• School Mathematics
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• v.11 no.3
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• pp.351-368
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• 2009

This study presents data from a year-long teaching experiment which illustrate how two seventh graders modified their multiplicative thinking and interacted with their representing symbols in the context of combinatorial problem situations. Damon was at the process of construction of recursively multiplicative thinking by modifying his multiplicative reasoning, but Carol appeared to remain at the stage of a binary multiplicative scheme. The two students' struggles with their representing symbols or represented symbols by the teacher show that even well-organized symbolic systems from teachers' perspective do not necessarily help students advance their mathematical capacity.

• Journal of the Korean School Mathematics Society
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• v.13 no.3
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• pp.345-356
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• 2010

Variables and expressions are essential for doing mathematics. Especially abbreviations of the multiplication sign ${\times}$ and the division sign ${\div}$ are current rules that we usually follow. In this paper, we devised a Card-Game for exercising abbreviations of the multiplication sign ${\times}$ and the division sign ${\div}$ in calculating expressions, designed a teaching unit for the calculation of expressions using the Card-Game in the variables and expressions strand, and discussed the implications of using the Card-Game for motivating students, cooperative learning, diagnosis and correction of errors, and so on.

• Journal of the Korean School Mathematics Society
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• v.15 no.4
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• pp.627-641
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• 2012

We found a few students had an error in the function and equation units, because most of mathematicians omitted the multiplication signs. In the mathematical history, the multiplication and parentheses signs had various changes. Based on the Histogenetic Principle, high level students know that the letter in the functions and equations represents a number and the related principles, so they have no big problems. But since the low level students stay in the early days in the mathematical history, they have some problems in the modern function and equation. Therefore, while we study the function and equation units with the low level students, we present that we have to be cautious when we omit the multiplication and parentheses signs.

• Journal of the Korean Institute of Telematics and Electronics D
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• v.35D no.10
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• pp.107-115
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• 1998

A multiplier bit-pair recoding technique derived from Booth algorithm is used as an effective method that can carry out a fast binary multiplication regardless of a sign of both multiplicand and multiplier. In this paper, we propose an implementation of an optical high-speed multiplier which consists of a symbolic substitution adder and an optical multiplication algorithm, which transforms and enhances the multiplier bit-pair recoding algorithm to be fit for optical characteristics. Specially, a symbolic substitution addition rules are coded with a dual-rail logic, and so the complement of the logic of the symbolic substitution adder is easily obtained with a shift operation because it is always present. We also construct the symbolic substitution system which makes superposition image by superimposing two shifted images in a serial connection and recognizes a reference image by feeding this superimposed image to a mask. Thus, the optical multiplier, which is compared with a typical system, is implemented to the smaller system by reducing the number of optical passive elements and the size of this system.

• Journal of Educational Research in Mathematics
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• v.19 no.2
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• pp.257-271
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• 2009

Stochastical independence is separated into two. One can be intuitively judged and the other is not. Independence is a concept based on assumption. However, It is defined as multiplication rule and it has produced extension of concept. Analysis on this issue is needed, assuming the cause is on the intersection sign which is used for both simultaneous events and compatible events. This study presented the extension process of independence concept in detail and constructed twofold interpretation of simultaneous events and compatible events which use the same sign $P(A\cap{B})$ with Pierce Semiotics.

• Journal for History of Mathematics
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• v.17 no.3
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• pp.23-32
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• 2004

In this paper, Ive investigated algebraic concepts which are contained in Euclid's Elements. In the Books II, V, and VII∼X of Elements, there are concepts of quadratic equation, ratio, irrational numbers, and so on. We also analyzed them for mathematical meaning with modem symbols and terms. From this, we can find the essence of the genesis of algebra, and the implications for students' mathematization through the experience of the situation where mathematics was made at first.

• School Mathematics
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• v.13 no.4
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• pp.581-598
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• 2011

Given the growing agreement that algebra should be taught in the early stage of the curriculum, considerable studies have been conducted with regard to early algebra in the elementary school. However, there has been lack of research on how to organize mathematic lessons to develop of algebraic reasoning ability of the elementary school students. This research attempted to gain specific and practical information on effective algebraic teaching and learning in the elementary school. An exploratory qualitative case study was conducted to the fourth graders. This paper focused on the associative law of the multiplication. This paper showed what kinds of activities a teacher may organize following three steps: (a) focus on the properties of numbers and operations in specific situations, (b) discovery of the properties of numbers and operations with many examples, and (c) generalization of the properties of numbers and operations in arbitrary situations. Given the steps, this paper included an analysis on how the students developed their algebraic reasoning. This study provides implications on the important factors that lead to the development of algebraic reasoning ability for elementary students.

• Communications of Mathematical Education
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• v.37 no.3
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• pp.419-442
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• 2023

This study investigated fifth graders' understanding of variables from a generalized arithmetic and a functional perspectives of early algebra. Specifically, regarding a generalized perspective, we included the property of 1, the commutative property of addition, the associative property of multiplication, and a problem context with indeterminate quantities. Regarding the functional perspective, we covered additive, multiplicative, squaring, and linear relationships. A total of 246 students from 11 schools participated in this study. The results showed that most students could find specific values for variables and understood that equations involving variables could be rewritten using different symbols. However, they struggled to generalize problem situations involving indeterminate quantities to equations with variables. They also tended to think that variables used in representing the property of 1 and the commutative property of addition could only be natural numbers, and about 25% of the students thought that variables were fixed to a single number. Based on these findings, this paper suggests implications for elementary school students' understanding and teaching of variables.

