• Title, Summary, Keyword: 나눗셈

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An Action Research on Instruction of Division of Fractions and Division of Decimal Numbers : Focused on Mathematical Connections (수학의 내적 연결성을 강조한 5학년 분수 나눗셈과 소수 나눗셈 수업의 실행 연구)

  • Kim, Jeong Won
    • Journal of Educational Research in Mathematics
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    • v.27 no.3
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    • pp.351-373
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    • 2017
  • The meanings of division don't change and rather are connected from whole numbers to rational numbers. In this respect, connecting division of natural numbers, division of fractions, and division of decimal numbers could help for students to study division in meaningful ways. Against this background, the units of division of fractions and division of decimal numbers in fifth grade were redesigned in a way for students to connect meanings of division and procedures of division. The results showed that most students were able to understand the division meanings and build correct expressions. In addition, the students were able to make appropriate division situations when given only division expressions. On the other hand, some students had difficulties in understanding division situations with fractions or decimal numbers and tended to use specific procedures without applying diverse principles. This study is expected to suggest implications for how to connect division throughout mathematics in elementary school.

분수 나눗셈의 개념적 이해를 위한 관련 지식의 연결 관계 분석

  • Jeon, Pyeong-Guk;Park, Hye-Gyeong
    • Communications of Mathematical Education
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    • v.15
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    • pp.71-76
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    • 2003
  • 학생들의 분수 나눗셈에 대한 이해는 개념적 이해를 바탕으로 수행되어야 함에도 불구하고 분수 나눗셈은 많은 학생들이 기계적인 절차적 지식으로 획득할 가능성이 높은 내용이다. 이것은 학생들이 학교에서 분수 나눗셈을 학습할 때에 일상생활에서의 경험과 선행 학습과의 연결이 잘 이루어지지 못하고 있는 것에 큰 원인이 있다고 본다. 본 연구에서는 학생들의 분수 나눗셈의 개념적 이해를 돕기 위하여 경험적 지식과의 연결 관계를 활용한 교수 방안을 실험 교수를 통해 조사하였다. 결과로서 번분수를 활용한 수업은 분수 나눗셈의 표준 알고리즘이 수행되는 이유를 알 수 있게 하는데 도움이 되나 여러 가지 절차적 지식이 뒷받침되어야 하며 분수 막대를 직접 잘라 보는 활동을 통한 수업은 분수 나눗셈에서의 나머지를 이해하는데 효과가 있다는 것을 알았다. 결론적으로, 학생들의 경험과 학교에서 이미 학습한 분수 나눗셈들의 관련 지식들을 적절히 연결하도록 한다면 수학적 연결을 통해 분수 나눗셈의 개념적 이해를 이끌 수 있다.

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Middle School Mathematics Teachers' Understanding of Division by Fractions (중학교 수학 교사들의 분수나눗셈에 대한 이해)

  • Kim, Young-Ok
    • Journal of Educational Research in Mathematics
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    • v.17 no.2
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    • pp.147-162
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    • 2007
  • This paper reports an analysis of 19 Chinese and Korean middles school mathematics teachers' understanding of division by fractions. The study analyzes the teachers' responses to the teaching task of generating a real-world situation representing the meaning of division by fractions. The findings of this study suggests that the teachers' conceptual models of division are dominated by the partitive model of division with whole numbers as equal sharing. The dominance of partitive model of division constraints the teachers' ability to generate real-world representations of the meaning of division by fractions, such that they are able to teach only the rule-based algorithm (invert-and-multiply) for handling division by fractions.

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Justifying the Fraction Division Algorithm in Mathematics of the Elementary School (초등학교 수학에서 분수 나눗셈의 알고리즘 정당화하기)

  • Park, Jungkyu;Lee, Kwangho;Sung, Chang-geun
    • Education of Primary School Mathematics
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    • v.22 no.2
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    • pp.113-127
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    • 2019
  • The purpose of this study is to justify the fraction division algorithm in elementary mathematics by applying the definition of natural number division to fraction division. First, we studied the contents which need to be taken into consideration in teaching fraction division in elementary mathematics and suggested the criteria. Based on this research, we examined whether the previous methods which are used to derive the standard algorithm are appropriate for the course of introducing the fraction division. Next, we defined division in fraction and suggested the unit-circle partition model and the square partition model which can visualize the definition. Finally, we confirmed that the standard algorithm of fraction division in both partition and measurement is naturally derived through these models.

Design and Implementation of Lok-up Table for Pre-scaling in Very-High Radix Divider (높은 자릿수 나눗셈 연산기에서의 영역변환상수를 위한 검색테이블 설계 및 구현)

  • 이병석;송문식;이정아
    • Proceedings of the Korean Information Science Society Conference
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    • pp.3-5
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    • 1999
  • 나눗셈 알고리즘은 다른 덧셈이나 곱셈 알고리즘에 비해 복잡하고, 수행 빈도수가 적다는 이유로 그동안 고속 나눗셈의 하드웨어 연구는 활발하지 않았다. 그러나 멀티미디어의 발전 및 고성능의 그래픽 랜더링을 위한 보다 빠른 부동소수점연산기(FPU)가 필요하게 되었으며, 이에 따라서 고속의 나눗셈 연산기의 필요성이 증가하게 되었다. 특히, 전체의 수행 시간 향상을 위해서라도 고속 나눗셈 연산기의 중용성은 더욱 부각되고 있다. 그러나 고속 나눗셈 연산기는 연산 속도와 크기라는 서로 상반되는 요소를 가지고 있다. 즉, 연산 속도가 빠르면 크기는 늘어나고, 크기를 줄이면 연산 속도는 늦어지게 된다. 본 논문은 높은 자릿수(Very-High Radix) 나눗셈 알고리즘에서 영역변환상수를 구하는 방법으로 연산이 아닌 검색테이블(Look-up Table)을 이용한다. 그리고 검색테이블의 크기를 줄이는 방법으로 영역변환상수의 범위 분석 및 캐리 저장형을 이용한 검색테이블 분할 방법을 이용하였다. 전체적으로는 영역변환상수를 구하는 연산주기가 필요없게 되므로 나눗셈 연산기의 영역 크기의 변화가 적으면서 연산 속도는 빨라졌음을 알 수 있다.

