• The Mathematical Education
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• v.48 no.3
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• pp.235-263
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• 2009

The purpose of the study was to investigate the influence of children's understanding of fractions in mathematics problem solving. Kieren has claimed that the concept of fractions is not a single construct, but consists of several interrelated subconstructs(i.e., part-whole, ratio, operator, quotient and measure). Later on, in the early 1980s, Behr et al. built on Kieren's conceptualization and suggested a theoretical model linking the five subconstructs of fractions to the operations of fractions, fraction equivalence and problem solving. In the present study we utilized this theoretical model as a reference to investigate children's understanding of fractions. The case study has been conducted with 6 children consisted of 4th to 5th graders to detect how they understand factions, and how their understanding influence problem solving of subconstructs, operations of fractions and equivalence. Children's understanding of fractions was categorized into "part-whole", "ratio", "operator", "quotient", "measure" and "result of operations". Most children solved the problems based on their conceptual structure of fractions. However, we could not find the particular relationships between children's understanding of fractions and fraction operations or fraction equivalence, while children's understanding of fractions significantly influences their solutions to the problems of five subconstructs of fractions. We suggested that the focus of teaching should be on the concept of fractions and the meaning of each operations of fractions rather than computational algorithm of fractions.

• Communications of Mathematical Education
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• v.24 no.2
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• pp.325-344
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• 2010

The purpose of this study is to investigate what influences students' preferences on empirical and deductive proofs and find their relations. Although empirical and deductive proofs have been seen as a significant aspect of school mathematics, literatures have indicated that students tend to have a preference for empirical proof when they are convinced a mathematical statement. Several studies highlighted students'views about empirical and deductive proof. However, there are few attempts to find the relations of their views about these two proofs. The study was conducted to 47 students in 7~9 grades in the transition from empirical proof to deductive proof according to their mathematics curriculum. The data was collected on the written questionnaire asking students to choose one between empirical and deductive proofs in verifying that the sum of angles in any triangles is $180^{\circ}$. Further, they were asked to provide explanations for their preferences. Students' responses were coded and these codes were categorized to find the relations. As a result, students' responses could be categorized by 3 factors; accuracy of measurement, representative of triangles, and mathematics principles. First, the preferences on empirical proof were derived from considering the measurement as an accurate method, while conceiving the possibility of errors in measurement derived the preferences on deductive proof. Second, a number of students thought that verifying the statement for three different types of triangles -acute, right, obtuse triangles - in empirical proof was enough to convince the statement, while other students regarded these different types of triangles merely as partial examples of triangles and so they preferred deductive proof. Finally, students preferring empirical proof thought that using mathematical principles such as the properties of alternate or corresponding angles made proof more difficult to understand. Students preferring deductive proof, on the other hand, explained roles of these mathematical principles as verification, explanation, and application to other problems. The results indicated that students' preferences were due to their different perceptions of these common factors.

• Journal of Elementary Mathematics Education in Korea
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• v.15 no.2
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• pp.317-332
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• 2011

The purpose of this study is to suggest an effective plan for teaching the definition of prism by integrating and analyzing the theories related to the instruction of definitions. The subjects in this study to realize these objectives were as follows. First, it looks to theoretical backgrounds regarding the instruction of the definition of solid by functions of definition in mathematics education. Second, it explores the instructional way to form the definition of solid through function of definition, by analyzing the unit of solid in the 6th grade. Third, after conducting the real practice with the 5th graders who before learn solid in 6th curriculum, according to plan of instruction, it examined student's response and testify its effectiveness, and then propose a teaching scheme which is designed to be useful based on the outcomes. In terms of theoretical background, it investigated the precedent research in relation to the instruction of the definition that mathematical definition is not given perfectly but the process of making knowledge that mathematization activity is necessary. It investigated the effects of the instruction of definitions, based on the effects of teaching and interviews with the 5th graders, and analysis of student's handout. The followings were the results of this study. First, 'Making Definitions' activities through remove counterexample process was possible to analytic thinking not intuitively thinking, and it effects the extend of awareness in definition that definition is not fixed but various. Second, it need the step of organize terms that is useful on solid's definition through activate of background knowledge. Third, it is effective that explore characters of the solids after construct the solids. Fourth, interactive discussion that students correct their mistakes each other through mathematical communication and they can think developmental is useful on making definition more than individual study.

• The Mathematical Education
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• v.56 no.3
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• pp.301-318
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• 2017

This paper explores students' question generation process and their study in small group discussion. The research is based on Anthropological Theory of the Didactic developed by Chevallard. He argues that the savior (knowledge) we are dealing with at school is based on a paradigm that we prevail over whether we 'learn' or 'study' socially. In other words, we haven't provided students with autonomous research and learning opportunities under 'the dominant paradigm of visiting works'. As an alternative, he suggests that we should move on to a new didactic paradigm for 'questioning the world a question', and proposes the Study and Research Courses (SRC) as its pedagogical structure. This study explores the SRC structure of small group activities in solving ill-structured problems. In order to explore the SRC structure generated in the small group discussion, one middle school teacher and 7 middle school students participated in this study. The students were divided into two groups with 4 students and 3 students. The teacher conducted the lesson with ill-structured problems provided by researchers. We collected students' presentation materials and classroom video records, and then analyzed based on SRC structure. As a result, we have identified that students were able to focus on the valuable information they needed to explore. We found that the nature of the questions generated by students focused on details more than the whole of the problem. In the SRC course, we also found pattern of a small group discussion. In other words, they generated questions relatively personally, but sought answer cooperatively. This study identified the possibility of SRC as a tool to provide a holistic learning mode of small group discussions in small class, which bring about future mathematics classrooms. This study is meaningful to investigate how students develop their own mathematical inquiry process through self-directed learning, learner-specific curriculum are emphasized and the paradigm shift is required.

