• Journal of the Korean School Mathematics Society
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• v.17 no.4
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• pp.507-539
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• 2014

The algebra is an important tool influencing on a mathematics in general. To make good use of the algebra, it is necessary to transfer from a given situation to a proper algebraic representation. But some research in related to algebraic word problems have reported the difficulty changing to a proper algebraic representation. Our study have focused on transformation and elaboration of algebraic representation. We investigated in detail the responses and perceptions of 29 Grade 7 students while transforming to algebraic representation, only concentrating on the literature expression form the problematic situations given. Most of students showed difficulties in transforming both descriptive and geometric problems to algebraic representation. 10% of them responded wrong answers except only a problem. Four of them were interviewed individually to show their thinking and find the factor influencing on a positive elaboration. As results, we could find some characteristics of their thinking including the misconception that regard the problem finding a functional formula because there are the variables x and y in the problematic situation. In addition, we could find the their fixation which student have to set up the equation. Furthermore we could check that making student explain own algebraic representation was able to become the factor influencing on a positive elaboration. From these, we also discussed about several didactical implications.

• Communications of Mathematical Education
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• v.19 no.1 s.21
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• pp.305-306
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• 2005

• Journal of Elementary Mathematics Education in Korea
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• v.16 no.3
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• pp.427-450
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• 2012

Using representations is essential for students to organize their thinking, to solve problems and to communicate each other. Students express information or situations suggested by problems easily and organize and infer them systematically using representations. Also, teachers are able to comprehend students' levels of understanding and thinking process better through them, and influence their representations. This study was conducted to understand mathematical representations of students uprightly and to seek implications for proper teaching of representations, by analyzing representations of students in mathematical problem solving process and the transformation process of representation via interactions.

• The Mathematical Education
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• v.44 no.4 s.111
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• pp.627-651
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• 2005

This study was conducted to attain an in-depth understanding of students' mathematical representations and to present the educational implications for teaching them. Twelve mathematical tasks were developed according to the six types of problems. A task performance was executed to 151 third graders from four classes in DaeJeon and GyeongGi. We analyzed the types and forms of representations generated by them. Then, qualitative case studies were conducted on two small-groups of five from two classes in GyeongGi. We analyzed how individuals' representations became elaborated into group representation and what patterns emerged during the collaborative small-group learning. From the results, most students used more than one representation in solving a problem, but they were not fluent enough to link them to successful problem solving or to transfer correctly among them. Students refined their representations into more meaningful group representation through peer interaction, self-reflection, etc.. Teachers need to give students opportunities to think through, and choose from, various representations in problem solving. We also need the in-depth understanding and great insights into students' representations for teaching.

• Education of Primary School Mathematics
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• v.18 no.3
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• pp.203-216
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• 2015

This study analyzed changes of representations which had come up in the problem-solving process of math-gifted 6th grade students that ACODESA had been applied. The class was designed on a ACODESA procedure that enhancing the use of varied representations, and conducted for 40minutes, 4 times over the period. The recorded videos and interviews with the students were transcribed for analysing data. According to the result of the analysis, which adopted Despina's using type of representation, there appeared types of 'adding', 'elaborating', and 'reducing'. This study found that there is need for a class design that can make personal representations into that of public through small group discussions and confirmation in the problem-solving process.

• Journal of The Korean Association For Science Education
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• v.34 no.3
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• pp.247-260
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• 2014

Purpose of this study is to analyze the roles and strategies of imagistic simulation observed in mental simulation about problematic situation of prediction, and thereby identify the process of generating prediction, explanation and sophistication. For this study, a framework for mental simulation process and strategy based on literary research was developed and content was validated from four experts of science education. This study was participated by 10 preliminary elementary school teachers, and a total of 20 cases were gathered for two thought experiment tasks based on the think-aloud method. The results were as follows: First, mental simulation process described based on the seven elements of 'perception,' 'interpretation,' 'statement of initial representation,' 'running imagistic simulation,' 'identifying result of simulation,' 'identifying alignment' and 'restatement structured representation.' The study confirmed that initial representation by interpreting related concepts and running imagistic simulation a number of times to develop explanation and prediction. Second, the study identified the use of strategies to enhance simulation such as 'zoom in,' 'partition,' 'dimensional enhancement,' 'dimensional reduction,' 'remove,' 'replace' and 'extreme case.' Running spatial transformation that uses strategy to enhance simulation contributed to discovering mechanism elements in problematic situations.

