## 논문 상세보기

한국수학교육학회> C-초등수학교육> CCSSM-CA와 미국 교과서에 제시된 분수의 연산 내용 분석 ### CCSSM-CA와 미국 교과서에 제시된 분수의 연산 내용 분석

An Analysis on the Contents of Fractional Operations in CCSSM-CA and its Textbooks

이대현 ( Lee Dae Hyun )
• : 한국수학교육학회
• : C-초등수학교육 22권2호
• : 연속간행물
• : 2019년 04월
• : 129-147(19pages) #### 목차

```I. 서론
Ⅱ. 분수 연산에 대한 이론적 탐색
Ⅲ. 연구 대상 및 방법
Ⅳ. 분석 결과
Ⅴ. 결론
참 고 문 헌```

#### 초록 보기

`본 연구에서는 CCSSM-CA와 그에 따른 미국 초등 교과서에 제시된 분수의 연산 내용을 분석하였다. 분석 결과, 분수를 단위분수나 분모가 같은 분수의 합으로 표현하게 하여 분수 개념과 연산을 연결 짓는 특징이 있었다. 또 분수의 곱셈에서는 곱하는 한 수의 크기에 기초하여 다른 수의 곱의 결과를 비교하도록 하거나, 나눗셈에서는 단위 분수가 포함된 나눗셈을 먼저 다루고, 다양한 방법으로 계산을 하도록 제시하는 특징 등이 있었다.`
```Because of the various concepts and meanings of fractions and the difficulty of learning, studies to improve the teaching methods of fraction have been carried out. Particularly, because there are various methods of teaching depending on the type of fractions or the models or methods used for problem solving in fraction operations, many researches have been implemented. In this study, I analyzed the fractional operations of CCSSM-CA and its U.S. textbooks. It was CCSSM-CA revised and presented in California and the textbooks of Houghton Mifflin Harcourt Publishing Co., which reflect the content and direction of CCSSM-CA.
As a result of the analysis, although the grades presented in CCSSM-CA and Korean textbooks were consistent in the addition and subtraction of fractions, there are the features of expressing fractions by the sum of fractions with the same denominator or unit fraction and the evaluation of the appropriateness of the answer. In the multiplication and division of fractions, there is a difference in the presentation according to the grades. There are the features of the comparison the results of products based on the number of factor, presenting the division including the unit fractions at first, and suggesting the solving of division problems using various ways.```

#### UCI(KEPA)

I410-ECN-0102-2019-300-001407169

### 간행물정보

• : 사회과학분야  > 교육
• : KCI등재
• :
• : 계간
• : 1226-6914
• : 2287-9927
• : 학술지
• : 연속간행물
• : 1997-2021
• : 348

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24권4호(2021년 10월) 수록논문
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| | | | ##### 1다전략 수학 문제해결 학습이 초등학생의 수학적 창의성과 수학적 태도에 미치는 영향

저자 : 김서령 ( Kim¸ Seoryeong ) , 박만구 ( Park¸ Mangoo )

발행기관 : 한국수학교육학회 간행물 : C-초등수학교육 24권 4호 발행 연도 : 2021 페이지 : pp. 175-187 (13 pages)

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`The purpose of this study is to investigate the effects of solving multi-strategic mathematics problems on mathematical creativity and attitudes of the 6th grade students. For this study, the researchers conducted a survey of forty nine (26 students in experimental group and 23 students in comparative group) 6th graders of S elementary school in Seoul with 19 lessons. The experimental group solved the multi-strategic mathematics problems after learning mathematics through mathematical strategies, whereas the group of comparative students were taught general mathematics problem solving. The researchers conducted pre- and post- isomorphic mathematical creativity and mathematical attitudes of students. They examined the t-test between the pre- and post- scores of sub-elements of fluency, flexibility and creativity and attitudes of the students by the i-STATistics. The researchers obtained the following conclusions. First, solving multi-strategic mathematics problems has a positive impact on mathematical creativity of the students. After learning solving the multi-strategic mathematics problems, the scores of mathematical creativity of the 6th grade elementary students were increased. Second, learning solving the multi-strategy mathematics problems impact the interest, value, will and efficacy factors in the mathematical attitudes of the students. However, no significant effect was found in the areas of desire for recognition and motivation. The researchers suggested that, by expanding the academic year and the number of people in the study, it is necessary to verify how mathematics learning through multi-strategic mathematics problem-solving affects mathematical creativity and mathematical attitudes, and to verify the effectiveness through long-term research, including qualitative research methods such as in-depth interviews and observations of students' solving problems.` ##### 2초등수학의 규칙성 영역 단원에 제시된 발문의 특성 분석