• Journal of the Korean School Mathematics Society
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• v.12 no.4
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• pp.545-562
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• 2009

Calculus is used in various parts of human life and the basis of social science such as economics and public administration. Yet that is still considered important in the field of science and technology only, and there have been a lot of disputes on that phenomenon. Fortunately, calculus is going to be taught as part of the academic high school second-year mathematics curriculum in and after 2010. Students who face calculus for the first time should be helped not to lose interest in differentiation learning, not to be apprehensive of it nor to avoid it. The purpose of this study was to examine the types of errors made by students in the course of solving differentiation problems in an effort to lay the foundation for differentiation education. A pilot test was conducted after generalized differentiation problems to which students were usually exposed were selected, and experts were asked to review the pilot test. And then a finalized test was implemented to make an error analysis according to an error type analysis framework to serve the purpose.

• Journal of the Korean School Mathematics Society
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• v.8 no.4
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• pp.509-523
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• 2005

This study empirically examines motivations of entering college of education and academic problems that pre-service teachers encounter under the curricular activities. We analyze the phenomena of professional development under the four categories: motivation toward entering college of education, pedagogical content knowledge, subject matter knowledge and future vision. We conducted survey for the S university students first and interviewed 3 selected participants. Almost 50 students from college of education participated answering to the surveys. Using SPSS package, there was no significant difference between freshmen, sophomore and junior students in any category Male students responded more positively than female students in all the categories. To explore survey results deeply, we selected 3 students from sophomore and junior levels and 2 extra senior students to conduct interviews. The interpretation of the data described how their academic problems unfold partly because they seek another major and how their professional development take place carrying out practicum activities. Most of the interviewees felt that their academic lives were affected motivations of entering college of education and difficulties of studying subject matter knowledge. At the end, several suggestions are added for future research.

• Journal of the Korean Society of School Health
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• v.1 no.2
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• pp.118-135
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• 1988

This study is designed to analyze the problems of health education in schools and explore the ways of enhancing health education from a historical perspective. It also shed light on the managerial aspect of health education (including medical-check-up for students disease management. school feeding and the health education law and its organization) as well as its educational aspect (including curriculum, teaching & learning, and wishes of teachers). At the same time it attempted to present the ways of resolving the problems in health education as identified her. Its major findings are as follows; I. Colculsion and Summary 1. Despite the importance of health education, the area remains relatively undeveloped. Students spend a greater part of their time in schools. Hence the government should develop a keener awareness of the importance of health education and invest more in it to ensure a healthy, comfortable life for students. 2. At the moment the outcomes of medical-check-up for students, which constitutes the mainstay of health education, are used only as statistical data to report to the relevant authorities. Needless to say they should be used to help improve the wellbeing of students. Specifically, nurse-teachers and home-room teachers should share the outcomes of medical-check-up to help the students wit shortcomings in growth or development or other physical handicaps more clearly recognize their problems and correct them if possible. 3. In the area of disease management, 62.6, 30.3 and 23.0 percent of primary, middle, and highschool students, respectively, were found to suffer from dental ailments. By contrast 2.2, 7.8, and 11.5 percent of primary, middle and highschool students suffered from visual disorders. The incidence of dental ailments decreases while that of visual impairments increases as students grow up. This signifies that students are under tremendous physical strain in their efforts to be admitted by schools of higher grade. Accordingly the relevant authorities should revise the current admission system as well as improve lighting system in classrooms. 4. Budget restraints have often been cited as a major bottleneck to the expansion of school feeding. Nevertheless it should be extended at least, to all primary schools even at the expense of parents to ensure the sound growth of children by improving their diet. 5. The existing health education law should be revised in such a way as to better meet the needs of schools. Also the manpower for health education should be strengthened. 6. Proper curriculum is essential to the effective implementation of health education. Hence it is necessary to remove those parts in the current health education curriculum that overlaps with other subjects. It is also necessary to make health education a compulsory course in teachers' college at the same time the teachers in charge of health education should be given an in-service training. 7. Currently health education is being taught as part of physical education, science, home economics or other courses. However these subjects tend to be overshadowed by English, mathematics, and other subjects which carry heavier weight in admission test. It is necessary among other things, to develop an educational plan specifying the course hours and teaching materials. 8. Health education is carried out by nurse-teachers or home-room teachers. In connection with health education, they expressed the hope that health education will be normalized with newly-developed teaching material, expanded opportunity for in-service training and increased budget, facilities and supply of manpower. These are the mainpoints that the decision-makers should take into account in the formation of future policy for health education. II. Recommendations for the Improvement of Health Education 1. Regular medical check-up for students, which now is the mainstay of health education, should be used as educational data in an appropriate manner. For instance the records of medical check-up could be transferred between schools. 2. School feeding should be expanded at least in primary schools at the expense of the government or even parents. It will help improve the physical wellbeing of youths and the diet for the people. 3. At the moment the health education law is only nominal. Hence the law should be revised in such a way as to ensure the physical wellbeing of students and faculty. 4. Health education should be made a compulsory course in teachers' college. Also the teachers in service should be offered training in health education. 5. The curriculum of health education should be revised. Also the course hours should be extended or readjusted to better meet the needs of students. 6. In the meantime the course hours should be strictly observed, while educational materials should be revised in no time. 7. The government should expand its investment in facilities, budget and personnel for health education in schools at all levels.

