• Title, Summary, Keyword: 분수의 개념

### A Case Study about Influence of Primary Mathematic Concepts on the Composition of Mathematic Concepts in 3rd Grade Prodigies of Elementary Schools -Focusing on Addition of Decimals- (수학의 1차적 개념이 초등학교 3학년 영재아의 수학적 개념구성 과정에 미치는 영향에 대한 사례연구 -소수의 덧셈을 중심으로-)

• Kim, Hwa-Soo
• The Journal of the Korea Contents Association
• /
• v.17 no.9
• /
• pp.437-448
• /
• 2017
• This study was conducted as a qualitative case study for examining what transformed primary concepts and transformed schemas were formed for the addition of decimals and how they were formed, and how the relational understanding of the addition of decimals was in three 3rd grade elementary school children who had studied the primary concepts of division, fraction and decimal. That is, this study investigated how the subjects approached problems of decimal addition using transformed primary concepts and transformed schemas formed by themselves, and how the subjects formed concepts and transformed schemas in problem solving. According to the results of this study, transformed primary concepts and transformed schemas formed through the learning of the primary concepts of division, fraction, and decimal functioned as important factors for the relational understanding of decimal addition.

### The Construction of Children's Partitioning Strategy on the Equal Sharing Situation (균등분배 상황에서 아이들의 분할전략의 구성)

• Kim, Ah-Young
• School Mathematics
• /
• v.14 no.1
• /
• pp.29-43
• /
• 2012
• This paper investigated the conceptual schemes in which four children constructed a strategy representing the situation as a figure and partitioning it related to the work which they quantify the result of partitioning to various types of fractions when an equal sharing situation was given to them in contextual or an abstract symbolic form of division. Also, the paper researched how the relationship of factors and multiples between the numerator and denominator, or between the divisor and dividend affected the construction. The children's partitioning strategies were developed such as: repeated halving stage ${\rightarrow}$ consuming all quantity stage ${\rightarrow}$ whole number objects leftover stage ${\rightarrow}$ singleton object analysis/multiple objects analysis ${\rightarrow}$ direct mapping stage. When children connected the singleton object analysis with multiple object analysis, they finally became able to conceptualize division as fractions and fractions as division.

### 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
• /
• v.19 no.1
• /
• pp.19-30
• /
• 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.

### Pre-Service Teachers' Understanding of the Concept and Representations of Irrational Numbers (예비교사의 무리수의 개념과 표현에 대한 이해)

• Choi, Eunah;Kang, Hyangim
• School Mathematics
• /
• v.18 no.3
• /
• pp.647-666
• /
• 2016
• This study investigates pre-service teacher's understanding of the concept and representations of irrational numbers. We classified the representations of irrational numbers into six categories; non-fraction, decimal, symbolic, geometric, point on a number line, approximation representation. The results of this study are as follows. First, pre-service teachers couldn't relate non-fractional definition and incommensurability of irrational numbers. Secondly, we observed the centralization tendency on symbolic representation and the little attention to other representations. Thirdly, pre-service teachers had more difficulty moving between symbolic representation and point on a number line representation of ${\pi}$ than that of $\sqrt{5}$ We suggested the concept of irrational numbers should be learned in relation to various representations of irrational numbers.

### University Students' Understanding and Reasoning about Rational Number Concept (유리수 개념에 대한 대학생들의 이해와 추론)

• Kang, Yun-Soo;Chae, Jeong-Lim
• Journal of the Korean School Mathematics Society
• /
• v.13 no.3
• /
• pp.483-498
• /
• 2010
• The purpose of this paper is to investigate the dispositions of university students' understanding and reasoning about rational number concept. For this, we surveyed for the subject groups of prospective math teachers(33), engineering major students(35), American engineering and science major students(28). The questionnaire consists of four problems related to understanding of rational number concept and three problems related to rational number operation reasoning. We asked multi-answers for the front four problem and the order of favorite algorithms for the back three problems. As a result, we found that university students don't understand exactly the facets of rational number and prefer the mechanic approaches rather than conceptual one. Furthermore, they reasoned illogically in many situations related to fraction, ratio, proportion, rational number and don't recognize exactly the connection between them, and confuse about rational number concept.

### An Investigation of Elementary School Teachers' Knowledge of Fraction Lessons through Classroom Video Analysis (수업 동영상 분석(CVA) 기법을 활용한 분수 수업에 관한 초등 교사의 지식 탐색)

• Song, KeunYoung;Pang, JeongSuk
• Journal of Elementary Mathematics Education in Korea
• /
• v.17 no.3
• /
• pp.457-481
• /
• 2013
• Since the importance of teacher knowledge in teaching mathematics has been emphasized, there have been many studies exploring the nature or characteristics of such knowledge. However, there has been lack of research on the tools of investigating teacher knowledge. Given this background, this study explored teachers' knowledge of fraction lessons using classroom video analysis. The analyses of this study showed that knowledge of teaching methods was activated better than that of student thinking or mathematical content. Knowledge of fraction operation was activated better than that of fraction concept. The degree by which teacher knowledge was activated depended on the characteristics of the video clips used in the study. This paper raised some issues about teachers' knowledge of fraction lessons and suggested classroom video analysis as an alternative tool to measure teacher knowledge in the Korean context.

