• Journal of Educational Research in Mathematics
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• v.22 no.4
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• pp.477-494
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• 2012

This study is to review the content organization and developmental ways of the unit on the mixed calculations and explore the alternatives on the basis of students' responsive examples and error patterns with relation to the mixed calculations, mnemonics of PEMDAS and historical context with relation to the order of operations. Then I analyzed the textbook and manual for teachers of the unit of mixed calculations of fourth grade and improvement about teaching the mixed calculations. First, I pointed out illogical connection between practical problem and rules of order of operations. Second, I suggested constructing a textbook by considering conventional character of order of operations. Third, I pointed out the importance of structural understanding of an expression of mixed calculations and various strategies with relation to teaching and learning. This study is suggestive for textbook development of the mixed calculations.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.39 no.6
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• pp.26-33
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• 2002

In this paper, a new four-quadrant MOS analog multiplier Is proposed using the quarter-square technique, which is based on the quadratic characteristics of MOS transistor operating in the saturation region and the difference operation of a source-coupled differential circuits. The proposed circuit has been fabricated in a p-well CMOS process. The multiplier achieves a total harmonic distortion of less than 1 percent for the both input ranges of 50 percent of power supply, a -3㏈ bandwidth of 30㎒ a dynamic range of 81㏈ and a power consumption of 40㎽. The active chip area is 0.54㎟. The supposed multiplier circuit is simple and adjust high frequency application because one input signal transfer output by one transistor.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.32 no.8C
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• pp.712-719
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• 2007

In this paper, we propose a new, effective, fast motion estimation algorithms using $4{\times}4$ pixels Hadamard transform. The Hadamard transform has the advantage of simplicity because it uses only addition and subtraction. Motion estimation is composed of three stages. First, it should be decided whether to terminate the search early and use a previous motion vector with DC(Direct Current) coefficients. Then the adaptive matching scan order for motion estimation should be determined according to the image complexity using AC(Alternating Current) coefficients. Experimentally, we adapted this algorithms to MVFAST and PMVFAST algorithms, and the proposed algorithms turn out to be very efficient in terms of computational speed while remaining almost the same in terms of PSNR(Peak Signal-to-Noise Ratio) compared to MVFAST and PMVFAST algorithms.

• 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.

• Journal of Educational Research in Mathematics
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• v.20 no.4
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• pp.445-458
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• 2010

This study intends to investigate the process of the development of quantity concept and how to deal with the quantity calculus in elementary school, and to find out the implication for improving the curriculum and mathematics textbooks of Korea. There had been the binary Greek categories of discrete number and continuous magnitude in quantity concept, but by the Stevin's introduction of decimal, the unification of these notions became complete. As a result of analyzing of the curriculum and mathematics textbooks of Korea, there is a tendency to disregard the teaching of quantity and its calculus compared to the other countries. Especially multiplication and division of quantity is seldom treated in elementary mathematics textbooks. So these should be reconsidered in order to seek the direction for improvement of mathematic teaching. And Korea's textbooks need the emphasis on the quantity calculus and on constructing quantity concept.

• Journal of Elementary Mathematics Education in Korea
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• v.19 no.4
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• pp.563-588
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• 2015

In elementary school, didactical transposition is inevitable due to several reasons. In mathematics, addition and multiplication are taught as binary operations, subtraction and division are taught as unary operations. But in elementary school, we try to teach all the four operations as binary operations by didactical transposition. In 'Mastering' the concepts of the four operations, the way of concept introduction is dealt importantantly. So it is different from understanding the four operations. In this study, we analyzed the four operations of natural numbers and fractions from two perspectives: concept understanding (how to introduce concepts and how to choose an operation) and connection between the operations. As a result, following implications were obtained. In division of fractions, students attempted a connection with multiplication of fractions right away without choosing an operation, based on the situation. Also, to understand division of fractions itself, integrate division of fractions presented from the second semester of the fifth grade to the first semester of the sixth grade are needed. In addition, this result can be useful in the future textbook development.

• Journal of Elementary Mathematics Education in Korea
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• v.14 no.3
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• pp.807-825
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• 2010

Educational interest has been paid to ADHD students. Because of being easily distracted, lacking concentration, and committing hyperactive acts, they lag much behind other students in academic grades and their teachers have many difficulties in teaching them. This study aims to provide a case of enhancing an ADHD student's fraction-related achievement. To do this, we investigated his mathematical abilities in a preliminary study, devised an individualized teaching for the fractions unit, and applied them to him. And analyzing the results from observations and interviews of the student we can induce the following results: First, the ADHD student showed such types of errors in relation to fraction as lack of the concept of dividing into equal parts, lack of the concept of numerator and denominator, and errors in adding or subtracting fractions anc mixed fractions whose denominators were the same. And secondly, the fraction-related achievements of the ADHD student have improved thanks to the systematic teaching plan based on the accurate understanding of his academic gap relative to other students, his learning attitude, and his time difference. In addition, this study suggests several implications for ADHD students' learning of fractions.

• Journal of the Korean Institute of Telematics and Electronics
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• v.27 no.2
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• pp.144-150
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• 1990

This paper describes radix-4 Fast Fourier Transform (FFT) Processor designed with the new twice perfect shuffle developed from a perfect shuffle used in radix-2 FFT algorithm. The FFT Processor consists of a butterfly arithmetic circuit, address generators for input, output and coefficient, input and output registers and controller. Also, it requires the external ROM for storage of coefficient and RAM for input and output. The butterfly circuit includes 12 bit-serial ($16{\times}8$) multipliers, adders, subtractors and delay shift registers. Operating on 25 MHz two phase clock, this processor can compute 256 point FFT in 6168 clocks, i.e. 247 us and provides flexibility by allowing the user to select any size among 4,16,64,and256points. Being fabricated with 2-um double metal CMOS process, it includes about 28000 transistors and 55 pads in $8.0{\times}8.2mm^2$area.

• The Journal of Engineering Research
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• v.2 no.1
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• pp.31-37
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• 1997

This paper describes the design and implementation of 8 bit ALU graphic simulator which helps students who study the structure and operation course of general ALU. ALU of this paper consists of three parts, arithmetic circuit, logic circuit, and shifter. Each of them performs as follows. Arithmetic circuit performs arithmetic operation such as addition, subtraction, 1 increment, 1 decrement, 2's complement, logic circuit performs logic operation such as OR, AND, XOR, NOT, and shifter performs shift operation and transfers the result of circuits of arithmetic, logic to data bus. The instructions which relate to these basic ALU functions was selected from Z80 instructions and ALU circuit was designed with those instructions and this designed ALU circuit was implemented on graphic screen. And all state of this data operation course in ALU was showed by bit and logic gate unit.

• Journal of the Korean Institute of Intelligent Systems
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• v.7 no.5
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• pp.34-45
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• 1997

In this paper, we present hardware implemcntation of self-organizing feature map (SOFM) neural networkwith constant adaptation gain and binary reinforcement function on FPGA. Whereas a tnme-varyingadaptation gain is used in the conventional SOFM, the proposed SOFM has a time-invariant adaptationgain and adds a binary reinforcement function in order to compensate for the lowered abilityof SOFM due to the constant adaptation gain. Since the proposed algorithm has no multiplication operation.it is much easier to implement than the original SOFM. Since a unit neuron is composed of 1adde $r_tracter and 2 adders, its structure is simple, and thus the number of neurons fabricated onFPGA is expected to he large. In addition, a few control signal: ;:rp sufficient for controlling !he neurons.Experimental results show that each componeni ot thi inipiemented neural network operates correctlyand the whole system also works well.stem also works well.