• The Mathematical Education
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• v.47 no.4
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• pp.519-543
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• 2008

The study has been conducted with 29 children from 4th to 6th grades to realize how they understand addition, subtraction, multiplication, and division of whole numbers, and how their understanding influences solving of one-step word problems. Children's understanding of operations was categorized into "adding" and "combination" for additions, "taking away" and "comparison" for subtractions, "equal groups," "rectangular arrange," "ratio," and "Cartesian product" for multiplications, and "sharing," "measuring," "comparison," "ratio," "multiplicative inverse," and "repeated subtraction" for divisions. Overall, additions were mostly understood additions as "adding"(86.2%), subtractions as "taking away"(86.2%), multiplications as "equal groups"(100%), and divisions as "sharing"(82.8%). This result consisted with the Fischbein's intuitive models except for additions. Most children tended to solve the word problems based on their conceptual structure of the four arithmetic operations. Even though their conceptual structure of arithmetic operations helps to better solve problems, this tendency resulted in wrong solutions when problem situations were not related to their conceptual structure. Children in the same category of understanding for each operations showed some common features while solving the word problems. As children's understanding of operations significantly influences their solutions to word problems, they needs to be exposed to many different problem situations of the four arithmetic operations. Furthermore, the focus of teaching needs to be the meaning of each operations rather than computational algorithm.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.28 no.2A
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• pp.80-85
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• 2003

This paper proposes Galois Field Arithmetic Unit(GFAU) whose structure does addition, multiplication and division in GF(2m). GFAU can execute maximum two additions, or two multiplications, or one addition and one multiplication. The base architecture of this GFAU is a divider based on modified Euclid's algorithm. The divider was modified to enable multiplication and addition, and the modified divider with the control logic became GFAU. The GFAU for GF(2193) was implemented with Verilog HDL with top-down methodology, and it was improved and verified by a cycle-based simulator written in C-language. The verified model was synthesized with Samsung 0.35um, 3.3V CMOS standard cell library, and it operates at 104.7MHz in the worst case of 3.0V, 85$^{\circ}C$, and it has about 25,889 gates.

• The KIPS Transactions:PartC
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• v.16C no.2
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• pp.199-208
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• 2009

Recently,IP-based broadcasting systems,such as Mobile-TV and IP-TV, have been widely deployed. These systems require a security system to allow only authorized subscribers access to broadcasting services. We analyzed the Conditional Access System, which is a security system used in the IP-based Pay-TV systems. A weakness of the system is that it does not scale well when the system experiences frequent membership changes. In this paper, we propose a group key distribution protocol which overcomes the scalability problem by reducing communication and computation overheads without loss of security strength. Our experimental results show that computation delay of the proposed protocol is smaller than one of the Conditional Access System. This is attributed to the fact that the proposed protocol replaces expensive encryption and decryption with relatively inexpensive arithmetic operations. In addition, the proposed protocol can help to set up a secure channel between a server and a client with the minimum additional overhead.

• Education of Primary School Mathematics
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• v.26 no.2
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• pp.83-97
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• 2023

Nominalization is one of the grammatical metaphors that makes it easier to mathematize the target that needs to be converted into a formula, but it has the disadvantage of making problem understanding difficult due to complex and compressed sentence structures. To investigate how this nominalization affects students' problem-solving processes, an analysis was conducted on 233 third-grade elementary school students' problem solving of eight arithmetic word problems with or without nominalization. The analysis showed that the presence or absence of nominalization did not have a significant impact on their problem understanding and their ability to convert sentences to formulas. Although the students did not have any prior experience in nominalization, they restructured the sentences by using nominalization or agnation in the problem understanding stage. When the types of nominalization change, the rate of setting the formula correctly appeared high. Through this, the use of nominalization can be a pedagogical strategy for solving word problems and can be expected to help facilitate deeper understanding.

• Journal of Elementary Mathematics Education in Korea
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• v.10 no.2
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• pp.221-242
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• 2006

For teaching division more effectively, it is necessary to know students' informal knowledge before they learned formal knowledge about division. The purpose of this study is to research students' informal knowledge of division and to analyze meaningful suggestions to link formal knowledge of division in elementary school mathematics. According to this purpose, two research questions were set up as follows: (1) What is the students' informal knowledge before they learned formal knowledge about division in elementary school mathematics? (2) What is the difference of thinking strategies between students who have learned formal knowledge and students who have not learned formal knowledge? The conclusions are as follows: First, informal knowledge of division of natural numbers used by grade 1 and 2 varies from using concrete materials to formal operations. Second, students learning formal knowledge do not use so various strategies because of limited problem solving methods by formal knowledge. Third, acquisition of algorithm is not a prior condition for solving problems. Fourth, it is necessary that formal knowledge is connected to informal knowledge when teaching mathematics. Fifth, it is necessary to teach not only algorithms but also various strategies in the area of number and operation.