저자 : 도주원 ( Do¸ Joowon )

발행기관 : 한국수학교육학회 간행물 : C-초등수학교육 24권 4호 발행 연도 : 2021 페이지 : pp. 189-202 (14 pages)

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`The teacher's questions presented in the problem-solving situation stimulate students' mathematical thinking and lead them to find a solution to the given problem situation. In this research, the types and functions of questions presented in chapters of Pattern area of the 2015 revised elementary school mathematics textbooks were compared and analyzed by grade cluster. Through this, it was attempted to obtain implications for teaching and learning in identifying the characteristics of questions and effectively using the questions when teaching Pattern area. As a result of this research, as grade clsuter increased, the number of questions per lesson presented in Pattern area increased. Frequency of the types of questions in textbooks was found to be high in the order of reasoning questions, factual questions, and open questions in common by grade cluster. In chapters of Pattern area, relatively many questions were presented that serve as functions to help guess, invent, and solve problems or to help mathematical reasoning in the process of finding rules. It can be inferred that these types of questions and their functions are related to the learning content by grade cluster and characteristics of grade cluster. Therefore, the results of this research can contribute to providing a reference material for devising questions when teaching Pattern area and further to the development of teaching and learning in Pattern area.` ##### 3경과시간 수업에서 제공되는 학습기회 분석: 양적 대상화를 중심으로

저자 : 한채린 ( Han¸ Chaereen )

발행기관 : 한국수학교육학회 간행물 : C-초등수학교육 24권 4호 발행 연도 : 2021 페이지 : pp. 203-216 (14 pages)

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`Seeing the elapsed time as a quantity that can be measured is quite challenging for students while making students see it is also challenging for teachers. Tuning on these challenges, this article reports on what learning opportunities elementary teachers provide when they teach elapsed time focusing on quantitative objectification. I observed three mathematics classrooms where the elapsed time was taught by three elementary teachers and did a narrative analysis on the instructions. All three teachers utilized certain tools to support students access to the elapsed time as a quantity. They appropriated various quantitative attributes of the tool. In the case of the analog clock, one teacher tried to quantification the elapsed time with the number of minute hand's turning, while the other teacher indicated the distance of minute hand's moving. One teacher represented the elapsed time with the longitudinal attribute of the time band. Standing on the findings, the didactical implications of various attempts for quantitative objectification of the elapsed time implemented were discussed.` ##### 4EBSmath를 활용한 거꾸로 수업이 수학 학습과 수학적 성향에 미치는 영향

저자 : 오혜진 ( Oh¸ Hyejin ) , 박성선 ( Park¸ Sungsun )

발행기관 : 한국수학교육학회 간행물 : C-초등수학교육 24권 4호 발행 연도 : 2021 페이지 : pp. 217-231 (15 pages)

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```The purpose of this study was to investigate the effects of flipped learning through EBSmath on Students' 'rate and ratio' learning. By increasing demands for change in education, an innovative teaching and learning paradigm, 'Flipped Learning', has been presented and drawing attentions. In South Korea, Flipped Learning is also highly recognized for its effectiveness by many scholars and various media. However, this innovative learning model has limitations in application and expansion due to the excessive burden of class preparation of teachers.
As remote learning becomes more active, it would be possible to overcome the limitations of Filliped learning by using the platform provided by the Korea Educational Broadcasting System (EBS). EBSmath is an online learning module that is designed to assist students' self-directed learning. Thus, EBSmath would reduce teachers' burden to prepare mathematics classes for the application of Flipped Learning; and led to students' better understanding of mathematical concepts and problem solving.
In this study, the effect of Flipped Learning through EBSmath on learning 'rate and ratio' was investigated. In order to scrutinize the effects of flipped learning, students' achievement and mathematical disposition were examined and analyzed. Students' achievement, specifically, was divided into two subcategories: concept understanding and problem solving.
As a result, Flipped learning through EBSmath had a positive effect on students' 'rate and ratio' problem solving. In addition, a statistically significant change was identified in the 'willingness', which is subdomain of students' mathematical disposition.``` ##### 5평면도형의 교수·학습 요소에 따른 삼각형에 관한 초등학교 교과서 분석

저자 : 권미선 ( Kwon¸ Misun )

발행기관 : 한국수학교육학회 간행물 : C-초등수학교육 24권 4호 발행 연도 : 2021 페이지 : pp. 233-246 (14 pages)