• Journal of The Korean Association For Science Education
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• v.34 no.5
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• pp.437-447
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• 2014

Learning progressions (LP), which describe how students may develop more sophisticated understanding over a defined period of time, can inform the design of instructional materials and assessment by providing a coherent, systematic measure of what can be regarded as "level appropriate." We developed LPs for the nature of matter for grades K-16. In order to empirically test Korean students, we revised one of the constructs and associated assessment items based on Korean National Science Standards. The assessment was administered to 124 Korean secondary students to measure their knowledge and submicroscopic representations, and to assign them to a level of learning progression for the particle nature of matter. We characterized the level of students' understanding and models of the particle nature of matter, and described how students interpret various representations of atoms and molecules to explain scientific phenomena. The results revealed that students have difficulties in understanding the relationship between the macroscopic and molecular levels of phenomena, even in high school science. Their difficulties may be attributed to a limited understanding of scientific modeling, a lack of understanding of the models used to represent the particle nature of matter, or limited understanding of the structure of matter. This work will inform assessment and curriculum materials development related to the fundamental relationship between macroscopic, observed phenomena and the behavior of atoms and molecules, and can be used to create individualized learning environments. In addition, the results contribute to scientific research literature on learning progressions on the nature of matter.

• Journal of the Korean Chemical Society
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• v.68 no.2
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• pp.107-116
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• 2024

The purpose of this study is to analyze changes in pre-service chemistry teachers' cognition of the nature of model in the evaluation and modification process of model using technology. Changes in cognition of the nature of model were analyzed focusing on the 'Abstraction' and 'Simplification' of the 'Representational aspect', 'Interpretation', 'Reasoning', 'Explanation' and 'Quantification' of the 'Explanatory aspect' that were deemed insufficient for pre-chemistry teachers in previous study. For this purpose, 19 third-year pre-service chemistry teachers at a teacher's college in Chungcheongbuk-do were asked to evaluate the model related to Boyle's law developed using technology, revise the model based on the evaluation results, and make a final evaluation. As a result of the study, it was confirmed that pre-service chemistry teachers' cognition of 'Simplification' of the 'Representational aspect' and 'Interpretation', 'Explanation', and 'Quantification' of the 'Explanatory aspect' changed positively through the evaluation and modification process of the model. Therefore, it was found that the evaluation and modification process of the model plays a key role in changing the cognition of the nature of model. However, there was little change in cognition of 'Abstraction' of the 'Representational aspect' and 'Reasoning' of the 'Explanatory aspect'. The cognition of these factors can be seen as more difficult to change than the cognition of other factors. To solve this problem, more sophisticated educational design for pre-service chemistry teachers is needed.

• Journal of the Korean earth science society
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• v.42 no.1
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• pp.88-101
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• 2021

The purpose of this study was to qualitatively examine the meaning of students' drawings in outdoor classes and modeling-based learning cycles. Ten students were observed in a gifted education center in Seoul. Under the theme of the Hantan River, three outdoor classes and three modeling activities were conducted. Data were collected to document all student activities during field trips and classroom modeling activities using simultaneous video and audio recording and observation notes made by the researcher and students. Please note it is unclear what this citation refers to. If it is the previous sentence it should be placed within that sentence's punctuation. Hatisaru (2020) Ddrawing typess were classified by modifying the representations in a learning context in geological field trips. We used deductive content analysis to describe the drawing characteristics, including students writing. The results suggest that students have symbolic images that consist of geologic concepts, visual images that describe topographical features, and affective images that express students' emotion domains. The characteristics were classified into explanation, generality, elaboration, evidence, coherence, and state-of-mind. The characteristics and drawing types are consecutive in the modeling-based learning cycle and reflect the students' positive attitude and cognitive scientific domain. Drawing is a useful tool for reflecting students' thoughts and opinions in both outdoor class and classroom modeling activities. This study provides implications for emphasizing the importance of drawing activities.

• School Mathematics
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• v.15 no.3
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• pp.651-665
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• 2013

The aim of this study is to find how unformal proof activities contribute to solving problems successfully and to confirm the role of teachers in the progress. For this, we developed a task that can help students communicate actively with the concept of unformal proof activities and conducted a case lesson with 6 graders in Elementary school. The study shows that unformal proof activities contribute to constructing representations which are needed to solve math problems, setting up plans for problem-solving and finding right answers accordingly as well as verifying the appropriation of the answers. However, to get more out of it, teachers need to develop a variety of tasks that can stimulate students and also help them talk as actively as they can manage to find right answers. Furthermore, encouraging their guessing and deepening their thought with appropriate remarks and utterances are also very important part of what teachers need to have in order to get more positive effect from these activities.