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Design of an ARM7 Core with a Singed Integer Division Instruction (Signed Integer Division 명령어를 추가한 ARM7 Core 설계)

  • 오민석;조태헌;남기훈;이광엽
    • Proceedings of the IEEK Conference
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    • pp.1391-1394
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    • 2003
  • 본 논문은 ARM7 TDMI 마이크로프로세서의 연산기능 중 구현되지 알은 나눗셈 연산 기능을 추가로 구현하였다. 이를 위해 ARM ISA(Instruction Set Architecture)에 부호를 고려한 나눗셈 명령어인 'SDIV' 명령어를 추가로 정의하였으며, 나눗셈 알고리즘 Signed Nonrestoring Division을 수행할 수 있도록 ARM7 TDMI 마이크로프로세서의 Data Path를 재 설계하였다. 제안된 방법의 타당성을 검증하기 위하여 현재 ARM7 TDMI 마이크로프로세서의 정수 나눗셈 연산처리 방법과 제안된 구조에서의 정수 나눗셈 연산 처리 방법을 비교하였으며, 그 겉과 수행 cycle의 수가 40%로 감소되는 것을 확인하였다

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A Study on the Quotient and Remainder in Division of Decimal (소수 나눗셈에서 몫과 나머지에 관한 소고)

  • Jeong, Sangtae
    • Education of Primary School Mathematics
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    • v.19 no.3
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    • pp.193-210
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    • 2016
  • In the $10{\div}2.4$ problem situation, we could find that curious upper and middle level students' solution. They solved $10{\div}2.4$ and wrote the result as quotient 4, remainder 4. In this curious response, we researched how students realize quotient and remainder in division of decimal. As a result, many students make errors in division of decimal especially in remainder. From these response, we constructed fraction based teaching method about division of decimal. This method provides new aspects about quotient and remainder in division of decimal, so we can compare each aspects' strong points and weak points.

An Analysis of Pre-service Teachers' Pedagogical Content Knowledge about Story Problem for Division of Fractions (분수 나눗셈 스토리 문제 만들기에 관한 예비교사 지식 조사 연구)

  • Noh, Jihwa;Ko, Ho Kyoung;Huh, Nan
    • Education of Primary School Mathematics
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    • v.19 no.1
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    • pp.19-30
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    • 2016
  • This study examined pre-service teachers' pedagogical content knowledge of fraction division in a context where they were asked to write a story problem for a symbolic expression illustrating a whole number divided by a proper fraction. Problem-posing is an important instructional strategy with the potential to create meaningful contexts for learning mathematical concepts, especially when real-world applications are intended. In this study, story problems written by 135 elementary pre-service teachers were analyzed with respect to mathematical correctness. error types, and division models. Patterns and tendencies in elementary pre-service teachers' knowledge of fraction division were identified. Implicaitons for teaching and teacher education are discussed.

Bit-Parallel Systolic Divider in Finite Field GF(2m) (유한 필드 GF(2m)상의 비트-패러럴 시스톨릭 나눗셈기)

  • 김창훈;김종진;안병규;홍춘표
    • The KIPS Transactions:PartA
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    • v.11A no.2
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    • pp.109-114
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    • 2004
  • This paper presents a high-speed bit-parallel systolic divider for computing modular division A($\chi$)/B($\chi$) mod G($\chi$) in finite fields GF$(2^m)$. The presented divider is based on the binary GCD algorithm and verified through FPGA implementation. The proposed architecture produces division results at a rate of one every 1 clock cycles after an initial delay of 5m-2. Analysis shows that the proposed divider provides a significant reduction in both chip area and computational delay time compared to previously proposed systolic dividers with the same I/O format. In addition, since the proposed architecture does not restrict the choice of irreducible polynomials and has regularity and modularity, it provides a high flexibility and Scalability with respect to the field size m. Therefore, the proposed divider is well suited to VLSI implementation.

A Design of Interger division instruction of Low Power ARM7 TDMI Microprocessor (저전력 ARM7 TDMI의 정수 나눗셈 명령어 설계)

  • 오민석;김재우;김영훈;남기훈;이광엽
    • Journal of the Institute of Electronics Engineers of Korea CI
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    • v.41 no.4
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    • pp.31-39
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    • 2004
  • The ARM7 TDMI microprocessor employ a software routine iteration method in order to handle integer division operation, but this method has long execution time and many execution instruction. In this paper, we proposed ARM7 TDMI microprocessor with integer division instruction. To make this, we additionally defined UDIV instruction for unsigned integer division operation and SDIV instruction for signed integer division operation, and proposed ARM7 TDMI microprocessor data Path to apply division algorithm. Applied division algorithm is nonrestoring division algorithm and additive hardware is reduced using existent ARM data path. To verify the proposed method, we designed proposed method on RTL level using HDL, and conducted logic simulation. we estimated the number of execution cycles and the number of execution instructions as compared proposed method with a software routine iteration method, and compared with other published integer divider from the number of execution cycles and hardware size.