• School Mathematics
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• v.10 no.3
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• pp.357-374
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• 2008

The complex number system is supposed to introduce first chapter in the first grade of high school. When number system is expanded to complex numbers, the main aim is to understand preservation of algebraic structure with regard to the flow of curriculum and textbook. This research reviewed overall alternative articulation and treatment of textbooks from a logical viewpoint. Two research questions are developed below. First, in the structure of the current curriculum, when we consider student's 'level', how are the alternative articulation and treatment of textbooks in complex unit on a logical point of view? Second, What are more logical alternative articulation and treatment? What alternative articulation and treatment are suitable for a running goal? and what are the improvement which is definitive?

• Education of Primary School Mathematics
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• v.21 no.3
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• pp.289-307
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• 2018

Although mixed calculation of natural numbers is important in that it completes arithmetic calculation of natural numbers in elementary school, few studies have been conducted regarding its instruction methods. Given this, this study analyzed Korean mathematics textbooks (from the fifth textbooks to the 2009 revised textbooks) along with Japanese and Singaporean textbooks in terms of the parentheses and the order of operations regarding mixed calculation of natural numbers. The results of this study showed that there were differences in introducing the parentheses and representing them in an explicit way per textbooks. In the Korean textbooks, the order of operations was presented mostly with the real-life contexts but it was not always in a diagrammatic representation. In contrast, in the Singaporean textbooks, the order of operations was presented without the real-life contexts and the use of calculators was emphasized. In the Japanese textbooks, the order of operations was presented with the real-life contexts and a hierarchy of operations was emphasized. Based on these results, this study suggested several implications of textbook development and instructional methods regarding mixed calculations of natural numbers.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.10 no.12
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• pp.3702-3707
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• 2009

In this paper, a new approximated MAP algorithm for soft bit decision from QAM symbols is proposed for Gray Coded QAM signals, based on the Max-Log-MAP and a Gray coded QAM signal can be separated into independent two Gray coded PAM signal, M-PAM on I axis with M symbols and N-PAM on Q axis with N symbols. The Max-Log-MAP used distance comparisons between symbols to get the soft bit decision instead of mathematical exponential or logarithm functions. But in accordance with the increase of the number of symbols, the number of comparisons also increase with high complexity. The proposed algorithm is used with the Euclidean distance and constituted with plain arithmetic functions, thus we can know intuitively that the algorithm has low implementing complexity comparing to conventional ones.

• Science of Emotion and Sensibility
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• v.14 no.3
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• pp.395-402
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• 2011

As the consumer market for odor products grows, companies producing healthcare products are beginning to pay more attention to the emotional aspect of an odor product in order to differentiate their products from competitors. In the following research, the affective effect of odor product was investigated while focusing on relaxation and working contexts using orange and pine scents, since these are typical odors in current domestic market. Two empirical studies were carried out. First, in experiment I, 18 subjects, all of whom were university students, spent 20 minutes sitting comfortably on a sofa while electrocardiogram assessments were made. After a five-minute break, in experiment II, the same subjects were provided with both arithmetic and geometric questions and their electroencephalogram readings was recorded from eight channels. All subjects participated in three sessions - no odor, an orange scent, and then a pine scent - with a minimum time interval of 24 hours. The results show that in the context of a pine scent, both the activation ratio of subjects' parasympathetic system and those of the Sensory Motor Rhythm waves and Mid Beta waves were at the highest peak. Therefore, the pine scent helped the subjects to feel more comfortable and more focused at the same time. In other words, it gave them a state of meditated attention. In addition, it was found that the right brain was activated twice the intensity when the subjects worked through the geometric questions, whereas both sides of the brain were activated in equal magnitude during the process of arithmetic tasks. This replicates previous studies of the functional aspect of the right brain - being responsible for spatial and creative thinking.

• Journal of Gifted/Talented Education
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• v.24 no.1
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• pp.17-43
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• 2014

On the subjects of elementary 3rd grade three child prodigies who had learned the four fundamental arithmetic operations and primary concepts of fraction, this study conducted a qualitative case research to examine how they composed schema of addition and multiplication of fractions and transformed schema through recognition of precise concepts and linking of concepts with addition and multiplication of fractions as the contents. That is to say, this study investigates what schema and transformed schema child prodigies form through composition of primary mathematic concepts to succeed in relational understanding of addition and multiplication of fractions, how they use their own formed schema and transformed schema for themselves to approach solutions to problems with addition and multiplication of fractions, and how the subjects' concept formation and schema in their problem solving competence proceed to carry out transformations. As a result, we can tell that precise recognition of primary concepts, schema, and transformed schema work as crucial factors when addition of fractions is associated with multiplication of fractions, and then that the schema and transformed schema that result from the connection among primary mathematic concepts and the precise recognition of the primary concepts play more important roles than any other factors in creative problem solving with respect to addition and multiplication of fractions.