• Title, Summary, Keyword: 분수의 개념

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A Study on Extension of Division Algorithm and Euclid Algorithm (나눗셈 알고리즘과 유클리드 알고리즘의 확장에 관한 연구)

  • Kim, Jin Hwan;Park, Kyosik
    • Journal of Educational Research in Mathematics
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    • v.23 no.1
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    • pp.17-35
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    • 2013
  • The purpose of this study was to analyze the extendibility of division algorithm and Euclid algorithm for integers to algorithms for rational numbers based on word problems of fraction division. This study serviced to upgrade professional development of elementary and secondary mathematics teachers. In this paper, fractions were used as expressions of rational numbers, and they also represent rational numbers. According to discrete context and continuous context, and measurement division and partition division etc, divisibility was classified into two types; one is an abstract algebraic point of view and the other is a generalizing view which preserves division algorithms for integers. In the second view, we raised some contextual problems that can be used in school mathematics and then we discussed division algorithm, the greatest common divisor and the least common multiple, and Euclid algorithm for fractions.

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Models and the Algorithm for Fraction Multiplication in Elementary Mathematics Textbooks (초등수학 교과서의 분수 곱셈 알고리즘 구성 활동 분석: 모델과 알고리즘의 연결성을 중심으로)

  • Yim, Jae-Hoon
    • School Mathematics
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    • v.14 no.1
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    • pp.135-150
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    • 2012
  • This paper analyzes the activities for (fraction) ${\times}$(fraction) in Korean elementary textbooks focusing on the connection between visual models and the algorithm. New Korean textbook attempts a new approach to use length model (as well as rectangular area model) for developing the standard algorithm for the multiplication of fractions, $\frac{a}{b}{\times}\frac{d}{c}=\frac{a{\times}d}{b{\times}c}$. However, activities with visual models in the textbook are not well connected to the algorithm. To bridge the gap between activities with models and the algorithm, distributive strategy should be emphasized. A wealth of experience of solving problems of fraction multiplication using the distributive strategy with visual models can serve as a strong basis for developing the algorithm for the multiplication of fractions.

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The Educational Significance of the Method of Teaching Natural and Fractional Numbers by Measurement of Quantity (양의 측정을 통한 자연수와 분수 지도의 교수학적 의의)

  • 강흥규;고정화
    • School Mathematics
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    • v.5 no.3
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    • pp.385-399
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    • 2003
  • In our present elementary mathematics curriculum, natural numbers are taught by using the a method of one-to-one correspondence or counting operation which are not related to measurement, and fractional numbers are taught by using a method which is partially related to measurement. The most serious limitation of these teaching methods is that natural numbers and fractional numbers are separated. To overcome this limitation, Dewey and Davydov insisted that the natural number and the fractional number should be taught by measurement of quantity. In this article, we suggested a method of teaching the natural number and the fractional number by measurement of quantity based on the claims of Dewey and Davydov, and compare it with our current method. In conclusion, we drew some educational implications of teaching the natural number and the fractional number by measurement of quantity as follows. First, the concepts of the natural number and the fractional number evolve from measurement of quantity. Second, the process of transition from the natural number to the fractional number became to continuous. Third, the natural number, the fractional number, and their lower categories are closely related.

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Analysis on the Problem-Solving Methods of Students on Contextual and Noncontextual problems of Fractional Computation and Comparing Quantities (분수의 연산과 크기 비교에서 맥락 문제와 비맥락 문제에 대한 학생들의 문제해결 방법 분석)

  • Beom, A Young;Lee, Dae Hyun
    • Education of Primary School Mathematics
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    • v.15 no.3
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    • pp.219-233
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    • 2012
  • Practicality and value of mathematics can be verified when different problems that we face in life are resolved through mathematical knowledge. This study intends to identify whether the fraction teaching is being taught and learned at current elementary schools for students to recognize practicality and value of mathematical knowledge and to have the ability to apply the concept when solving problems in the real world. Accordingly, contextual problems and noncontextual problems are proposed around fractional arithmetic area, and compared and analyze the achievement level and problem solving processes of them. Analysis showed that there was significant difference in achievement level and solving process between contextual problems and noncontextual problems. To instruct more meaningful learning for student, contextual problems including historical context or practical situation should be presented for students to experience mathematics of creating mathematical knowledge on their own.