### A Comparative Analysis of Decimal Numbers in Elementary Mathematics Textbooks of Korea, Japan, Singapore and The US (한국, 일본, 싱가포르, 미국의 초등학교 수학 교과서에 제시된 소수 개념 지도 방안에 대한 비교 분석)

• Kim, JeongWon;Kwon, Sungyong
• School Mathematics
• /
• v.19 no.1
• /
• pp.209-228
• /
• 2017
• Understanding decimal numbers is important in mathematics as well as real-life contexts. However, lots of students focus on procedures or algorithms of decimal numbers without understanding its meanings. This study analyzed teaching method related to decimal numbers in a series of mathematics textbooks of Korea, Japan, Singapore and the US. The results showed that three countries except Japan introduced the decimal numbers as another name of fraction, which highlights the relation between the concept of decimal numbers and fractions. And limited meanings of decimal numbers were shown such as 'equal parts of a whole' and 'measurement'. Especially in the korean textbooks, relationships between the decimals were dealt instrumentally and small number of models such as number lines or $10{\times}10$ grids were used repeatedly. Based these results, this study provides implications on what and how to deal with decimal numbers in teaching and learning decimal numbers with textbooks.

### Sensitivity Analysis of Groundwater Model Predictions Associated with Uncertainty of Boundary Conditions: A Case Study (지하수 모델의 주요 경계조건에 대한 민감도 분석 사례)

• Na, Han-Na;Koo, Min-Ho;Cha, Jang-Hawn;Kim, Yong-Je
• Journal of Soil and Groundwater Environment
• /
• v.12 no.3
• /
• pp.53-65
• /
• 2007
• Appropriate representation of hydrologic boundaries in groundwater models is critical to the development of a reliable model. This paper examines how the model predictions are affected by the uncertainty in the conceptualization of the hydrologic boundaries including groundwater divides, streams, and the lower boundaries of the flow system. The problem is analyzed for a study area where a number of field data for model inputs were available. First, a groundwater flow model is constructed and calibrated for the area using the Visual Modflow code. Recharge rate is used for the unknown variable determined through the calibration process. Secondly, a series of sensitivity analyses are conducted to evaluate the effects of model uncertainties embedded in specifying boundary conditions for streams and groundwater divides and specifying lower boundary of the bedrock. Finally, this paper provides some guidelines and discussions on how to deal with such hydrologic boundaries in view of developing a reliable conceptual model for the groundwater flow system of Korea.

### An Analysis of Teaching Divisor and Multiple in Elementary School Mathematics Textbooks (초등학교 수학 교과서에 나타난 약수와 배수지도 방법 분석)

• Choi Ji Young;Kang Wan
• Journal of Elementary Mathematics Education in Korea
• /
• v.7 no.1
• /
• pp.45-64
• /
• 2003
• This study analyzes divisor and multiple in elementary school mathematics textbooks published according to the first to the 7th curriculum, in a view point of the didactic transposition theory. In the first and second textbooks, the divisor and the multiple are taught in the chapter whose subject is on the calculations of the fractions. In the third and fourth textbooks, divisor and multiple became an independent chapter but instructed with the concept of set theory. In the fifth, the sixth, and the seventh textbooks, not only divisor multiple was educated as an independent chapter but also began to be instructed without any conjunction with set theory or a fractions. Especially, in the seventh textbook, the understanding through activities of students itself are strongly emphasized. The analysis on the each curriculum periods shows that the divisor and the multiple and the reduction of a fractions to the lowest terms and to a common denominator are treated at the same period. Learning activity elements are increase steadily as the textbooks and the mathematical systems are revised. The following conclusion can be deduced based on the textbook analysis and discussion for each curriculum periods. First, loaming instruction method also developed systematically with time. Second, teaching method of the divisor and multiple has been sophisticated during the 1st to 7th curriculum textbooks. And the variation of the teaching sequences of the divisor and multiple is identified. Third, we must present concrete models in real life and construct textbooks for students to abstract the concepts by themselves. Fourth, it is necessary to develop some didactics for students' contextualization and personalization of the greatest common divisor and least common multiple. Fifth, the 7th curriculum textbooks emphasize inquiries in real life which teaming activities by the student himself or herself.

### An Analysis on Cognitive Obstacles While Doing Addition and Subtraction with Fractions (분수 덧셈, 뺄셈에서 나타나는 인지적 장애 현상 분석)

• Kim, Mi-Young;Paik, Suck-Yoon
• Journal of Elementary Mathematics Education in Korea
• /
• v.14 no.2
• /
• pp.241-262
• /
• 2010
• This study was carried out to identify the cognitive obstacles while using addition and subtraction with fractions, and to analyze the sources of cognitive obstacles. For this purpose, the following research questions were established : 1. What errors do elementary students make while performing the operations with fractions, and what cognitive obstacles do they have? 2. What sources cause the cognitive obstacles to occur? The results obtained in this study were as follows : First, the student's cognitive obstacles were classified as those operating with same denominators, different denominators, and both. Some common cognitive obstacles that occurred when operating with same denominators and with different denominators were: the students would use division instead of addition and subtraction to solve their problems, when adding fractions, the students would make a natural number as their answer, the students incorporated different solving methods when working with improper fractions, as well as, making errors when reducing fractions. Cognitive obstacles in operating with same denominators were: adding the natural number to the numerator, subtracting the small number from the big number without carrying over, and making errors when doing so. Cognitive obstacles while operating with different denominators were their understanding of how to work with the denominators and numerators, and they made errors when reducing fractions to common denominators. Second, the factors that affected these cognitive obstacles were classified as epistemological factors, psychological factors, and didactical factors. The epistemological factors that affected the cognitive obstacles when using addition and subtraction with fractions were focused on hasty generalizations, intuition, linguistic representation, portions. The psychological factors that affected the cognitive obstacles were focused on instrumental understanding, notion image, obsession with operation of natural numbers, and constraint satisfaction.