• Journal of Elementary Mathematics Education in Korea
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• v.16 no.3
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• pp.359-388
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• 2012

The study aims to extract the framework of sub-factors of spatial sense, to develop test instruments based on the framework to investigate the actual spatial sense ability of fourth to sixth graders in elementary school and to analyze the results. According to the framework of sub-factors of spatial sense of the study, spatial sense has two factors of spatial visualization and spatial orientation. Spatial visualization is divided into mental rotation, mental transformation and figure-ground perception while spatial orientation is categorized into direction sense, distance sense, and location sense. Based on the framework, the test instrument for spatial sense ability was developed and the test was conducted to 430 fourth to sixth students in five elementary schools in capital areas. The following conclusions were drawn from the results obtained in the study. Firstly, the higher school year gets, the more spatial sense grows. However, spatial visualization is developed much more than spatial orientation and their order is reversed with higher graders. Secondly, the most insufficient abilities among fourth to sixth elementary school students' spatial sense were mental transformation of spatial visualization and location sense of spatial orientation. Thirdly, the reasons of differences in sub-factors of spatial sense and graders seem to be from effects of students' learning experiences of spatial sense of mathematics curriculum and the complexities of test items.

• Journal of Educational Research in Mathematics
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• v.23 no.2
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• pp.253-267
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• 2013

The newly revised mathematics curriculum of 2007 speaks of ultimate goal to develop ability to think and communicate mathematically, in order to develop ability to rationally deal with problems arising from the life around, which puts emphasize on mathematical communication. In this study, analysis on mathematical communication and analogical thinking process of group of students with similar level of academic achievement and that with different level, and thus analyzed if such communication has affected analogical thinking process in any way. This study contains following subjects: 1. Forms of mathematical communication took placed at the two groups based on achievement level were analyzed. 2. Analogical thinking process was observed through trapezoid's area obtaining activity and analyzed if communication within groups has affected such process anyhow. A framework to analyze analogical thinking process was developed with reference of problem solving procedure based on analogy, suggested by Rattermann(1997). 15 from 24 students of year 5 form of N elementary school at Gunpo Uiwang, Syeonggi-do, were selected and 3 groups (group A, B and C) of students sharing the same achievement level and 2 groups (group D and E) of different level were made. The students were led to obtain areas of parallelogram and trapezoid for twice, and communication process and analogical thinking process was observed, recorded and analyzed. The results of this study are as follow: 1. The more significant mathematical communication was observed at groups sharing medium and low level of achievement than other groups. 2. Despite of individual and group differences, there is overall improvement in students' analogical thinking: activities of obtaining areas of parallelogram and trapezoid showed that discussion within subgroups could induce analogical thinking thus expand students' analogical thinking stage.

• Journal of the Korean earth science society
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• v.42 no.3
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• pp.344-364
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• 2021

The study explored how two elementary school teachers perceived computational thinking, reflected them into curriculum revision, and taught them in the classroom during longitudinal professional developed program (PDP) for nine months. Computational thinking is a new direction in educational policy-making including science education; therefore we planned to investigate participating teachers' perception of computational thinking to provide their fundamental understandings. Nine meetings, lasting about two hours each, were held with the participating teachers and they developed 11 lesson plans for one unit each, as they formed new understandings about computational thinking. Data were collected through PDP program while two teachers started perceiving computational thinking, revising their curriculum, and implementing it into their class for nine months. The results were as follows; first, elementary school teachers' perception of computational thinking was that the definition of scientific literacy as the purpose of science education was extended, i.e., it refers to scientific literacy to prepare students to be creative problem solvers. Second, STEAM (science, technology, engineering, arts, and mathematics) lessons were divided into two stages; concept formation stage where scientific thinking is emphasized, and concept application, where computational thinking is emphasized. Thirdly, computational thinking is a cognitive thinking process, and ICT (informational and communications technology) is a functional tool. Fourth, computational thinking components appear repeatedly and may not be sequential. Finally, STEAM education can be improved by utilizing computational thinking. Based on this study, we imply that STEAM education can be activated by computational thinking when teachers are equipped with competencies of understanding and implementing computational thinking within the systematic PDPs, which is very essential for newly policies.