An Analysis on the Elementary Students' Problem Solving about Equal Sharing Problem and Fraction Order (균등 분배 문제와 분수의 크기 비교에 대한 초등학생들의 문제해결 분석)

  • Lee, Daehyun
    • Journal of the Korean School Mathematics Society
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    • v.21 no.4
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    • pp.303-326
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    • 2018
  • Fraction has difficulties in learning because of the diversity of meanings, the ways of presenting contents and teaching methods in elementary school mathematics. Therefore, the various strategies of teaching of fraction concept is proposed as an alternative. The problem of equal sharing problem is that children can experience the concept of fractions naturally in the context of everyday distribution. Even before learning formal fractions, children can solve them in various ways based on their own experiences. The purpose of this study is to investigate the degree of problem solving and problem solving strategies for children in 2nd, 4th, and 6th grades in elementary school. As a result of the research, the percentage of correct answers increased as the grade increased, but the grade levels showed a difference depending on the numbers given to the problems. Also, there were differences in the problem solving strategies according to the grade levels. Also, according to the numbers presented in the problem, the percentage of correct answers was high in items that were easy to divide, and the percentage of correct answers was low in items that were difficult to divide. When children solved the problems, they were affected by the strategies they could use immediately according to the number presented in the problem, and their learning experiences were also affected.

Fifth Grade Students' Understanding on the Big Ideas Related to Addition of Fractions with Different Denominators (이분모분수 덧셈의 핵심 아이디어에 대한 초등학교 5학년 학생들의 이해)

  • Lee, Jiyoung;Pang, JeongSuk
    • School Mathematics
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    • v.18 no.4
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    • pp.793-818
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    • 2016
  • The purpose of this study is to explore in detail $5^{th}$ grade students' understanding on the big ideas related to addition of fraction with different denominators: fixed whole unit, necessity of common measure, and recursive partitioning connected to algorithms. We conducted teaching experiments on 15 fifth grade students who had learned about addition of fractions with different denominators using the current textbook. Most students approached to the big ideas related to addition of fractions in a procedural way. However, some students were able to conceptually understand the interpretations and algorithms of fraction addition by quantitatively thinking about the context and focusing on the structures of units. Building on these results, this study is expected to suggest specific implications on instruction methods for addition of fractions with different denominators.

A Study on a Fraction Instruction via Partitioning and Iterating Operations (분할과 반복 조작을 통한 분수지도 탐구)

  • Choi, Keun-Bae
    • School Mathematics
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    • v.12 no.3
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    • pp.411-424
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    • 2010
  • The fractional concept consists of various meaning, so that it is difficult to understand in primary school mathematics. In this article, we intend to analyze the cognition of 54 pre-service elementary teachers about the operations of partitioning and iterating that are based on Steffe's fraction schemes. The following fraction problem is used in this analysis: If the bar $\Box$ represent 3/8, then create a bar that is equivalent to 4/3. In our analysis, the 43% of pre-service elementary teachers can be well to treat the operations of partitioning and iteration. The 33% are use the equivalent fractions. But the 19% is not good. From the our analysis, it is important that pre-service elementary teachers must be have experimental(operational) thinking as the science education. And in this study we apply the operations of partitioning and iterating to the fraction activity of textbooks.

