• Proceedings of the Korean Society for Language and Information Conference
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• 2001.06a
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• pp.237-257
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• 2001

This paper investigates the idiosyncratic understanding of universal quantifiers such as every, each or all by young children at the ages of 4 to 7, and argues that the phenomenon is explicable in terms of the maturation of both the cognitive system and the linguistic system. Evidence for this dual explanation comes from the fact that the visual input, a picture, plays a key role in determining the children’s conceptual representation, suggesting the need for the central integration of visual and linguistic elements; and from the fact that a quantifier in the linguistic input has an intrinsic property, i.e. a <+focus> feature. I have tried to explain the nature of the cognitive factors in terms of the function of the central system, suggesting a modified form of Smith & Tsimpli’s (1995) version of Fodor’s (1983) modularity hypothesis. Conceptual representations of two kinds are in competition with each other and they are integrated into a neutral LOT (Language of Thought) representation at some point . In the process of this integration, the representations from the visual input predominate over those from the auditory input, though the quantize. (treated as new information provided by the latter) is salient in the final representations. When visual conceptual representations predominate over purely linguistic ones, quantifier spreading errors occur. By contrast, when the relevant grammatical knowledge has developed sufficiently to counteract the conceptual representations, this peculiar behaviour by children should disappear. It is argued that children have to learn two kinds of grammatical fact with regard to universal quantification: (i) they have to learn the status of the quantifier as a functional head of DP so that it has to be positioned inside DP; and (ii) they have to learn the Left-Branch Condition which specifies that movement of an element in the left-branch position is possible only by pied-piping the entire phrase.

• Journal of Educational Research in Mathematics
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• v.25 no.2
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• pp.189-206
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• 2015

There has been a recurring call for using visual representations in textbooks to improve the teaching and learning of proportional reasoning. However, the quantity as well as quality of visual representations used in textbooks is still very limited. In this article, we analyzed visual representations presented in a Grade 6 textbook from two perspectives of proportional reasoning, multiple-batches perspective and variable-parts perspective, and discussed the potential of the double number line and the double tape diagram to help develop the idea 'things covary while something stays the same', which is critical to reason proportionally. We also classified situations that require proportional reasoning into five categories and provided ways of using the double number line and the double tape diagram for each category.

• Education of Primary School Mathematics
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• v.26 no.3
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• pp.125-140
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• 2023

In elementary school mathematics, the addition and subtraction of fractions are difficult for students to understand but very important concepts. This study aims to examine the teaching methods and visual aids utilized in the context of common denominator fraction addition and subtraction. The analysis focuses on evaluating the lesson flow and the utilization of visual representations in one national textbook and ten certified textbooks aligned with the current 2015 revised curriculum. The results show that each textbook is composed of chapter sequences and topics that reflect the curriculum faithfully, with each textbook considering its own order and content. Additionally, each textbook uses a different variety and number of visual representations, presumably intended to aid in learning the operations of fractions through the consistency or diversity of the visual representations. Identifying the characteristics of each textbook can lead to more effective instruction in fraction operations.

• Journal of Science Education
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• v.45 no.2
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• pp.247-256
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• 2021

Visual representation has been a useful tool in mathematical problem solving because it vividly express and structure the variables in the problem. But its effects may vary according to the types of problems. So, this study analyzes the survey results on the 5^th graders' visual representations using questionnaire consisting of the routine problems and the non-routine problems. The results are follows: The rate of correct answers in routine problems was higher than that of the non-routine problems. Even though the subjects were asked to solve the problem using visual representations, the ratio of solving the problem using the numerical expression was high in the routine problems. On the other hand, the rate of solving the problem using visual representation was high in the non-routine problems. The number of respondents who used visual representation in the non-routine problems was twice as many as that of the routine problems. But, among the subjects who used visual representation in the non-routine problems, the proportion of incorrect answers was also high, which resulted in using visual pictures. So, it is necessary to provide an experience that can use various types of the visual representations for problem solving and pay attention to the process of converting problems into visual representations.

• Journal of Science Education
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• v.41 no.1
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• pp.152-165
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• 2017

The magnetic field due to a current is one of the core concepts in electromagnetism which has been taught in secondary science education. In addition, it is a representative example of using visual representations to explain the relation between invisible physical quantities; current and magnetic field. In this study we investigated middle school students' representational competence into three components; interpretation, construction, and application of visual representations. According to the analysis, more than 75 % of the respondents interpreted the meaning of the arrows for current and magnetic field correctly. However, half of them confused the movement of electric charges with the direction of magnetic field. Over 60 % of the students constructed the magnetic field representation as circular closed curves, but many of them could not express the density of field lines properly. In application of visual representations, more than half failed to draw the direction of compass needle correctly. The scores were in order of interpretation, construction and application. There were also significant correlations among three components of representational competence. More attention and research on students' representational competence and effective use of visual representations is needed to better support science learning and teaching.

