Patterns area. Based on this research, several suggestions were made for the development of future textbooks.

• Journal of the Korean School Mathematics Society
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• v.17 no.2
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• pp.235-249
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• 2014

In this paper, teaching contents in area between Korea and Japan's first grade math textbooks are compared. Based on the results of this comparison, implications for improving our grade 1 math textbooks are obtained as follows. Firstly, when describing the configuration of two-digit numbers, it needs to be considered that, after the mathematical description of a concrete material representing two-digit numbers, then it should be processed mathematically. Secondly, with respect to the composition and decomposition of numbers, use of the expression of 'some number and some number' needs to be considered. Thirdly, when reading addition expression and subtraction expression with an equal sign, the way of reading them with terms 'sum' and 'difference' respectively needs to be reconsidered. Fourthly, use of the distinct expression for the supplementing situation and the merging situation respectively and use of the distinct expression for the removing situation and the comparing situation respectively need to be considered. Fifthly, the jump in representing the expression of subtraction of two numbers as the expression of the subtraction or mixed operation of three numbers to explain (some number)-(some number) with borrowing need to be resolved.

• Journal of Elementary Mathematics Education in Korea
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• v.15 no.1
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• pp.95-120
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• 2011

Modern society is the age of the information. As new information is springing up every day and pace of change becomes faster, the importance of communication skills is growing. The recent mathematics education is recognized as not a fragmentary mathematical knowledge or results of the learning, but a procedure of mathematical thinking, and the effective expression skill of their mathematical ideas and the ability to forward it to others are regarded very serious. As the method of mathematics evaluation, mathematical essay is introduced to replace the existing multiple-choice written test. This method assess the ability which students have, that express the reorganized knowledge and information according to given situation by themselves. Ultimately, it is expected to help that students get the higher order thinking skills such as logical thinking and creativity. However, definition of elementary mathematical essay is unclear, and proper teaching methods is lacking for each stage of elementary school students. Thus, in this paper, I have defined the concept of elementary mathematical essay and made a foundation of elementary mathematical essay research, then researched about the effective utilization of elementary mathematical essay using school education. Also elementary mathematical essay teaching-learning materials is developed and applied to analyzed the students' responses. Using this program, in real elementary school education, the implications has deduced.

• Communications of Mathematical Education
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• v.38 no.2
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• pp.187-213
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• 2024

This study aims to investigate the impact of mathematical journal writing activities on sixth-grade students' mathematics anxiety and the 'writing' aspect of mathematical communication. For this purpose, 27 sixth-grade students participated in 14 sessions of mathematical journal writing activities while learning division with fractions and decimals. Mathematics anxiety was measured using a questionnaire, with pre- and post-test results statistically analyzed. Mathematical communication in the 'writing' domain was quantitatively measured using an analytical framework to track changes in levels. Additionally, 13 students were interviewed to examine the impact of journal writing on mathematics anxiety and mathematical communication in more detail. The study found that among the four main factors of mathematics anxiety, there was a significant reduction in the subject-specific and environmental factors. The average levels of 'expression' and 'explanation' in the 'writing' domain of mathematical communication gradually increased, with specific teacher feedback supporting improvements in students' communication levels. Based on these findings, the study suggests implications for the use and guidance of mathematical journal writing activities in school settings.