• Title/Summary/Keyword: concept image

### Error analysis related to a learner's geometrical concept image in mathematical problem solving (학생이 지닌 기하적 심상과 문제해결과정에서의 오류)

• Do, Jong-Hoon
• Journal of the Korean School Mathematics Society
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• v.9 no.2
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• pp.195-208
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• 2006
• Among different geometrical representations of a mathematical concept, learners are likely to form their geometrical concept image of the given concept based on a specific one. A learner's image is not always in accord with the definition of a concept. This can induce his or her errors in mathematical problem solving. We need to analyse types of such errors and the cause of the errors. In this study, we analyse learners' geometrical concept images for geometrical concepts and errors related to such images. Furthermore we propose a theoretical framework for error analysis related to a learner's concept image for a general mathematical concept in mathematical problem solving.

### A Study on Elementary School Students' Understanding of Fractions (초등학생의 분수이해에 관한 연구)

• 권성룡
• School Mathematics
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• v.5 no.2
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• pp.259-273
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• 2003
• A fraction is one of the most important concepts that students have to learn in elementary school. But it is a challenge for students to understand fraction concept because of its conceptual complexity. The focus of fraction learning is understanding the concept. Then the problem is how we can facilitate the conceptual understanding and estimate it. In this study, Moore's concept understanding scheme(concept definition, concept image, concept usage) was adopted as an theoretical framework to investigate students' fraction understanding. The questions of this study were a) what concept image do students have\ulcorner b) How well do students solve fraction problems\ulcorner c) How do students use fraction concept to generate fraction word problem\ulcorner By analyzing the data gathered from three elementary school, several conclusion was drawn. 1) The students' concept image of fraction is restricted to part-whole sub-construct. So is students' fraction understanding. 2) Students can solve part-whole fraction problems well but others less. This also imply that students' fraction understanding is partial. 3) Half of the subject(N=98) cannot pose problems that involve fraction and fraction operation. And some succeeded applied the concept mistakenly. To understand fraction, various fraction subconstructs have to be integrated as whole one. To facilitate this integration, fraction program should focus on unit, partitioning and quantity. This may be achieved by following activities: * Building on informal knowledge of fraction * Focusing on meaning other than symbol * Various partitioning activities * Facing various representation * Emphasizing quantitative aspects of fraction * Understanding the meanings of fraction operation Through these activities, teacher must help students construct various faction concept image and apply it to meaningful situation. Especially, to help students to construct various concept image and to use fraction meaningfully to pose problems, much time should be spent to problem posing using fraction.

### An Analysis of 2nd Grade Students' Concept Image about the Triangle (초등학교 2학년 학생들의 삼각형에 대한 개념 이미지 분석)

• Kim, Jiwon
• School Mathematics
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• v.18 no.2
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• pp.425-440
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• 2016
• Concept images play an important role in the acquisition of mathematical concept. However, sometimes concept images are derivatives of student's misconceptions. In addition, students always learn concept images despite teachers' efforts to teach concept definitions. Therefore, teachers need to know about all the concept images of a particular concept. This study aimed to analyze the concept image that students have about the triangle when they have already learned about the triangle in school. It was found that some students have different concept images about the triangle between Semo. Moreover, many students have misconceptions about vertices, sides, and angles. In particular, students think Gak denotes a side, although it means angle. Based on these results, I suggest that the curriculum and textbook require improvement.

### A Study on Students' Understanding of Figures through Descriptive Assessments (서술형 평가를 통한 학생들의 도형에 대한 이해 고찰)

• Choi, Su Im;Kim, Sung Joon
• East Asian mathematical journal
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• v.29 no.2
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• pp.207-239
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• 2013
• This research is a study on student's understanding fundamental concepts of mathematical curriculum, especially in geometry domain. The goal of researching is to analyze student's concepts about that domain and get the mathematical teaching methods. We developed various questions of descriptive assessment. Then we set up the term, procedure of research for the understanding student's knowledge of geometric figures. And we analyze the student's understanding extent through investigating questions of descriptive assessment. In this research, we concluded that most of students are having difficulty with defining the fundamental concepts of mathematics, especially in geometry. Almost all the students defined the fundamental conceptions of mathematics obscurely and sometimes even missed indispensable properties. And they can't distinguish between concept definition and concept image. Prior to this study, we couldn't identify this problem. Here are some suggestions. First, take time to reflect on your previous mathematics method. And then compile some well-selected questions of descriptive assessment that tell us more about student's understanding in geometric concepts.