• Education of Primary School Mathematics
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• v.21 no.4
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• pp.445-459
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• 2018

The purpose of this study is to provide a method to help elementary school students learn ratio-related concepts effectively through visual representations. This study was conducted to identify the differences in the composition of ratio-related concepts between Korean and Singaporean textbooks, reconstruct a unit of proportional expressions and distributions by using visual representations and confirm the differences in performance between an experimental and a comparison group of 6th grade students. While the experimental group mathematics lessons is from the reconstructed textbook, the comparison group lessons is from an existing textbook that does not include any reconstructive representations. A t-test of mean was applied to determine the differences between the experimental and comparison group. Analysis revealed significant differences in the mean between the experimental group and the comparison group, and the intermediate level group showed more improvement compared to the higher and lower level groups. An implication of this study is that the application of visual representations can assist students' understanding of ratio-related concepts.

• The Mathematical Education
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• v.48 no.3
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• pp.303-328
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• 2009

In this study, we developed the teaching methods using manipulative materials to teach regular polytopes, and applied these to first-year student of middle school who is attending the extra math class. In that class, we focused on the change of the mathematical representations -especially verval, visual and symbolic representations- and mathematical behavioral. By analyzing characterstics the students' work sheets, we obtained affirmative results as follows. First, manipulative materials played an important role on drawing a development figure of regular polyhtopes describing the verval representation definition of regular polytopes. Second, classes utilizing manipulative materials changed students verbalism level of representations the definition of regular polytopes. For example, in the first class about 60% of students are in the $0{\sim}2$ vervalism level, but in the third class, about 65% of students are in the $6{\sim}7$ level. Third, classes utilizing manipulative materials improved visual representation about development figure. After experiences making several development figures about regular octahedron directly, and discussion, students found out key points to be considered for draws development figure and this helped to draw development figures about other regular polytopes. Fourth, students were unaccustomed to make symbolic representations of regular polytopes. But, they obtained same improvement in symbolic representations, so in fifth the class some students try to make symbol about something in common of whole regular polytopes. Fifth, after the classes, we have significant differences in the students, especially behavioral characteristics in II items such as mind that want to study own fitness, interest, attachment, spirit of inquiry, continuously mathematics posthumously. This means that classes using manipulative materials. Specially, 'mind that want to study mathematics continuously' showed the biggest difference, and it may give positive influence to inculcates mathematics studying volition while suitable practical use of manipulative materials. To conclude, classes using manipulative materials may help students enhance the verbal, visual representation, and gestates symbol representation. Also, the class using manipulative materials may give positive influence in some part of mathematical behavioral characteristic. Therefore, if we use manipulative materials properly in the class, we have more positive effects on the students cognitive perspect and behavioral cteristics.

• The Mathematical Education
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• v.57 no.1
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• pp.37-54
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• 2018

Despite the significance of fraction in elementary mathematics education, it is not easy to teach it meaningfully in connection with real life in Korea. This study aims to investigate and analyze 3rd grade students' understanding on unit fraction concepts and on comparison of unit fractions and to identify the parts which need to be supplemented in relation to unit fraction. For these purposes, I reviewed previous studies and extracted chapters which cover unit fractions in elementary mathematics textbooks based on 2009 revised curriculums and analyzed teaching contexts and visual representations of unit fractions. From this point of view, I constructed a test which consists of three problems based on Chval et al(2013) to investigate students' understanding on unit fraction. To apply this test, I selected forty-one 3rd grade students and examined that students' aspects of understanding on unit fraction. The results were analyzed both qualitatively and quantitatively. In this study, I present the analysis results and provide implications and some didactical suggestions for teaching contexts and visual representations of unit fraction based on the discussion.

• Journal of Information Technology Applications and Management
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• v.23 no.3
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• pp.1-12
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• 2016

Visual representations for concepts in business management are quite challenging, especially those abstract concepts in Accountancy discipline. For example, there might not be a consensus on what to use to represent such abstraction as an asset, liability, or owner equity. This is because asset can be property, estate, resources, equipment, or any tangible or non-tangible valuables. Cognitive science concepts and behavior engagement have been used to develop visual representations for financial data. The concepts include spatial processing, big picture thinking, and metaphor. Review of past studies together with a brief research plan to test the usability for learning of four new augmented reality 0visuals are provided in the present paper.

• Journal of The Korean Association For Science Education
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• v.29 no.2
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• pp.156-167
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• 2009

This study investigated the effects of dynamic visual on students' field independence-dependence on connecting errors and conceptual understanding in learning chemistry concepts with multiple representations. Seventh graders (N=123) at a co-ed middle school were assigned to a static visual (SV) group learning with text and static visual, and a dynamic visual (DV) group learning with text and dynamic visual. The students then learned 'Boyle's Law' and 'Charles's Law' for two class periods. Results revealed that the percentages of the DV group were lower than those of the SV group on connecting errors. However, the percentages of the students' connecting errors were still high regardless of their field independence-dependence. There was a little different tendency in the percentages of connecting errors between the two groups by students' field independence-dependence according to the types of connecting errors. The scores of the DV group were significantly higher than those of the SV group in a test on conceptual understanding. However, there was no significant interaction between the instruction and the students' field independence-dependence. Educational implications of these findings are discussed.