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`Two-dimensional shapes have a great influence on elementary school students' learning and are closely related to other content areas. Therefore, in this study, The Teaching and Learning Elements that should be taught in two-dimensional shapes were extracted from the literature. It also was analyzed that revised mathematics textbooks in the year 2015 were properly implemented with the teaching and learning elements. As a result of the analysis, in the case of Understanding The Concept, the activities in the textbooks are not able to recognize 2-D shapes which are focusing on shapes of the actual object. In the case of Classifying two-dimensional shapes according to the Criteria, the classification criteria were presented differently from what was learned in the previous course. In the aspect of Applying the Concept, the activities in order to Discuss two-dimensional shapes were not sufficient. Lastly, in view of the fact the 2015 revised curriculum is not considered with the relationship between two-dimensional shapes. For that reason, the following Knowing Relationships parts are insufficiently presented; Understanding the Relationship Between shapes through Definitions and Properties, Identifying the relationship between shapes throughout classification activities, and Discussing the relationship between shapes. Based on the analysis result of two-dimensional shapes, it is suggested that the finding of this research helps to enlarge the teaching methodology of triangles and provide educational perspectives for development in other shape areas.` ##### 6Dienes의 수학학습이론에 따른 사다리꼴의 넓이 학습에서 학생들이 구성한 예 공간 분석

저자 : 오민영 ( Oh¸ Min Young ) , 김남균 ( Kim¸ Nam Gyun )

발행기관 : 한국수학교육학회 간행물 : C-초등수학교육 24권 4호 발행 연도 : 2021 페이지 : pp. 247-264 (18 pages)

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`The area of a trapezoid is an important concept to develop mathematical thinking and competency, but many students tend to understand the formula for the area of a trapezoid instrumentally. A clue to solving these problems could be found in Dienes' theory of learning mathematics and Watson and Mason' concept of example spaces. The purpose of this study is to obtain implications for the teaching and learning of the area of the trapezoid. This study analyzed the example spaces constructed by students in learning the area of a trapezoid based on Dienes' theory of learning mathematics. As a result of the analysis, the example spaces for each stage of math learning constructed by the students were a trapezoidal variation example spaces in the play stage, a common representation example spaces in the comparison-representation stage, and a trapezoidal area formula example spaces in the symbolization-formalization stage. The type, generation, extent, and relevance of examples constituting example spaces were analyzed, and the structure of the example spaces was presented as a map. This study also analyzed general examples, special examples, conventional examples of example spaces, and discussed how to utilize examples and example spaces in teaching and learning the area of a trapezoid. Through this study, it was found that it is appropriate to apply Dienes' theory of learning mathematics to learning the are of a trapezoid, and this study can be a model for learning the area of the trapezoid.`

권호별 보기
같은 권호 다른 논문
| | | | 다운로드 ##### 1초등학교 수학에서 분수 나눗셈의 알고리즘 정당화하기

저자 : 박중규 ( Park Jungkyu ) , 이광호 ( Lee Kwangho ) , 성창근 ( Sung Chang-geun )

발행기관 : 한국수학교육학회 간행물 : C-초등수학교육 22권 2호 발행 연도 : 2019 페이지 : pp. 113-127 (15 pages)

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`본 연구의 목적은 자연수 나눗셈의 정의를 확장하여 분수 나눗셈에 적용함으로써 초등학교 수학에서 분수 나눗셈의 알고리즘을 정당화하는데 있다. 먼저 초등학교 수학에서 분수 나눗셈을 도입할 때 고려해야 할 준거들을 도출하여 제시하였다. 이를 바탕으로 분수 나눗셈의 표준 알고리즘을 유도하는 기존의 방식들이 분수 나눗셈 도입 과정에 적절한지를 고찰하였다. 또한 분수 나눗셈을 정의하였으며, 단위원 분할 모델과 정사각형 분할 모델을 통하여 구체적 조작 활동을 함으로써 등분제와 포함제 상황의 분수 나눗셈에서 표준 알고리즘을 자연스럽게 정당화하였다.` ##### 2CCSSM-CA와 미국 교과서에 제시된 분수의 연산 내용 분석

저자 : 이대현 ( Lee Dae Hyun )

발행기관 : 한국수학교육학회 간행물 : C-초등수학교육 22권 2호 발행 연도 : 2019 페이지 : pp. 129-147 (19 pages)

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`본 연구에서는 CCSSM-CA와 그에 따른 미국 초등 교과서에 제시된 분수의 연산 내용을 분석하였다. 분석 결과, 분수를 단위분수나 분모가 같은 분수의 합으로 표현하게 하여 분수 개념과 연산을 연결 짓는 특징이 있었다. 또 분수의 곱셈에서는 곱하는 한 수의 크기에 기초하여 다른 수의 곱의 결과를 비교하도록 하거나, 나눗셈에서는 단위 분수가 포함된 나눗셈을 먼저 다루고, 다양한 방법으로 계산을 하도록 제시하는 특징 등이 있었다.`

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