### A study for Build the Concept Image about Natural Logarithm under GeoGebra Environment (GeoGebra 환경에서 정적분을 이용한 자연로그의 개념이미지 형성 학습 개선방안)

• Lee, Jeong-Gon
• Journal for History of Mathematics
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• v.25 no.1
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• pp.71-88
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• 2012
• The purpose of this study is to find the way to build the concept image about natural logarithm and the method is using definite integral in calculus under GeoGebra environment. When the students approach to natural logarithm, need to use dynamic program about the definite integral in calculus. Visible reasoning process through using dynamic program(GeoGebra) is the most important part that make the concept image to students. Also, for understand mathematical concept to students, using GeoGebra environment in dynamic program is not only useful but helpful method of teaching and studying. In this article, about graph of natural logarithm using the definite integral, to explore process of understand and to find special feature under GeoGebra environment. And it was obtained from a survey of undergraduate students of mathmatics. Also, relate to this process, examine an aspect of students, how understand about connection between natural logarithm and the definite integral, definition of natural logarithm and mathematical link of e. As a result, we found that undergraduate students of mathmatics can understand clearly more about the graph of natural logarithm using the definite integral when using GeoGebra environment. Futhermore, in process of handling the dynamic program that provide opportunity that to observe and analysis about process for problem solving and real concept of mathematics.

### High School Textbook Definition and Students' Understanding of Continuity of Functions (연속함수에 대한 고등학교 교과서의 정의와 고등학생들의 이해)

• Park, Dal-Won;Hong, Soon-Sang;Shin, Min-Young
• Journal of the Korean School Mathematics Society
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• v.15 no.3
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• pp.453-465
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• 2012
• In this paper, we first analysis definition of continuity of functions in high school textbooks, the mathematics high school curriculum and university mathematics textbooks. We surveyed what was causing the students to struggle in their concept image of continuity of functions. We arrived at that students' concept for errors in images of continuity of function were caused by definition of continuity of functions in high school textbooks.

### Conceptual Understanding of Functions through a Graphing Calculator (그래핑 계산기를 이용한 함수의 개념적 이해)

• Choi-Koh Sangsook;Lee Yunkyoungs
• Journal of the Korean School Mathematics Society
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• v.8 no.2
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• pp.203-222
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• 2005
• The purpose of this study is to investigate students' understanding of functions based on concept image and concept definition suggested by Vinner, For the study a graphing calculator was provided as a tool for students to use for their exploration. Three students participated in the study using the qualitative research method to identify their processes of understanding functions. The student with previous experiences of the functions had various concept images about the functions and did not have many opportunities to modify their images because the student did not want to depend on the calculator. However, the student who did not have many chances to study about the functions before used the calculator effectively for developing the concept definition on the functions. The calculator played an important role in connecting different representations and finding relationships between these representations supported by dynamic exploration.

### A Study on the comparison of models for teaching the concept of function (함수개념 지도를 위한 모델 비교 연구)

• Heo, Hae-Ja;Kim, Jong-Myung;Kim, Dong-Won
• Journal for History of Mathematics
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• v.24 no.4
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• pp.97-118
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• 2011
• This study aimed finding effective models for the teaching the concept of function. We selected two models. One is discrete model which focuses on the 'corresponding relation of the elements of the sets(domain and range). The other is continuous model which focuses on the dependent relationship of the two variables connected in variable phenomenon. A vending machine model was used as a discrete model, and a water bucket model was used as a continuous model in our study. We taught 2 times about the concept of function using two models to the 60 students (7th grade, 2 classes) living in Taebak city, and tested it twice, after class and about 3 months later. A vending machine model was helpful in understanding the definition of function in the 7th grade math textbook. Also, it was helpful to making concept image and to recalling it. On the other hand, students who used the water bucket model had a difficultly in understanding the all independent variables of the domain corresponding to the dependent variables. But they excelled in tasks making formula expression and understanding changing situations.

### User experience of responsive web on multi-device environment (멀티 디바이스 환경에서 반응형 웹의 사용자 경험)

• Kang, Jae-Shin;Lee, Young-Ju
• Journal of Digital Convergence
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• v.16 no.11
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• pp.465-470
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• 2018
• This study investigated how layouts can be arranged to improve the user experience in response to changes in the size of responsive webs in a multi - device environment. The layout elements of the responsive web are largely divided into a header, a main concept image, a main content, a sub-content, and a footer. As the screen becomes smaller, the use of drawers and the menu of the scrolling menus rather than the vertical menus will help improve the user experience. The main concept image should be consistent and not lose readability through the use of system fonts. The main content and the sub content should be prevented from being long in the vertical scroll, and the card UI, the table list and the grid list could be alternatively presented for this purpose. Another problem with vertical scrolling is that the placement of user-selectable menus, such as more or new content corrections, is helpful in improving the user experience.

### A Case Study on Students' Concept Images of the Uniform Convergence of Sequences of Continuous Functions

• Jeong, Moonja;Kim, Seong-A
• Research in Mathematical Education
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• v.17 no.2
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• pp.133-152
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• 2013
• In this research, we investigated students' understanding of the definitions of sequence of continuous functions and its uniform convergence. We selected three female and three male students out of the senior class of a university and conducted questionnaire surveys 4 times. We examined students' concept images of sequence of continuous functions and its uniform convergence and also how they approach to the right concept definitions for those through several progressive questions. Furthermore, we presented some suggestions for effective teaching-learning for the sequences of continuous functions.