• 한국공간정보시스템학회:학술대회논문집
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• 2007.06a
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• pp.111-116
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• 2007

현재 한강수계를 제외한 3대강 수계에서 수질오염총량관리제도가 의무제로써 시행되고 있다. 그러나 과학적 타당성과 외국의 성공사례들로 하여금 한강수계에 대해서도 수질오염총량제도를 의무제화 하려는 시도가 추진되고 있고 있는 실정이다. 이 제도가 한강수계에도 도입된다면, 한강권역에 포함되는 모든 지자체는 해당 유역에서 하천으로 유입되는 배출부하량을 할당받은 할당부하량 이하로 관리하여야만 정해진 유역의 목표수질을 달성할 수 있으며, 배출부하량 관리를 계획한데로 이행하지 못한 지자체는 범칙금 내지는 행정제재를 받게 된다. 따라서 체계적이고 과학적인 모니터링 및 분석 수단이 필요하다. 이 연구는 환경부 고시 한강기술지침에 의거하여 GIS를 이용하여 인천일대의 오폐수 발생부하량 및 배출부하량을 제시하고 과학적인 오염물질 삭감방안을 모색하는 것을 목적으로 진행되었다. 생활계, 산업계, 축산계, 양식계의 4 가지로 분류된 점오염원과 토지 이용 분류에 따른 비점오염원에 대한 각각의 발생부하량을 GIS를 통해 산정하고, 모든 오염원별로 처리경로를 고려하고 처리시설별, 방법별 삭감 효율을 반영하여 배출부하량을 산정하여 GIS상에서 제시하고 분석하였다. 인천일대는 인근지역에 비해 인구밀도가 높고 산업단지가 발달하여 생활계와 산업계 오염원에 의한 발생부하량 및 배출부하량이 많았으며, 특정 오염물에 대해서는 삭감 계획이 필요함을 확인할 수 있었다. 따라서 수질오염총량관리제도에 대비하고 실제 수질 개선을 위하여 본 연구의 결과를 바탕으로 수질관리를 위한 시스템의 보완 및 삭감계획의 수립에 관한 연구가 필요하다.알 수 있었다. 이상의 결과를 토대로 기존 압출추출방법과 초임계 추출 방법을 비교한 결과 $\gamma$-토코페롤의 농도가 1.3${\~}$1.6배 증가함을 확인할 수 있었다.게 상관성이 있어 앞으로 심도 있는 연구가 더욱 필요하다.qrt{F}}}{\pm}e_0$)에서 단정도실수 및 배정도실수의 역수 제곱근 계산에 필요한 평균 곱셈 횟수를 계산한다 이들 평균 곱셈 횟수를 종래 알고리즘과 비교하여 본 논문에서 제안한 알고리즘의 우수성을 증명한다. 본 논문에서 제안한 알고리즘은 오차가 일정한 값보다 작아질 때까지만 반복하므로 역수 제곱근 계산기의 성능을 높일 수 있다. 또한 최적의 근사 역수 제곱근 테이블을 구성할 수 있다. 본 논문의 연구 결과는 디지털 신호처리, 컴퓨터 그라픽스, 멀티미디어, 과학 기술 연산 등 부동소수점 계산기가 사용되는 분야에서 폭 넓게 사용될 수 있다.>16$\%$>0$\%$ 순으로 좋게 평가되었다. 결론적으로 감농축액의 첨가는 당과 탄닌성분을 함유함으로써 인절미의 노화를 지연시키고 저장성을 높이는데 효과가 있는 것으로 생각된다. 또한 인절미를 제조할 때 찹쌀가루에 8$\%$의 감농축액을 첨가하는 것이 감인절미의 색, 향, 단맛, 씹힘성이 적당하고 쓴맛과 떫은맛은 약하게 느끼면서 촉촉한 정도와 부드러운 정도는 강하게 느낄수 있어서 전반적인 기호도에서 가장 적절한 방법으로 사료된다.비위생 점수가 유의적으로 높은 점수를 나타내었다. 조리종사자의 위생지식 점수와 위생관리

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

This study investigated the mathematical notation used today in terms of skip ping the parenthesis. At first we have studied the elementary and secondary curriculum content related to omitted rules. As a result, it is difficult to find explicit evidence to answer that question 'What is the calculation of the $48{\div}2(9+3)$?'. In order to inquire the notation fundamentally, we checked the characteristics on prefix, infix and postfix, and looked into the advantages and disadvantages on infix. At the same time we illuminated the development of mathematical notation from the point of view of skipping the parenthesis. From this investigation, we could check that this interpretation was smooth in the point of view that skipping the parentheses are the image of the function. Through this we proposed some teaching methods including 'teaching mathematical notation based on historic genetic principle', 'reproduction of efforts to overcome the disadvantages of infix and understand the context to choose infix', 'finding the omitted parentheses to identify the fundamental formula' and 'specifying the viewpoint that skipping the multiplication notation can be considered as an image of the function'.