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An Analytical Study on Drawbacks Related to Contents Handled in Elementary Mathematics Textbooks in Korea (우리나라 초등학교 수학 교과서에서 취급하는 내용과 관련한 문제점 분석)

  • Park, Kyo Sik
    • School Mathematics
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    • v.18 no.1
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    • pp.1-14
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    • 2016
  • In this paper, in order to lay the foundation for clearly determining the scope of contents handled in elementary math textbooks in Korea, what may be issues are discussed with respect to the contents handled in the current math textbooks. First of all, handling of percent point, concave polygons, and possibilities of event that will happen are discussed, the handling of them can be a issue in the sense of inconsistencies to the curriculum. Next, handling of fractions attaching units of discrete quantities and fractions attaching 'times' are discussed, the handling of them can be a issue in the sense of gap between everyday life and definition in math textbooks. Finally, handling of representing natural numbers into fractions and the positional relationship of geometrical figures are discussed, the handling of them can be a issue in the sense of a logical jump. The following three implications obtained from these discussions are presented as conclusions. First, it is necessary to establish clearly the relationship of textbooks and curriculum. Second, it is necessary to give attention to using the way to define or deal with concepts in math textbooks mixed with the way to use them in everyday life. Third, it is necessary to identify and eliminate the logical jumps in math textbooks.

Impacting Student Confidence : The effects of using virtual manipulatives and increasing fraction understanding. (수학에 대한 자신감 증진: 가상학습교구를 통한 분수 개념 이해의 결과)

  • ;Jenifer Suh;Patricia S. Moyer
    • Journal of Educational Research in Mathematics
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    • v.14 no.2
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    • pp.207-219
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    • 2004
  • There have been studies reporting the increase in student confidence in mathematics when using technology. However, past studies indicating a positive correlation between technology and confidence in mathematics do not explain why they see this positive outcome. With increased availability and easy access to the Internet in schools and the development of free online virtual manipulatives, this research was interested in how the use of virtual manipulatives in mathematics can affect students confidence in their mathematical abilities. Our hypothesis was that the classes using virtual manipulatives which allows students to connecting dynamic visual image with abstract symbols will help students gain a deeper conceptual understanding of math concept thus increasing their confidence and ability in mathematics. The participants in this study were 46 fifth-grade students in three ability groups: one high, one middle and one low. During a two-week unit on fractions, students in three groups interacted with several virtual manipulative applets in a computer lab. Data sources in the project included a pre and posttest of students mathematics content knowledge, Confidence in Learning Mathematics Scale, field notes and student interviews, and classroom videotapes. Our aim was to find evidence for increased level of confidence in mathematics as students strengthened their understanding of fraction concepts. Results from the achievement score indicated an overall main effect showing significant improvement for all ability groups following the treatment and an increase in the confidence level from the preassessment of the Confidence in Learning Mathematics Scale in the middle and high ability groups. An interesting finding was that the confidence level for the low ability group students who had the highest confidence level in the beginning did not change much in the final confidence scale assessment. In the middle and high ability groups, the confidence level did increase according to the improvement of the contest posttest. Through interviews, students expressed how the virtual manipulatives assisted their understanding by verifying their answers as they worked and facilitated their ability to figure out math concept in their mind and visually.

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Development of Korean Preschoolers' Understanding of Fractional Concepts II : Proportional Reasoning for Continuous and Discontinuous Quantities (한국 유아들의 분수개념에 대한 이해의 발달 II : 연속적 양과 비연속적 양에서의 비율추리)

  • Park, Young-Shin
    • Korean Journal of Child Studies
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    • v.26 no.6
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    • pp.161-171
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    • 2005
  • In Experiment 1, 4- and 5-year-olds were shown either continuous(i.e., pizza) or discontinuous Stimuli(i.e., biscuit) by the experimenter. After a proportion(e.g., 2/8, 4/8, or 6/8) was removed, children were asked to remove an equivalent proportion. Whereas 4-year-olds proportional reasoning was correct only when they shared the same stimulus with the experimenter, 5-year-olds reasoned correctly regardless whether or not they shared the stimulus with the experimenter. In Experiment 2, where the discontinuous stimulus was changed, 4-year-olds also made correct proportional reasoning even when their stimulus was different from the experimenter's. Contrary to other studies, quantity didn't affect children's proportional reasoning except the proportion 1/4, where problems with discontinuous quantity were solved more successfully than problems with continuous quantity.

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